iProver---3.9.4.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SWC418-1 : 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 : n001.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 03:09:43 PM UTC 2026

% Result   : Unsatisfiable 60.53s 10.43s
% Output   : CNFRefutation 70.22s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f231ERROR: Could not build tree for root c_88342ERROR: MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause3) ).

fof(f4,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause4) ).

fof(f8,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).

fof(f62,axiom,
    ! [X0] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause62) ).

fof(f63,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ lt(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause63) ).

fof(f66,axiom,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause66) ).

fof(f67,axiom,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause67) ).

fof(f73,axiom,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).

fof(f74,axiom,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).

fof(f75,axiom,
    ! [X0] :
      ( nil = X0
      | ssList(tl(X0))
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).

fof(f76,axiom,
    ! [X0] :
      ( nil = X0
      | ssItem(hd(X0))
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).

fof(f85,axiom,
    ! [X0,X1] :
      ( ssList(app(X1,X0))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).

fof(f86,axiom,
    ! [X0,X1] :
      ( ssList(cons(X0,X1))
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).

fof(f96,axiom,
    ! [X0,X1] :
      ( tl(cons(X0,X1)) = X1
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).

fof(f97,axiom,
    ! [X0,X1] :
      ( hd(cons(X0,X1)) = X0
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).

fof(f98,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssItem(X0)
      | cons(X0,X1) != nil ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssItem(X0)
      | nil != cons(X0,X1) ),
    inference(reorient_equations,[],[f98]) ).

fof(f100,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssItem(X0)
      | cons(X0,X1) != X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).

fof(f101,axiom,
    ! [X0,X1] :
      ( X1 = X0
      | neq(X1,X0)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).

fof(f102,plain,
    ! [X0,X1] :
      ( X0 = X1
      | neq(X1,X0)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(reorient_equations,[],[f101]) ).

fof(f106,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ lt(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause103) ).

fof(f107,axiom,
    ! [X0] :
      ( nil = X0
      | cons(hd(X0),tl(X0)) = X0
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).

fof(f117,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ lt(X1,X0)
      | ~ lt(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause114) ).

fof(f121,axiom,
    ! [X0,X1] :
      ( nil = X0
      | ~ ssList(X0)
      | ~ ssList(X1)
      | app(X0,X1) != nil ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).

fof(f122,plain,
    ! [X0,X1] :
      ( nil = X0
      | ~ ssList(X0)
      | ~ ssList(X1)
      | nil != app(X0,X1) ),
    inference(reorient_equations,[],[f121]) ).

fof(f123,axiom,
    ! [X0,X1] :
      ( nil = X1
      | ~ ssList(X0)
      | ~ ssList(X1)
      | app(X0,X1) != nil ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).

fof(f124,plain,
    ! [X0,X1] :
      ( nil = X1
      | ~ ssList(X0)
      | ~ ssList(X1)
      | nil != app(X0,X1) ),
    inference(reorient_equations,[],[f123]) ).

fof(f125,axiom,
    ! [X0,X1] :
      ( app(cons(X0,nil),X1) = cons(X0,X1)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).

fof(f126,plain,
    ! [X0,X1] :
      ( cons(X0,X1) = app(cons(X0,nil),X1)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(reorient_equations,[],[f125]) ).

fof(f127,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | lt(X0,X1)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ leq(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause121) ).

fof(f129,axiom,
    ! [X0,X1] :
      ( hd(app(X1,X0)) = hd(X1)
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause123) ).

fof(f130,axiom,
    ! [X0,X1] :
      ( nil = X1
      | strictorderedP(X1)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(cons(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause124) ).

fof(f131,axiom,
    ! [X0,X1] :
      ( nil = X1
      | totalorderedP(X1)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(cons(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause125) ).

fof(f140,axiom,
    ! [X0,X1] :
      ( X1 = X0
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X1,X0)
      | ~ leq(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause130) ).

fof(f141,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X1,X0)
      | ~ leq(X0,X1) ),
    inference(reorient_equations,[],[f140]) ).

fof(f144,axiom,
    ! [X0,X1] :
      ( tl(app(X1,X0)) = app(tl(X1),X0)
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause133) ).

fof(f145,axiom,
    ! [X0,X1] :
      ( nil = X1
      | lt(X0,hd(X1))
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(cons(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause134) ).

fof(f146,axiom,
    ! [X0,X1] :
      ( nil = X1
      | leq(X0,hd(X1))
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(cons(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause135) ).

fof(f159,axiom,
    ! [X2,X0,X1] :
      ( lt(X0,X2)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X2)
      | ~ lt(X1,X2)
      | ~ leq(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause147) ).

fof(f161,axiom,
    ! [X2,X0,X1] :
      ( app(app(X2,X1),X0) = app(X2,app(X1,X0))
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).

fof(f162,axiom,
    ! [X2,X0,X1] :
      ( X1 = X2
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | app(X0,X1) != app(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause150) ).

fof(f163,axiom,
    ! [X2,X0,X1] :
      ( X0 = X2
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | app(X0,X1) != app(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause151) ).

fof(f167,axiom,
    ! [X2,X0,X1] :
      ( lt(X0,X2)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X2)
      | ~ lt(X1,X2)
      | ~ lt(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause155) ).

fof(f168,axiom,
    ! [X2,X0,X1] :
      ( leq(X0,X2)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X2)
      | ~ leq(X1,X2)
      | ~ leq(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause156) ).

fof(f169,axiom,
    ! [X2,X0,X1] :
      ( cons(X0,app(X1,X2)) = app(cons(X0,X1),X2)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).

fof(f171,axiom,
    ! [X0,X1] :
      ( nil = X1
      | totalorderedP(cons(X0,X1))
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(X1)
      | ~ leq(X0,hd(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause159) ).

fof(f172,axiom,
    ! [X0,X1] :
      ( nil = X1
      | strictorderedP(cons(X0,X1))
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(X1)
      | ~ lt(X0,hd(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause160) ).

fof(f183,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | ~ ssList(X1)
      | ~ ssList(X3)
      | ~ ssItem(X0)
      | ~ ssItem(X2)
      | cons(X0,X1) != cons(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause170) ).

fof(f184,axiom,
    ! [X2,X3,X0,X1] :
      ( X3 = X1
      | ~ ssList(X1)
      | ~ ssList(X3)
      | ~ ssItem(X0)
      | ~ ssItem(X2)
      | cons(X0,X1) != cons(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause171) ).

fof(f185,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X3
      | ~ ssList(X1)
      | ~ ssList(X3)
      | ~ ssItem(X0)
      | ~ ssItem(X2)
      | cons(X0,X1) != cons(X2,X3) ),
    inference(reorient_equations,[],[f184]) ).

fof(f191,axiom,
    ! [X0,X1] :
      ( nil = X0
      | X0 = X1
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0)
      | hd(X0) != hd(X1)
      | tl(X0) != tl(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause177) ).

fof(f195,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( lt(X1,X3)
      | ~ ssList(X5)
      | ~ strictorderedP(X5)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X4)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause181) ).

fof(f196,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( leq(X1,X3)
      | ~ ssList(X5)
      | ~ totalorderedP(X5)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X4)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause182) ).

fof(f202,negated_conjecture,
    ssList(sk3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).

fof(f203,negated_conjecture,
    ssList(sk4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).

fof(f204,negated_conjecture,
    sk2 = sk4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).

fof(f205,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).

fof(f206,negated_conjecture,
    neq(sk2,nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

fof(f207,negated_conjecture,
    ! [X2,X0,X1] :
      ( app(app(X2,cons(X0,nil)),X1) != sk1
      | app(app(X1,cons(X0,nil)),X2) != sk2
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

fof(f208,plain,
    ! [X2,X0,X1] :
      ( sk1 != app(app(X2,cons(X0,nil)),X1)
      | sk2 != app(app(X1,cons(X0,nil)),X2)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(reorient_equations,[],[f207]) ).

fof(f213,plain,
    neq(sk4,nil),
    inference(definition_unfolding,[],[f206,f204]) ).

fof(f214,plain,
    ! [X2,X0,X1] :
      ( sk3 != app(app(X2,cons(X0,nil)),X1)
      | sk4 != app(app(X1,cons(X0,nil)),X2)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f208,f204,f205]) ).

fof(f223,plain,
    ! [X2,X3,X0,X1,X4] :
      ( lt(X1,X3)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X4) ),
    inference(equality_resolution,[],[f195]) ).

fof(f226,plain,
    ! [X2,X3,X0,X1,X4] :
      ( leq(X1,X3)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X4) ),
    inference(equality_resolution,[],[f196]) ).

tcf(c_246,negated_conjecture,
    ssList(sk3),
    inference(cnf_transformation,[],[f202]) ).

tcf(c_247,negated_conjecture,
    ssList(sk4),
    inference(cnf_transformation,[],[f203]) ).

tcf(c_248,negated_conjecture,
    neq(sk4,nil),
    inference(cnf_transformation,[],[f213]) ).

tcf(c_249,negated_conjecture,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ( app(app(X2,cons(X1,nil)),X0) != sk4 )
      | ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
    inference(cnf_transformation,[],[f214]) ).

tcf(c_251,negated_conjecture,
    ( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssItem(hd(sk4))
    | ~ neq(nil,sk4)
    | ~ neq(sk4,nil)
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
    inference(cnf_transformation,[],[f228]) ).

tcf(c_252,plain,
    ( ( app(nil,nil) = nil )
    | ~ ssList(nil) ),
    inference(cnf_transformation,[],[f229]) ).

tcf(c_253,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(cons(X1,nil),X0) = cons(X1,X0) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f126]) ).

tcf(c_254,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = nil )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ( app(X0,X1) != nil ) ),
    inference(cnf_transformation,[],[f124]) ).

tcf(c_255,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ( app(X0,X1) != nil ) ),
    inference(cnf_transformation,[],[f122]) ).

tcf(c_256,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ( cons(X0,X1) != nil ) ),
    inference(cnf_transformation,[],[f99]) ).

tcf(c_257,plain,
    ! [X0: $i] :
      ( ( app(nil,X0) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f74]) ).

tcf(c_258,plain,
    ! [X0: $i] :
      ( ( app(X0,nil) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f73]) ).

tcf(c_259,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f8]) ).

tcf(c_261,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ neq(X0,X0) ),
    inference(cnf_transformation,[],[f231]) ).

tcf(c_263,plain,
    ! [X0: $i,X1: $i] :
      ( neq(X1,X0)
      | ( X0 = X1 )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f102]) ).

tcf(c_264,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X3 )
      | ~ ssItem(X2)
      | ~ ssItem(X0)
      | ~ ssList(X3)
      | ~ ssList(X1)
      | ( cons(X0,X1) != cons(X2,X3) ) ),
    inference(cnf_transformation,[],[f185]) ).

tcf(c_265,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = X2 )
      | ~ ssItem(X2)
      | ~ ssItem(X0)
      | ~ ssList(X3)
      | ~ ssList(X1)
      | ( cons(X0,X1) != cons(X2,X3) ) ),
    inference(cnf_transformation,[],[f183]) ).

tcf(c_266,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X2,app(X0,X1)) = app(cons(X2,X0),X1) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f169]) ).

tcf(c_267,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ( cons(X0,X1) != X1 ) ),
    inference(cnf_transformation,[],[f100]) ).

tcf(c_268,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f86]) ).

tcf(c_269,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ( app(X0,X1) != app(X2,X1) ) ),
    inference(cnf_transformation,[],[f163]) ).

tcf(c_270,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ( app(X0,X1) != app(X0,X2) ) ),
    inference(cnf_transformation,[],[f162]) ).

tcf(c_271,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(app(X2,X1),X0) = app(X2,app(X1,X0)) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f161]) ).

tcf(c_272,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(app(X1,X0))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f85]) ).

tcf(c_273,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = nil )
      | ( X0 = nil )
      | ( X0 = X1 )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ( hd(X0) != hd(X1) )
      | ( tl(X0) != tl(X1) ) ),
    inference(cnf_transformation,[],[f191]) ).

tcf(c_274,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = nil )
      | ( app(tl(X1),X0) = tl(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f144]) ).

tcf(c_275,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(X0),tl(X0)) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f107]) ).

tcf(c_276,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(cons(X1,X0)) = X0 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f96]) ).

tcf(c_278,plain,
    ! [X0: $i] :
      ( ssList(tl(X0))
      | ( X0 = nil )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f75]) ).

tcf(c_279,plain,
    ! [X0: $i,X1: $i] :
      ( strictorderedP(cons(X0,X1))
      | ( X1 = nil )
      | ~ strictorderedP(X1)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ lt(X0,hd(X1)) ),
    inference(cnf_transformation,[],[f172]) ).

tcf(c_280,plain,
    ! [X0: $i,X1: $i] :
      ( totalorderedP(cons(X0,X1))
      | ( X1 = nil )
      | ~ totalorderedP(X1)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ leq(X0,hd(X1)) ),
    inference(cnf_transformation,[],[f171]) ).

tcf(c_281,plain,
    ! [X0: $i,X1: $i] :
      ( leq(X0,hd(X1))
      | ( X1 = nil )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f146]) ).

tcf(c_282,plain,
    ! [X0: $i,X1: $i] :
      ( lt(X0,hd(X1))
      | ( X1 = nil )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f145]) ).

tcf(c_283,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = nil )
      | ( hd(app(X1,X0)) = hd(X1) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f129]) ).

tcf(c_284,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,X0)) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f97]) ).

tcf(c_286,plain,
    ! [X0: $i] :
      ( ssItem(hd(X0))
      | ( X0 = nil )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f76]) ).

tcf(c_287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( lt(X1,X3)
      | ~ ssItem(X3)
      | ~ ssItem(X1)
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
    inference(cnf_transformation,[],[f223]) ).

tcf(c_288,plain,
    ! [X0: $i,X1: $i] :
      ( strictorderedP(X1)
      | ( X1 = nil )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f130]) ).

tcf(c_290,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f66]) ).

tcf(c_291,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[],[f3]) ).

tcf(c_292,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X0,X2)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ lt(X1,X2)
      | ~ lt(X0,X1) ),
    inference(cnf_transformation,[],[f167]) ).

tcf(c_293,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X0,X2)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ lt(X1,X2)
      | ~ leq(X0,X1) ),
    inference(cnf_transformation,[],[f159]) ).

tcf(c_295,plain,
    ! [X0: $i,X1: $i] :
      ( lt(X0,X1)
      | ( X0 = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X0,X1) ),
    inference(cnf_transformation,[],[f127]) ).

tcf(c_296,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ lt(X1,X0)
      | ~ lt(X0,X1) ),
    inference(cnf_transformation,[],[f117]) ).

tcf(c_298,plain,
    ! [X0: $i,X1: $i] :
      ( leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ lt(X0,X1) ),
    inference(cnf_transformation,[],[f106]) ).

tcf(c_299,plain,
    ! [X0: $i] :
      ( ~ ssItem(X0)
      | ~ lt(X0,X0) ),
    inference(cnf_transformation,[],[f63]) ).

tcf(c_300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( leq(X1,X3)
      | ~ ssItem(X3)
      | ~ ssItem(X1)
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
    inference(cnf_transformation,[],[f226]) ).

tcf(c_301,plain,
    ! [X0: $i,X1: $i] :
      ( totalorderedP(X1)
      | ( X1 = nil )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f131]) ).

tcf(c_303,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f67]) ).

tcf(c_304,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f4]) ).

tcf(c_305,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X0,X2)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X1,X2)
      | ~ leq(X0,X1) ),
    inference(cnf_transformation,[],[f168]) ).

tcf(c_306,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X1,X0)
      | ~ leq(X0,X1) ),
    inference(cnf_transformation,[],[f141]) ).

tcf(c_307,plain,
    ! [X0: $i] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f62]) ).

tcf(c_314,plain,
    ( ( app(nil,nil) = nil )
    | ~ ssList(nil) ),
    inference(instantiation,[status(thm)],[c_258]) ).

tcf(c_340,plain,
    app(nil,nil) = nil,
    inference(global_subsumption_just,[status(thm)],[c_252,c_259,c_314]) ).

tcf(c_346,plain,
    ( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssItem(hd(sk4))
    | ~ neq(nil,sk4)
    | ~ ssList(app(tl(sk4),cons(hd(sk4),nil)))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4)) ),
    inference(global_subsumption_just,[status(thm)],[c_251,c_248,c_251]) ).

tcf(c_347,negated_conjecture,
    ( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssItem(hd(sk4))
    | ~ neq(nil,sk4)
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
    inference(renaming,[status(thm)],[c_346]) ).

tcf(c_410,plain,
    ( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssItem(hd(sk4))
    | ~ neq(nil,sk4)
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_347,c_272]) ).

tcf(c_1187,plain,
    ( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ( sk4 != nil ) ),
    inference(resolution_lifted,[status(thm)],[c_410,c_248]) ).

tcf(c_1225,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ ssList(cons(hd(sk4),nil))
      | ( X1 != nil )
      | ( X0 != sk4 ) ),
    inference(resolution_lifted,[status(thm)],[c_410,c_263]) ).

tcf(c_1226,plain,
    ( ( sk4 = nil )
    | ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssList(nil)
    | ~ ssList(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(unflattening,[status(thm)],[c_1225]) ).

tcf(c_1227,plain,
    ( ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4))
    | ~ ssItem(hd(sk4))
    | ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) ),
    inference(global_subsumption_just,[status(thm)],[c_1226,c_247,c_259,c_1187,c_1226]) ).

tcf(c_1228,plain,
    ( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(renaming,[status(thm)],[c_1227]) ).

tcf(c_1241,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ( X0 != nil )
      | ( X0 != sk4 ) ),
    inference(resolution_lifted,[status(thm)],[c_248,c_261]) ).

tcf(c_1242,plain,
    ( ~ ssList(sk4)
    | ( sk4 != nil ) ),
    inference(unflattening,[status(thm)],[c_1241]) ).

tcf(c_1243,plain,
    sk4 != nil,
    inference(global_subsumption_just,[status(thm)],[c_1242,c_247,c_1242]) ).

tcf(c_3002,plain,
    app(nil,sk3) = sk3,
    inference(superposition,[status(thm)],[c_246,c_257]) ).

tcf(c_3003,plain,
    app(nil,sk4) = sk4,
    inference(superposition,[status(thm)],[c_247,c_257]) ).

tcf(c_3009,plain,
    app(sk3,nil) = sk3,
    inference(superposition,[status(thm)],[c_246,c_258]) ).

tcf(c_3010,plain,
    app(sk4,nil) = sk4,
    inference(superposition,[status(thm)],[c_247,c_258]) ).

tcf(c_3018,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(cons(X1,X0),nil) = cons(X1,X0) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_258]) ).

tcf(c_3019,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(nil,cons(X1,X0)) = cons(X1,X0) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_257]) ).

tcf(c_3020,plain,
    ( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssList(nil)
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(superposition,[status(thm)],[c_268,c_1228]) ).

tcf(c_3027,plain,
    ( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3020,c_259]) ).

tcf(c_3049,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,X0),nil) = app(X1,X0) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_258]) ).

tcf(c_3050,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(nil,app(X1,X0)) = app(X1,X0) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_257]) ).

tcf(c_3065,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(tl(X0),nil) = tl(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_258]) ).

tcf(c_3066,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(nil,tl(X0)) = tl(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_257]) ).

tcf(c_3079,plain,
    ( ( sk4 = nil )
    | ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssList(sk4)
    | ~ ssList(tl(sk4)) ),
    inference(superposition,[status(thm)],[c_286,c_3027]) ).

tcf(c_3080,plain,
    ( ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssList(tl(sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3079,c_1243,c_247]) ).

tcf(c_3087,plain,
    ( ( sk4 = nil )
    | ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssList(sk4) ),
    inference(superposition,[status(thm)],[c_278,c_3080]) ).

tcf(c_3088,plain,
    app(tl(sk4),cons(hd(sk4),nil)) = sk3,
    inference(forward_subsumption_resolution,[status(thm)],[c_3087,c_1243,c_247]) ).

tcf(c_3089,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ( app(sk3,X0) != sk3 )
      | ( app(app(X0,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_3088,c_249]) ).

tcf(c_3115,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,sk3)) = sk3 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_276]) ).

tcf(c_3116,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,sk4)) = sk4 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_276]) ).

tcf(c_3117,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,nil)) = nil )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_276]) ).

tcf(c_3118,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( tl(cons(X1,tl(X0))) = tl(X0) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_276]) ).

tcf(c_3119,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( tl(cons(X2,app(X1,X0))) = app(X1,X0) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_276]) ).

tcf(c_3120,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( tl(cons(X2,cons(X1,X0))) = cons(X1,X0) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_276]) ).

tcf(c_3150,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,sk3)) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_284]) ).

tcf(c_3151,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,sk4)) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_284]) ).

tcf(c_3152,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,nil)) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_284]) ).

tcf(c_3153,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X1,tl(X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_284]) ).

tcf(c_3154,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(cons(X2,app(X1,X0))) = X2 )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_284]) ).

tcf(c_3155,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(cons(X2,cons(X1,X0))) = X2 )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_284]) ).

tcf(c_3183,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),sk3)) = sk3 )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3115]) ).

tcf(c_3191,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),sk4)) = sk4 )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3116]) ).

tcf(c_3199,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),nil)) = nil )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3117]) ).

tcf(c_3207,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),sk3)) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3150]) ).

tcf(c_3215,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),sk4)) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3151]) ).

tcf(c_3229,plain,
    ( ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ( app(sk3,tl(sk4)) != sk4 )
    | ( app(sk3,tl(sk4)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3088,c_3089]) ).

tcf(c_3240,plain,
    ( ( sk3 = nil )
    | ( tl(cons(hd(sk3),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_246,c_3183]) ).

tcf(c_3241,plain,
    ( ( sk4 = nil )
    | ( tl(cons(hd(sk4),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_247,c_3183]) ).

tcf(c_3243,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( tl(cons(hd(tl(X0)),sk3)) = sk3 )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3183]) ).

tcf(c_3244,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( tl(cons(hd(app(X1,X0)),sk3)) = sk3 )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3183]) ).

tcf(c_3245,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( tl(cons(hd(cons(X1,X0)),sk3)) = sk3 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3183]) ).

tcf(c_3246,plain,
    tl(cons(hd(sk4),sk3)) = sk3,
    inference(forward_subsumption_resolution,[status(thm)],[c_3241,c_1243]) ).

tcf(c_3274,plain,
    ( ( sk3 = nil )
    | ( tl(cons(hd(sk3),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_246,c_3191]) ).

tcf(c_3275,plain,
    ( ( sk4 = nil )
    | ( tl(cons(hd(sk4),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_247,c_3191]) ).

tcf(c_3277,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( tl(cons(hd(tl(X0)),sk4)) = sk4 )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3191]) ).

tcf(c_3278,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( tl(cons(hd(app(X1,X0)),sk4)) = sk4 )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3191]) ).

tcf(c_3279,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( tl(cons(hd(cons(X1,X0)),sk4)) = sk4 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3191]) ).

tcf(c_3280,plain,
    tl(cons(hd(sk4),sk4)) = sk4,
    inference(forward_subsumption_resolution,[status(thm)],[c_3275,c_1243]) ).

tcf(c_3308,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,sk3),nil) = cons(X0,sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_3018]) ).

tcf(c_3309,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,sk4),nil) = cons(X0,sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_3018]) ).

tcf(c_3310,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),nil) = cons(X0,nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_3018]) ).

tcf(c_3311,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( app(cons(X1,tl(X0)),nil) = cons(X1,tl(X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3018]) ).

tcf(c_3312,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(cons(X2,app(X1,X0)),nil) = cons(X2,app(X1,X0)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3018]) ).

tcf(c_3313,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(cons(X2,cons(X1,X0)),nil) = cons(X2,cons(X1,X0)) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3018]) ).

tcf(c_3359,plain,
    ( ( sk3 = nil )
    | ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_246,c_275]) ).

tcf(c_3360,plain,
    ( ( sk4 = nil )
    | ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_247,c_275]) ).

tcf(c_3362,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( cons(hd(tl(X0)),tl(tl(X0))) = tl(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_275]) ).

tcf(c_3363,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( cons(hd(app(X1,X0)),tl(app(X1,X0))) = app(X1,X0) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_275]) ).

tcf(c_3364,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( cons(hd(cons(X1,X0)),tl(cons(X1,X0))) = cons(X1,X0) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_275]) ).

tcf(c_3365,plain,
    cons(hd(sk4),tl(sk4)) = sk4,
    inference(forward_subsumption_resolution,[status(thm)],[c_3360,c_1243]) ).

tcf(c_3387,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),sk3) = cons(X0,sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_253]) ).

tcf(c_3388,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_253]) ).

tcf(c_3390,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( app(cons(X1,nil),tl(X0)) = cons(X1,tl(X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_253]) ).

tcf(c_3391,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(cons(X2,nil),app(X1,X0)) = cons(X2,app(X1,X0)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_253]) ).

tcf(c_3392,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(cons(X2,nil),cons(X1,X0)) = cons(X2,cons(X1,X0)) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_253]) ).

tcf(c_3414,plain,
    ( ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ( tl(sk4) != sk4 ) ),
    inference(superposition,[status(thm)],[c_3365,c_267]) ).

tcf(c_3423,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),nil)) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3152]) ).

tcf(c_3427,plain,
    ( ssList(tl(sk4))
    | ( sk4 = nil )
    | ~ ssList(sk4) ),
    inference(instantiation,[status(thm)],[c_278]) ).

tcf(c_3433,plain,
    ( ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ( tl(sk3) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3359,c_267]) ).

tcf(c_3439,plain,
    ( ssItem(hd(sk4))
    | ( sk4 = nil )
    | ~ ssList(sk4) ),
    inference(instantiation,[status(thm)],[c_286]) ).

tcf(c_3444,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),sk3),nil) = cons(hd(X0),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3308]) ).

tcf(c_3452,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),sk4),nil) = cons(hd(X0),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3309]) ).

tcf(c_3460,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),nil),sk3) = cons(hd(X0),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3387]) ).

tcf(c_3464,plain,
    ! [X0: $i] :
      ( ( sk4 = nil )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ( app(X0,sk4) != nil ) ),
    inference(instantiation,[status(thm)],[c_254]) ).

tcf(c_3470,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),nil),sk4) = cons(hd(X0),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3388]) ).

tcf(c_3482,plain,
    ( ( sk3 = nil )
    | ( hd(cons(hd(sk3),sk3)) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_3207]) ).

tcf(c_3483,plain,
    ( ( sk4 = nil )
    | ( hd(cons(hd(sk4),sk3)) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_3207]) ).

tcf(c_3485,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),sk3)) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3207]) ).

tcf(c_3486,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),sk3)) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3207]) ).

tcf(c_3487,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),sk3)) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3207]) ).

tcf(c_3488,plain,
    hd(cons(hd(sk4),sk3)) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_3483,c_1243]) ).

tcf(c_3512,plain,
    ( ssItem(hd(sk3))
    | ( sk3 = nil )
    | ( cons(hd(sk3),sk3) = nil )
    | ~ ssList(cons(hd(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_3482,c_286]) ).

tcf(c_3519,plain,
    ( ssItem(hd(sk4))
    | ( cons(hd(sk4),sk3) = nil )
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_3488,c_286]) ).

tcf(c_3531,plain,
    ( ( sk3 = nil )
    | ( hd(cons(hd(sk3),sk4)) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_3215]) ).

tcf(c_3532,plain,
    ( ( sk4 = nil )
    | ( hd(cons(hd(sk4),sk4)) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_3215]) ).

tcf(c_3534,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),sk4)) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3215]) ).

tcf(c_3535,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),sk4)) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3215]) ).

tcf(c_3536,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),sk4)) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3215]) ).

tcf(c_3537,plain,
    hd(cons(hd(sk4),sk4)) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_3532,c_1243]) ).

tcf(c_3563,plain,
    ( ssItem(hd(sk3))
    | ( sk3 = nil )
    | ( cons(hd(sk3),sk4) = nil )
    | ~ ssList(cons(hd(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_3531,c_286]) ).

tcf(c_3569,plain,
    ( ssItem(hd(sk4))
    | ( cons(hd(sk4),sk4) = nil )
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_3537,c_286]) ).

tcf(c_3582,plain,
    ( ( cons(hd(sk4),nil) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ( sk3 != nil ) ),
    inference(superposition,[status(thm)],[c_3088,c_254]) ).

tcf(c_3600,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ( sk3 != nil ) ),
    inference(superposition,[status(thm)],[c_3088,c_255]) ).

tcf(c_3621,plain,
    ( strictorderedP(tl(sk3))
    | ( sk3 = nil )
    | ( tl(sk3) = nil )
    | ~ strictorderedP(sk3)
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3)) ),
    inference(superposition,[status(thm)],[c_3359,c_288]) ).

tcf(c_3622,plain,
    ( strictorderedP(tl(sk4))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(superposition,[status(thm)],[c_3365,c_288]) ).

tcf(c_3653,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),nil),nil) = cons(hd(X0),nil) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3310]) ).

tcf(c_3659,plain,
    tl(sk4) != sk4,
    inference(global_subsumption_just,[status(thm)],[c_3414,c_247,c_1242,c_3414,c_3427,c_3439]) ).

tcf(c_3667,plain,
    ( ( sk3 = nil )
    | ( app(tl(sk3),nil) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_3065]) ).

tcf(c_3668,plain,
    ( ( sk4 = nil )
    | ( app(tl(sk4),nil) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_3065]) ).

tcf(c_3670,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(tl(tl(X0)),nil) = tl(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3065]) ).

tcf(c_3671,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(tl(app(X1,X0)),nil) = tl(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3065]) ).

tcf(c_3672,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(tl(cons(X1,X0)),nil) = tl(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3065]) ).

tcf(c_3673,plain,
    app(tl(sk4),nil) = tl(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_3668,c_1243]) ).

tcf(c_3698,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ( cons(hd(sk4),X0) != nil ) ),
    inference(instantiation,[status(thm)],[c_256]) ).

tcf(c_3699,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4)) ),
    inference(instantiation,[status(thm)],[c_307]) ).

tcf(c_3700,plain,
    ( ~ ssItem(hd(sk4))
    | ~ lt(hd(sk4),hd(sk4)) ),
    inference(instantiation,[status(thm)],[c_299]) ).

tcf(c_3703,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sk4))
    | ( cons(hd(sk4),nil) != nil ) ),
    inference(instantiation,[status(thm)],[c_3698]) ).

tcf(c_3712,plain,
    ! [X0: $i] :
      ( ssList(cons(hd(sk4),X0))
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4)) ),
    inference(instantiation,[status(thm)],[c_268]) ).

tcf(c_3715,plain,
    ( ssList(cons(hd(sk4),nil))
    | ~ ssList(nil)
    | ~ ssItem(hd(sk4)) ),
    inference(instantiation,[status(thm)],[c_3712]) ).

tcf(c_3727,plain,
    app(tl(sk3),nil) = tl(sk3),
    inference(global_subsumption_just,[status(thm)],[c_3667,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3667,c_3703,c_3715]) ).

tcf(c_3732,plain,
    ( ( tl(sk3) != sk3 )
    | ~ ssList(tl(sk3))
    | ~ ssItem(hd(sk3)) ),
    inference(global_subsumption_just,[status(thm)],[c_3433,c_247,c_259,c_1242,c_3427,c_3433,c_3439,c_3582,c_3703,c_3715]) ).

tcf(c_3733,plain,
    ( ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ( tl(sk3) != sk3 ) ),
    inference(renaming,[status(thm)],[c_3732]) ).

tcf(c_3746,plain,
    ( ( sk3 = nil )
    | ( app(cons(hd(sk3),sk3),nil) = cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_3444]) ).

tcf(c_3747,plain,
    ( ( sk4 = nil )
    | ( app(cons(hd(sk4),sk3),nil) = cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_247,c_3444]) ).

tcf(c_3749,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(cons(hd(tl(X0)),sk3),nil) = cons(hd(tl(X0)),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3444]) ).

tcf(c_3750,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(cons(hd(app(X1,X0)),sk3),nil) = cons(hd(app(X1,X0)),sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3444]) ).

tcf(c_3751,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(cons(hd(cons(X1,X0)),sk3),nil) = cons(hd(cons(X1,X0)),sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3444]) ).

tcf(c_3752,plain,
    app(cons(hd(sk4),sk3),nil) = cons(hd(sk4),sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_3747,c_1243]) ).

tcf(c_3768,plain,
    app(cons(hd(sk3),sk3),nil) = cons(hd(sk3),sk3),
    inference(global_subsumption_just,[status(thm)],[c_3746,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_3746]) ).

tcf(c_3782,plain,
    ( ( sk3 = nil )
    | ( app(cons(hd(sk3),sk4),nil) = cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_246,c_3452]) ).

tcf(c_3783,plain,
    ( ( sk4 = nil )
    | ( app(cons(hd(sk4),sk4),nil) = cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_3452]) ).

tcf(c_3785,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(cons(hd(tl(X0)),sk4),nil) = cons(hd(tl(X0)),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3452]) ).

tcf(c_3786,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(cons(hd(app(X1,X0)),sk4),nil) = cons(hd(app(X1,X0)),sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3452]) ).

tcf(c_3787,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(cons(hd(cons(X1,X0)),sk4),nil) = cons(hd(cons(X1,X0)),sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3452]) ).

tcf(c_3788,plain,
    app(cons(hd(sk4),sk4),nil) = cons(hd(sk4),sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_3783,c_1243]) ).

tcf(c_3804,plain,
    app(cons(hd(sk3),sk4),nil) = cons(hd(sk3),sk4),
    inference(global_subsumption_just,[status(thm)],[c_3782,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_3782]) ).

tcf(c_3818,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,sk3)) = cons(X0,sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_3019]) ).

tcf(c_3819,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,sk4)) = cons(X0,sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_3019]) ).

tcf(c_3820,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,nil)) = cons(X0,nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_3019]) ).

tcf(c_3821,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( app(nil,cons(X1,tl(X0))) = cons(X1,tl(X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3019]) ).

tcf(c_3822,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(nil,cons(X2,app(X1,X0))) = cons(X2,app(X1,X0)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3019]) ).

tcf(c_3823,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(nil,cons(X2,cons(X1,X0))) = cons(X2,cons(X1,X0)) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3019]) ).

tcf(c_3858,plain,
    ( totalorderedP(tl(sk3))
    | ( sk3 = nil )
    | ( tl(sk3) = nil )
    | ~ totalorderedP(sk3)
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3)) ),
    inference(superposition,[status(thm)],[c_3359,c_301]) ).

tcf(c_3859,plain,
    ( totalorderedP(tl(sk4))
    | ( tl(sk4) = nil )
    | ~ totalorderedP(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(superposition,[status(thm)],[c_3365,c_301]) ).

tcf(c_3879,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ( hd(app(sk3,X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_283]) ).

tcf(c_3880,plain,
    ! [X0: $i] :
      ( ( sk4 = nil )
      | ( hd(app(sk4,X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_283]) ).

tcf(c_3882,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(tl(X0),X1)) = hd(tl(X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_283]) ).

tcf(c_3883,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(app(X1,X0),X2)) = hd(app(X1,X0)) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_283]) ).

tcf(c_3884,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X2,X0) = nil )
      | ( hd(app(cons(X2,X0),X1)) = hd(cons(X2,X0)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_283]) ).

tcf(c_3885,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3880,c_1243]) ).

tcf(c_3931,plain,
    ( leq(hd(sk3),hd(tl(sk3)))
    | ( sk3 = nil )
    | ( tl(sk3) = nil )
    | ~ totalorderedP(sk3)
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3)) ),
    inference(superposition,[status(thm)],[c_3359,c_281]) ).

tcf(c_3932,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ totalorderedP(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(superposition,[status(thm)],[c_3365,c_281]) ).

tcf(c_3948,plain,
    hd(app(sk4,sk3)) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_3885]) ).

tcf(c_3949,plain,
    hd(app(sk4,sk4)) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_3885]) ).

tcf(c_3950,plain,
    hd(app(sk4,nil)) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_3885]) ).

tcf(c_3951,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,tl(X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3885]) ).

tcf(c_3952,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(X1,X0))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3885]) ).

tcf(c_3953,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,cons(X1,X0))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3885]) ).

tcf(c_4002,plain,
    ( ssItem(hd(sk4))
    | ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_3948,c_286]) ).

tcf(c_4006,plain,
    ( ssItem(hd(sk4))
    | ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_3949,c_286]) ).

tcf(c_4014,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(nil,cons(hd(X0),sk3)) = cons(hd(X0),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3818]) ).

tcf(c_4022,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(nil,cons(hd(X0),sk4)) = cons(hd(X0),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3819]) ).

tcf(c_4026,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ( hd(app(sk3,X0)) = hd(sk3) ) ),
    inference(global_subsumption_just,[status(thm)],[c_3879,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_3879]) ).

tcf(c_4027,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(renaming,[status(thm)],[c_4026]) ).

tcf(c_4033,plain,
    hd(app(sk3,sk3)) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_4027]) ).

tcf(c_4034,plain,
    hd(app(sk3,sk4)) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_4027]) ).

tcf(c_4035,plain,
    hd(app(sk3,nil)) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_4027]) ).

tcf(c_4036,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,tl(X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4027]) ).

tcf(c_4037,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(X1,X0))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4027]) ).

tcf(c_4038,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,cons(X1,X0))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4027]) ).

tcf(c_4051,plain,
    ( ssItem(hd(sk3))
    | ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4033,c_286]) ).

tcf(c_4055,plain,
    ( ssItem(hd(sk3))
    | ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4034,c_286]) ).

tcf(c_4059,plain,
    ssItem(hd(sk4)),
    inference(global_subsumption_just,[status(thm)],[c_4002,c_247,c_1242,c_3439]) ).

tcf(c_4061,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ( app(sk3,X0) != sk3 )
      | ( app(app(X0,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_3089,c_4059]) ).

tcf(c_4067,plain,
    app(nil,cons(hd(sk4),sk4)) = cons(hd(sk4),sk4),
    inference(superposition,[status(thm)],[c_4059,c_3819]) ).

tcf(c_4068,plain,
    app(nil,cons(hd(sk4),sk3)) = cons(hd(sk4),sk3),
    inference(superposition,[status(thm)],[c_4059,c_3818]) ).

tcf(c_4069,plain,
    app(cons(hd(sk4),nil),nil) = cons(hd(sk4),nil),
    inference(superposition,[status(thm)],[c_4059,c_3310]) ).

tcf(c_4070,plain,
    app(cons(hd(sk4),nil),sk4) = cons(hd(sk4),sk4),
    inference(superposition,[status(thm)],[c_4059,c_3388]) ).

tcf(c_4071,plain,
    app(cons(hd(sk4),nil),sk3) = cons(hd(sk4),sk3),
    inference(superposition,[status(thm)],[c_4059,c_3387]) ).

tcf(c_4074,plain,
    hd(cons(hd(sk4),nil)) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_3152]) ).

tcf(c_4077,plain,
    tl(cons(hd(sk4),nil)) = nil,
    inference(superposition,[status(thm)],[c_4059,c_3117]) ).

tcf(c_4087,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),sk4) != nil ) ),
    inference(superposition,[status(thm)],[c_4070,c_254]) ).

tcf(c_4088,plain,
    ( ssList(cons(hd(sk4),sk4))
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(superposition,[status(thm)],[c_4070,c_272]) ).

tcf(c_4089,plain,
    ( ssList(cons(hd(sk4),sk4))
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4088,c_247]) ).

tcf(c_4092,plain,
    ( ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),sk4) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4087,c_1243,c_247]) ).

tcf(c_4109,plain,
    ( lt(hd(sk3),hd(tl(sk3)))
    | ( sk3 = nil )
    | ( tl(sk3) = nil )
    | ~ strictorderedP(sk3)
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3)) ),
    inference(superposition,[status(thm)],[c_3359,c_282]) ).

tcf(c_4110,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(superposition,[status(thm)],[c_3365,c_282]) ).

tcf(c_4111,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4)
    | ~ ssList(tl(sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4110,c_4059]) ).

tcf(c_4130,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ( app(tl(sk3),X0) = tl(app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_274]) ).

tcf(c_4131,plain,
    ! [X0: $i] :
      ( ( sk4 = nil )
      | ( app(tl(sk4),X0) = tl(app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_274]) ).

tcf(c_4133,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(tl(tl(X0)),X1) = tl(app(tl(X0),X1)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_274]) ).

tcf(c_4134,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(tl(app(X1,X0)),X2) = tl(app(app(X1,X0),X2)) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_274]) ).

tcf(c_4135,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X2,X0) = nil )
      | ( app(tl(cons(X2,X0)),X1) = tl(app(cons(X2,X0),X1)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_274]) ).

tcf(c_4136,plain,
    ! [X0: $i] :
      ( ( app(tl(sk4),X0) = tl(app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4131,c_1243]) ).

tcf(c_4223,plain,
    ssList(cons(hd(sk4),sk4)),
    inference(global_subsumption_just,[status(thm)],[c_4089,c_247,c_259,c_1242,c_3439,c_3715,c_4089]) ).

tcf(c_4225,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = nil )
      | ( app(tl(cons(hd(sk4),sk4)),X0) = tl(app(cons(hd(sk4),sk4),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_274]) ).

tcf(c_4226,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = nil )
      | ( hd(app(cons(hd(sk4),sk4),X0)) = hd(cons(hd(sk4),sk4)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_283]) ).

tcf(c_4227,plain,
    hd(app(sk3,cons(hd(sk4),sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_4027]) ).

tcf(c_4228,plain,
    hd(app(sk4,cons(hd(sk4),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_3885]) ).

tcf(c_4229,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk4),sk4))) = cons(X0,cons(hd(sk4),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3019]) ).

tcf(c_4230,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk4)),sk4),nil) = cons(hd(cons(hd(sk4),sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3452]) ).

tcf(c_4231,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk4)),sk3),nil) = cons(hd(cons(hd(sk4),sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3444]) ).

tcf(c_4232,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(tl(cons(hd(sk4),sk4)),nil) = tl(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3065]) ).

tcf(c_4233,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),sk4)) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3215]) ).

tcf(c_4234,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),sk3)) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3207]) ).

tcf(c_4235,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk4),sk4)) = cons(X0,cons(hd(sk4),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_253]) ).

tcf(c_4236,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( cons(hd(cons(hd(sk4),sk4)),tl(cons(hd(sk4),sk4))) = cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_275]) ).

tcf(c_4237,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk4),sk4)),nil) = cons(X0,cons(hd(sk4),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3018]) ).

tcf(c_4238,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk4)),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_4223,c_3191]) ).

tcf(c_4239,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk4)),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_4223,c_3183]) ).

tcf(c_4240,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk4),sk4))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_284]) ).

tcf(c_4241,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk4),sk4))) = cons(hd(sk4),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_276]) ).

tcf(c_4260,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = nil )
      | ( hd(app(cons(hd(sk4),sk4),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_4226,c_3537]) ).

tcf(c_4266,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = nil )
      | ( tl(app(cons(hd(sk4),sk4),X0)) = app(sk4,X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_4225,c_3280]) ).

tcf(c_4277,plain,
    ( ssItem(hd(sk3))
    | ( app(sk3,cons(hd(sk4),sk4)) = nil )
    | ~ ssList(app(sk3,cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_4227,c_286]) ).

tcf(c_4281,plain,
    cons(hd(sk4),sk4) != nil,
    inference(global_subsumption_just,[status(thm)],[c_4092,c_247,c_259,c_1242,c_3439,c_3715,c_4092]) ).

tcf(c_4283,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ( app(tl(sk3),X0) = tl(app(sk3,X0)) ) ),
    inference(global_subsumption_just,[status(thm)],[c_4130,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_4130]) ).

tcf(c_4284,plain,
    ! [X0: $i] :
      ( ( app(tl(sk3),X0) = tl(app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(renaming,[status(thm)],[c_4283]) ).

tcf(c_4290,plain,
    app(tl(sk3),sk3) = tl(app(sk3,sk3)),
    inference(superposition,[status(thm)],[c_246,c_4284]) ).

tcf(c_4291,plain,
    app(tl(sk3),sk4) = tl(app(sk3,sk4)),
    inference(superposition,[status(thm)],[c_247,c_4284]) ).

tcf(c_4292,plain,
    app(tl(sk3),nil) = tl(app(sk3,nil)),
    inference(superposition,[status(thm)],[c_259,c_4284]) ).

tcf(c_4293,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(tl(sk3),tl(X0)) = tl(app(sk3,tl(X0))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4284]) ).

tcf(c_4294,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(tl(sk3),app(X1,X0)) = tl(app(sk3,app(X1,X0))) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4284]) ).

tcf(c_4295,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(tl(sk3),cons(X1,X0)) = tl(app(sk3,cons(X1,X0))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4284]) ).

tcf(c_4296,plain,
    app(tl(sk3),cons(hd(sk4),sk4)) = tl(app(sk3,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_4223,c_4284]) ).

tcf(c_4309,plain,
    ( ssList(app(tl(sk3),sk3))
    | ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4290,c_278]) ).

tcf(c_4313,plain,
    ( ssList(app(tl(sk3),sk4))
    | ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4291,c_278]) ).

tcf(c_4331,plain,
    ( ( cons(hd(sk4),nil) = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),sk3) != nil ) ),
    inference(superposition,[status(thm)],[c_4071,c_255]) ).

tcf(c_4332,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),sk3) != nil ) ),
    inference(superposition,[status(thm)],[c_4071,c_254]) ).

tcf(c_4333,plain,
    ( ssList(cons(hd(sk4),sk3))
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(superposition,[status(thm)],[c_4071,c_272]) ).

tcf(c_4334,plain,
    ( ssList(cons(hd(sk4),sk3))
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4333,c_246]) ).

tcf(c_4337,plain,
    ( ( sk3 = nil )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),sk3) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4332,c_246]) ).

tcf(c_4341,plain,
    ( ( cons(hd(sk4),nil) = nil )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),sk3) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4331,c_246]) ).

tcf(c_4358,plain,
    ssList(cons(hd(sk4),sk3)),
    inference(global_subsumption_just,[status(thm)],[c_4334,c_247,c_259,c_1242,c_3439,c_3715,c_4334]) ).

tcf(c_4360,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = nil )
      | ( app(tl(cons(hd(sk4),sk3)),X0) = tl(app(cons(hd(sk4),sk3),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_274]) ).

tcf(c_4361,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = nil )
      | ( hd(app(cons(hd(sk4),sk3),X0)) = hd(cons(hd(sk4),sk3)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_283]) ).

tcf(c_4362,plain,
    app(tl(sk3),cons(hd(sk4),sk3)) = tl(app(sk3,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_4358,c_4284]) ).

tcf(c_4363,plain,
    hd(app(sk3,cons(hd(sk4),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_4027]) ).

tcf(c_4364,plain,
    hd(app(sk4,cons(hd(sk4),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_3885]) ).

tcf(c_4365,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk4),sk3))) = cons(X0,cons(hd(sk4),sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3019]) ).

tcf(c_4366,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk3)),sk4),nil) = cons(hd(cons(hd(sk4),sk3)),sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3452]) ).

tcf(c_4367,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk3)),sk3),nil) = cons(hd(cons(hd(sk4),sk3)),sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3444]) ).

tcf(c_4368,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(tl(cons(hd(sk4),sk3)),nil) = tl(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3065]) ).

tcf(c_4369,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),sk4)) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3215]) ).

tcf(c_4370,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),sk3)) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3207]) ).

tcf(c_4371,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk4),sk3)) = cons(X0,cons(hd(sk4),sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_253]) ).

tcf(c_4372,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( cons(hd(cons(hd(sk4),sk3)),tl(cons(hd(sk4),sk3))) = cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_275]) ).

tcf(c_4373,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk4),sk3)),nil) = cons(X0,cons(hd(sk4),sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3018]) ).

tcf(c_4374,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk3)),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_4358,c_3191]) ).

tcf(c_4375,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk3)),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_4358,c_3183]) ).

tcf(c_4376,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk4),sk3))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_284]) ).

tcf(c_4377,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk4),sk3))) = cons(hd(sk4),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_276]) ).

tcf(c_4396,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = nil )
      | ( hd(app(cons(hd(sk4),sk3),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_4361,c_3488]) ).

tcf(c_4402,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = nil )
      | ( tl(app(cons(hd(sk4),sk3),X0)) = app(sk3,X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_4360,c_3246]) ).

tcf(c_4430,plain,
    cons(hd(sk4),sk3) != nil,
    inference(global_subsumption_just,[status(thm)],[c_4337,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_4337]) ).

tcf(c_4432,plain,
    ( ssList(app(tl(sk3),cons(hd(sk4),sk4)))
    | ( app(sk3,cons(hd(sk4),sk4)) = nil )
    | ~ ssList(app(sk3,cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_4296,c_278]) ).

tcf(c_4461,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,sk3)) = app(cons(X1,X0),sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_266]) ).

tcf(c_4462,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,sk4)) = app(cons(X1,X0),sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_266]) ).

tcf(c_4463,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,nil)) = app(cons(X1,X0),nil) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_266]) ).

tcf(c_4464,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = nil )
      | ( cons(X2,app(X1,tl(X0))) = app(cons(X2,X1),tl(X0)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_266]) ).

tcf(c_4465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( cons(X3,app(X2,app(X1,X0))) = app(cons(X3,X2),app(X1,X0)) )
      | ~ ssItem(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_266]) ).

tcf(c_4466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( cons(X3,app(X1,cons(X2,X0))) = app(cons(X3,X1),cons(X2,X0)) )
      | ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_266]) ).

tcf(c_4467,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk4),sk3))) = app(cons(X1,X0),cons(hd(sk4),sk3)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_266]) ).

tcf(c_4468,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk4),sk4))) = app(cons(X1,X0),cons(hd(sk4),sk4)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_266]) ).

tcf(c_4539,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,sk3),X0) = app(X1,app(sk3,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_271]) ).

tcf(c_4540,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,sk4),X0) = app(X1,app(sk4,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_271]) ).

tcf(c_4541,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,nil),X0) = app(X1,app(nil,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_271]) ).

tcf(c_4542,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = nil )
      | ( app(app(X2,tl(X0)),X1) = app(X2,app(tl(X0),X1)) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_271]) ).

tcf(c_4543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( app(app(X3,app(X1,X0)),X2) = app(X3,app(app(X1,X0),X2)) )
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_271]) ).

tcf(c_4544,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( app(app(X2,cons(X3,X0)),X1) = app(X2,app(cons(X3,X0),X1)) )
      | ~ ssItem(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_271]) ).

tcf(c_4545,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk4),sk3)),X0) = app(X1,app(cons(hd(sk4),sk3),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_271]) ).

tcf(c_4546,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk4),sk4)),X0) = app(X1,app(cons(hd(sk4),sk4),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_271]) ).

tcf(c_4649,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(X0,cons(hd(sk4),nil)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3088,c_269]) ).

tcf(c_4650,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ( app(X0,nil) != nil ) ),
    inference(superposition,[status(thm)],[c_340,c_269]) ).

tcf(c_4651,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ( app(X0,sk3) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3002,c_269]) ).

tcf(c_4652,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ( app(X0,sk4) != sk4 ) ),
    inference(superposition,[status(thm)],[c_3003,c_269]) ).

tcf(c_4653,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ( app(X0,nil) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3009,c_269]) ).

tcf(c_4654,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ( app(X0,nil) != sk4 ) ),
    inference(superposition,[status(thm)],[c_3010,c_269]) ).

tcf(c_4655,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ( app(X0,nil) != tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_3673,c_269]) ).

tcf(c_4656,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ( app(X0,nil) != tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_3727,c_269]) ).

tcf(c_4657,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( cons(hd(sk4),nil) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_4069,c_269]) ).

tcf(c_4658,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( cons(hd(sk3),sk3) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_3768,c_269]) ).

tcf(c_4659,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( cons(hd(sk4),sk3) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_3752,c_269]) ).

tcf(c_4660,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( cons(hd(sk3),sk4) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_3804,c_269]) ).

tcf(c_4661,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( cons(hd(sk4),sk4) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_3788,c_269]) ).

tcf(c_4662,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(X0,cons(hd(sk4),sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4067,c_269]) ).

tcf(c_4663,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(X0,cons(hd(sk4),sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4068,c_269]) ).

tcf(c_4664,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( cons(hd(sk4),sk4) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_269]) ).

tcf(c_4665,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( cons(hd(sk4),sk3) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_269]) ).

tcf(c_4667,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,nil) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4650,c_259]) ).

tcf(c_4671,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ( app(X0,nil) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4654,c_259,c_247]) ).

tcf(c_4675,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ( app(X0,nil) != sk3 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4653,c_259,c_246]) ).

tcf(c_4679,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,sk4) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4652,c_259,c_247]) ).

tcf(c_4683,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,sk3) != sk3 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4651,c_259,c_246]) ).

tcf(c_4687,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ( app(X0,nil) != tl(sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4656,c_259]) ).

tcf(c_4692,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ( app(X0,nil) != tl(sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4655,c_259]) ).

tcf(c_4702,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( cons(hd(sk4),sk3) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4665,c_246]) ).

tcf(c_4707,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( cons(hd(sk4),sk4) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4664,c_247]) ).

tcf(c_4712,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk4),sk3)) != cons(hd(sk4),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4663,c_259,c_4358]) ).

tcf(c_4716,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk4),sk4)) != cons(hd(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4662,c_259,c_4223]) ).

tcf(c_4720,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),sk4) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4661,c_259,c_4223]) ).

tcf(c_4724,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( cons(hd(sk3),sk4) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4660,c_259]) ).

tcf(c_4729,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),sk3) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4659,c_259,c_4358]) ).

tcf(c_4733,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( cons(hd(sk3),sk3) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4658,c_259]) ).

tcf(c_4738,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( cons(hd(sk4),nil) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4657,c_259]) ).

tcf(c_4808,plain,
    ( ssItem(hd(sk3))
    | ( app(sk3,cons(hd(sk4),sk3)) = nil )
    | ~ ssList(app(sk3,cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_4363,c_286]) ).

tcf(c_4817,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(nil,cons(hd(X0),nil)) = cons(hd(X0),nil) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_3820]) ).

tcf(c_4818,plain,
    app(nil,cons(hd(sk4),nil)) = cons(hd(sk4),nil),
    inference(superposition,[status(thm)],[c_4059,c_3820]) ).

tcf(c_4852,plain,
    ! [X0: $i] :
      ( ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ( app(cons(hd(sk4),nil),X0) != sk3 )
      | ( app(app(X0,cons(hd(sk4),nil)),nil) != sk4 ) ),
    inference(superposition,[status(thm)],[c_4818,c_249]) ).

tcf(c_4857,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(X0,cons(hd(sk4),nil)) != cons(hd(sk4),nil) ) ),
    inference(superposition,[status(thm)],[c_4818,c_269]) ).

tcf(c_4858,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(X0,cons(hd(sk4),nil)) != cons(hd(sk4),nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4857,c_259]) ).

tcf(c_4863,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ( app(cons(hd(sk4),nil),X0) != sk3 )
      | ( app(app(X0,cons(hd(sk4),nil)),nil) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4852,c_259,c_4059]) ).

tcf(c_4907,plain,
    ( ( cons(hd(sk4),nil) = nil )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),sk4) != sk4 ) ),
    inference(superposition,[status(thm)],[c_4070,c_4679]) ).

tcf(c_4918,plain,
    ( ( cons(hd(sk4),nil) = nil )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),sk3) != sk3 ) ),
    inference(superposition,[status(thm)],[c_4071,c_4683]) ).

tcf(c_4928,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(sk3,sk3)) = app(cons(X0,sk3),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_4461]) ).

tcf(c_4929,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(sk4,sk3)) = app(cons(X0,sk4),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_4461]) ).

tcf(c_4930,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(nil,sk3)) = app(cons(X0,nil),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_4461]) ).

tcf(c_4931,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( cons(X1,app(tl(X0),sk3)) = app(cons(X1,tl(X0)),sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4461]) ).

tcf(c_4932,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X2,app(app(X1,X0),sk3)) = app(cons(X2,app(X1,X0)),sk3) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4461]) ).

tcf(c_4933,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X2,app(cons(X1,X0),sk3)) = app(cons(X2,cons(X1,X0)),sk3) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4461]) ).

tcf(c_4934,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),sk3),sk3)) = app(cons(X0,cons(hd(sk4),sk3)),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_4461]) ).

tcf(c_4935,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),sk4),sk3)) = app(cons(X0,cons(hd(sk4),sk4)),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_4461]) ).

tcf(c_4975,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(X0),app(sk3,sk3)) = app(cons(hd(X0),sk3),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_4928]) ).

tcf(c_4976,plain,
    cons(hd(sk4),app(sk3,sk3)) = app(cons(hd(sk4),sk3),sk3),
    inference(superposition,[status(thm)],[c_4059,c_4928]) ).

tcf(c_4998,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(X0),app(sk4,sk3)) = app(cons(hd(X0),sk4),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_4929]) ).

tcf(c_4999,plain,
    cons(hd(sk4),app(sk4,sk3)) = app(cons(hd(sk4),sk4),sk3),
    inference(superposition,[status(thm)],[c_4059,c_4929]) ).

tcf(c_5009,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(sk3,sk4)) = app(cons(X0,sk3),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_4462]) ).

tcf(c_5010,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(sk4,sk4)) = app(cons(X0,sk4),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_4462]) ).

tcf(c_5011,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(nil,sk4)) = app(cons(X0,nil),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_4462]) ).

tcf(c_5012,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( cons(X1,app(tl(X0),sk4)) = app(cons(X1,tl(X0)),sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4462]) ).

tcf(c_5013,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X2,app(app(X1,X0),sk4)) = app(cons(X2,app(X1,X0)),sk4) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4462]) ).

tcf(c_5014,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X2,app(cons(X1,X0),sk4)) = app(cons(X2,cons(X1,X0)),sk4) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4462]) ).

tcf(c_5015,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),sk3),sk4)) = app(cons(X0,cons(hd(sk4),sk3)),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_4462]) ).

tcf(c_5016,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),sk4),sk4)) = app(cons(X0,cons(hd(sk4),sk4)),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_4462]) ).

tcf(c_5086,plain,
    ( ssList(app(tl(sk3),cons(hd(sk4),sk3)))
    | ( app(sk3,cons(hd(sk4),sk3)) = nil )
    | ~ ssList(app(sk3,cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_4362,c_278]) ).

tcf(c_5118,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(tl(sk4),X0) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3088,c_270]) ).

tcf(c_5119,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ( app(nil,X0) != nil ) ),
    inference(superposition,[status(thm)],[c_340,c_270]) ).

tcf(c_5120,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ( app(nil,X0) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3002,c_270]) ).

tcf(c_5121,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ( app(nil,X0) != sk4 ) ),
    inference(superposition,[status(thm)],[c_3003,c_270]) ).

tcf(c_5122,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ( app(sk3,X0) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3009,c_270]) ).

tcf(c_5123,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ( app(sk4,X0) != sk4 ) ),
    inference(superposition,[status(thm)],[c_3010,c_270]) ).

tcf(c_5124,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( cons(hd(sk4),nil) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_4818,c_270]) ).

tcf(c_5125,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ( app(tl(sk4),X0) != tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_3673,c_270]) ).

tcf(c_5126,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ( app(tl(sk3),X0) != tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_3727,c_270]) ).

tcf(c_5127,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(cons(hd(sk4),nil),X0) != cons(hd(sk4),nil) ) ),
    inference(superposition,[status(thm)],[c_4069,c_270]) ).

tcf(c_5128,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( app(cons(hd(sk3),sk3),X0) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_3768,c_270]) ).

tcf(c_5129,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(cons(hd(sk4),sk3),X0) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_3752,c_270]) ).

tcf(c_5130,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( app(cons(hd(sk3),sk4),X0) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_3804,c_270]) ).

tcf(c_5131,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(cons(hd(sk4),sk4),X0) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_3788,c_270]) ).

tcf(c_5132,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( cons(hd(sk4),sk4) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_4067,c_270]) ).

tcf(c_5133,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( cons(hd(sk4),sk3) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_4068,c_270]) ).

tcf(c_5134,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(cons(hd(sk4),nil),X0) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_270]) ).

tcf(c_5135,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(cons(hd(sk4),nil),X0) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_270]) ).

tcf(c_5137,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(nil,X0) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5119,c_259]) ).

tcf(c_5141,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(sk4,X0) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5123,c_259,c_247]) ).

tcf(c_5145,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(sk3,X0) != sk3 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5122,c_259,c_246]) ).

tcf(c_5149,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ( app(nil,X0) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5121,c_259,c_247]) ).

tcf(c_5153,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ( app(nil,X0) != sk3 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5120,c_259,c_246]) ).

tcf(c_5157,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ( app(tl(sk3),X0) != tl(sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5126,c_259]) ).

tcf(c_5162,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ( app(tl(sk4),X0) != tl(sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5125,c_259]) ).

tcf(c_5172,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(cons(hd(sk4),nil),X0) != cons(hd(sk4),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5135,c_246]) ).

tcf(c_5177,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(cons(hd(sk4),nil),X0) != cons(hd(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5134,c_247]) ).

tcf(c_5182,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),sk3) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5133,c_259,c_4358]) ).

tcf(c_5186,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),sk4) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5132,c_259,c_4223]) ).

tcf(c_5190,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),sk4),X0) != cons(hd(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5131,c_259,c_4223]) ).

tcf(c_5194,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( app(cons(hd(sk3),sk4),X0) != cons(hd(sk3),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5130,c_259]) ).

tcf(c_5199,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),sk3),X0) != cons(hd(sk4),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5129,c_259,c_4358]) ).

tcf(c_5203,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( app(cons(hd(sk3),sk3),X0) != cons(hd(sk3),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5128,c_259]) ).

tcf(c_5208,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(cons(hd(sk4),nil),X0) != cons(hd(sk4),nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5127,c_259]) ).

tcf(c_5213,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( cons(hd(sk4),nil) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5124,c_259]) ).

tcf(c_5289,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),sk3)))
      | ( sk3 = nil )
      | ( cons(hd(sk3),sk3) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),sk3))
      | ~ ssList(cons(hd(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_3482,c_279]) ).

tcf(c_5290,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),sk3)))
      | ( cons(hd(sk4),sk3) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),sk3))
      | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_3488,c_279]) ).

tcf(c_5291,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),sk4)))
      | ( sk3 = nil )
      | ( cons(hd(sk3),sk4) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),sk4))
      | ~ ssList(cons(hd(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_3531,c_279]) ).

tcf(c_5292,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),sk4)))
      | ( cons(hd(sk4),sk4) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),sk4))
      | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_3537,c_279]) ).

tcf(c_5293,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),nil)))
      | ( cons(hd(sk4),nil) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),nil))
      | ~ ssList(cons(hd(sk4),nil)) ),
    inference(superposition,[status(thm)],[c_4074,c_279]) ).

tcf(c_5294,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,sk3)))
      | ( app(sk4,sk3) = nil )
      | ~ ssItem(X0)
      | ~ strictorderedP(app(sk4,sk3))
      | ~ ssList(app(sk4,sk3))
      | ~ lt(X0,hd(sk4)) ),
    inference(superposition,[status(thm)],[c_3948,c_279]) ).

tcf(c_5295,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,sk4)))
      | ( app(sk4,sk4) = nil )
      | ~ ssItem(X0)
      | ~ strictorderedP(app(sk4,sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ lt(X0,hd(sk4)) ),
    inference(superposition,[status(thm)],[c_3949,c_279]) ).

tcf(c_5296,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,sk3)))
      | ( app(sk3,sk3) = nil )
      | ~ ssItem(X0)
      | ~ strictorderedP(app(sk3,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ lt(X0,hd(sk3)) ),
    inference(superposition,[status(thm)],[c_4033,c_279]) ).

tcf(c_5297,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,sk4)))
      | ( app(sk3,sk4) = nil )
      | ~ ssItem(X0)
      | ~ strictorderedP(app(sk3,sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ lt(X0,hd(sk3)) ),
    inference(superposition,[status(thm)],[c_4034,c_279]) ).

tcf(c_5298,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),sk4))))
      | ( app(sk3,cons(hd(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),sk4)))
      | ~ ssList(app(sk3,cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_4227,c_279]) ).

tcf(c_5299,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),sk4))))
      | ( app(sk4,cons(hd(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),sk4)))
      | ~ ssList(app(sk4,cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_4228,c_279]) ).

tcf(c_5300,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),sk3))))
      | ( app(sk3,cons(hd(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),sk3)))
      | ~ ssList(app(sk3,cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_4363,c_279]) ).

tcf(c_5301,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),sk3))))
      | ( app(sk4,cons(hd(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),sk3)))
      | ~ ssList(app(sk4,cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_4364,c_279]) ).

tcf(c_5332,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),sk4)))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5292,c_4281,c_4223]) ).

tcf(c_5337,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),sk3)))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5290,c_4430,c_4358]) ).

tcf(c_5405,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(hd(X0),X0))
      | ( X0 = nil )
      | ~ totalorderedP(X0)
      | ~ ssList(X0)
      | ~ ssItem(hd(X0)) ),
    inference(superposition,[status(thm)],[c_307,c_280]) ).

tcf(c_5406,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),sk3)))
      | ( sk3 = nil )
      | ( cons(hd(sk3),sk3) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),sk3))
      | ~ ssList(cons(hd(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_3482,c_280]) ).

tcf(c_5407,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),sk3)))
      | ( cons(hd(sk4),sk3) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),sk3))
      | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_3488,c_280]) ).

tcf(c_5408,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),sk4)))
      | ( sk3 = nil )
      | ( cons(hd(sk3),sk4) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),sk4))
      | ~ ssList(cons(hd(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_3531,c_280]) ).

tcf(c_5409,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),sk4)))
      | ( cons(hd(sk4),sk4) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),sk4))
      | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_3537,c_280]) ).

tcf(c_5410,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),nil)))
      | ( cons(hd(sk4),nil) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),nil))
      | ~ ssList(cons(hd(sk4),nil)) ),
    inference(superposition,[status(thm)],[c_4074,c_280]) ).

tcf(c_5411,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,sk3)))
      | ( app(sk4,sk3) = nil )
      | ~ ssItem(X0)
      | ~ totalorderedP(app(sk4,sk3))
      | ~ ssList(app(sk4,sk3))
      | ~ leq(X0,hd(sk4)) ),
    inference(superposition,[status(thm)],[c_3948,c_280]) ).

tcf(c_5412,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,sk4)))
      | ( app(sk4,sk4) = nil )
      | ~ ssItem(X0)
      | ~ totalorderedP(app(sk4,sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ leq(X0,hd(sk4)) ),
    inference(superposition,[status(thm)],[c_3949,c_280]) ).

tcf(c_5413,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,sk3)))
      | ( app(sk3,sk3) = nil )
      | ~ ssItem(X0)
      | ~ totalorderedP(app(sk3,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ leq(X0,hd(sk3)) ),
    inference(superposition,[status(thm)],[c_4033,c_280]) ).

tcf(c_5414,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,sk4)))
      | ( app(sk3,sk4) = nil )
      | ~ ssItem(X0)
      | ~ totalorderedP(app(sk3,sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ leq(X0,hd(sk3)) ),
    inference(superposition,[status(thm)],[c_4034,c_280]) ).

tcf(c_5415,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),sk4))))
      | ( app(sk3,cons(hd(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),sk4)))
      | ~ ssList(app(sk3,cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_4227,c_280]) ).

tcf(c_5416,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),sk4))))
      | ( app(sk4,cons(hd(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),sk4)))
      | ~ ssList(app(sk4,cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_4228,c_280]) ).

tcf(c_5417,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),sk3))))
      | ( app(sk3,cons(hd(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),sk3)))
      | ~ ssList(app(sk3,cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_4363,c_280]) ).

tcf(c_5418,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),sk3))))
      | ( app(sk4,cons(hd(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),sk3)))
      | ~ ssList(app(sk4,cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_4364,c_280]) ).

tcf(c_5454,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),sk4)))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5409,c_4281,c_4223]) ).

tcf(c_5459,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),sk3)))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5407,c_4430,c_4358]) ).

tcf(c_5567,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk3 = nil )
      | ( tl(sk3) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk3))
      | ( cons(X0,X1) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3359,c_264]) ).

tcf(c_5568,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk4) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ( cons(X0,X1) != sk4 ) ),
    inference(superposition,[status(thm)],[c_3365,c_264]) ).

tcf(c_5570,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk4) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(tl(sk4))
      | ( cons(X0,X1) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5568,c_4059]) ).

tcf(c_5589,plain,
    app(tl(sk4),sk3) = tl(app(sk4,sk3)),
    inference(superposition,[status(thm)],[c_246,c_4136]) ).

tcf(c_5590,plain,
    app(tl(sk4),sk4) = tl(app(sk4,sk4)),
    inference(superposition,[status(thm)],[c_247,c_4136]) ).

tcf(c_5591,plain,
    app(tl(sk4),nil) = tl(app(sk4,nil)),
    inference(superposition,[status(thm)],[c_259,c_4136]) ).

tcf(c_5592,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(tl(sk4),tl(X0)) = tl(app(sk4,tl(X0))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4136]) ).

tcf(c_5593,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(tl(sk4),app(X1,X0)) = tl(app(sk4,app(X1,X0))) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4136]) ).

tcf(c_5594,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(tl(sk4),cons(X1,X0)) = tl(app(sk4,cons(X1,X0))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4136]) ).

tcf(c_5595,plain,
    app(tl(sk4),cons(hd(sk4),sk3)) = tl(app(sk4,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_4358,c_4136]) ).

tcf(c_5596,plain,
    app(tl(sk4),cons(hd(sk4),sk4)) = tl(app(sk4,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_4223,c_4136]) ).

tcf(c_5634,plain,
    ( ssList(app(tl(sk4),sk3))
    | ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5589,c_278]) ).

tcf(c_5638,plain,
    ( ssList(app(tl(sk4),sk4))
    | ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_5590,c_278]) ).

tcf(c_5646,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk4),sk4))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_4240]) ).

tcf(c_5647,plain,
    hd(cons(hd(sk4),cons(hd(sk4),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_4240]) ).

tcf(c_5701,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(X0),app(sk3,sk4)) = app(cons(hd(X0),sk3),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_5009]) ).

tcf(c_5702,plain,
    cons(hd(sk4),app(sk3,sk4)) = app(cons(hd(sk4),sk3),sk4),
    inference(superposition,[status(thm)],[c_4059,c_5009]) ).

tcf(c_5718,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(X0),app(sk4,sk4)) = app(cons(hd(X0),sk4),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_5010]) ).

tcf(c_5719,plain,
    cons(hd(sk4),app(sk4,sk4)) = app(cons(hd(sk4),sk4),sk4),
    inference(superposition,[status(thm)],[c_4059,c_5010]) ).

tcf(c_5737,plain,
    ! [X0: $i] :
      ( ( app(app(sk3,sk3),X0) = app(sk3,app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_4539]) ).

tcf(c_5738,plain,
    ! [X0: $i] :
      ( ( app(app(sk4,sk3),X0) = app(sk4,app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_4539]) ).

tcf(c_5739,plain,
    ! [X0: $i] :
      ( ( app(app(nil,sk3),X0) = app(nil,app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_4539]) ).

tcf(c_5740,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( app(app(tl(X0),sk3),X1) = app(tl(X0),app(sk3,X1)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4539]) ).

tcf(c_5741,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(app(app(X1,X0),sk3),X2) = app(app(X1,X0),app(sk3,X2)) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4539]) ).

tcf(c_5742,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(app(cons(X2,X0),sk3),X1) = app(cons(X2,X0),app(sk3,X1)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4539]) ).

tcf(c_5743,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),sk3),sk3),X0) = app(cons(hd(sk4),sk3),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_4539]) ).

tcf(c_5744,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),sk4),sk3),X0) = app(cons(hd(sk4),sk4),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_4539]) ).

tcf(c_5745,plain,
    ! [X0: $i] :
      ( ( app(nil,app(sk3,X0)) = app(sk3,X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_5739,c_3002]) ).

tcf(c_5752,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),app(sk4,sk3)),X0) = app(cons(hd(sk4),sk4),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_5744,c_4999]) ).

tcf(c_5755,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),app(sk3,sk3)),X0) = app(cons(hd(sk4),sk3),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_5743,c_4976]) ).

tcf(c_5817,plain,
    app(app(sk3,sk3),sk3) = app(sk3,app(sk3,sk3)),
    inference(superposition,[status(thm)],[c_246,c_5737]) ).

tcf(c_5818,plain,
    app(app(sk3,sk3),sk4) = app(sk3,app(sk3,sk4)),
    inference(superposition,[status(thm)],[c_247,c_5737]) ).

tcf(c_5819,plain,
    app(app(sk3,sk3),nil) = app(sk3,app(sk3,nil)),
    inference(superposition,[status(thm)],[c_259,c_5737]) ).

tcf(c_5820,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(app(sk3,sk3),tl(X0)) = app(sk3,app(sk3,tl(X0))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_5737]) ).

tcf(c_5821,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk3,sk3),app(X1,X0)) = app(sk3,app(sk3,app(X1,X0))) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_5737]) ).

tcf(c_5822,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk3,sk3),cons(X1,X0)) = app(sk3,app(sk3,cons(X1,X0))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_5737]) ).

tcf(c_5823,plain,
    app(app(sk3,sk3),cons(hd(sk4),sk3)) = app(sk3,app(sk3,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_4358,c_5737]) ).

tcf(c_5824,plain,
    app(app(sk3,sk3),cons(hd(sk4),sk4)) = app(sk3,app(sk3,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_4223,c_5737]) ).

tcf(c_5825,plain,
    app(app(sk3,sk3),nil) = app(sk3,sk3),
    inference(light_normalisation,[status(thm)],[c_5819,c_3009]) ).

tcf(c_5880,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_4976,c_255]) ).

tcf(c_5881,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_4976,c_254]) ).

tcf(c_5882,plain,
    ( ssList(cons(hd(sk4),app(sk3,sk3)))
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_4976,c_272]) ).

tcf(c_5883,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(cons(hd(sk4),sk3),X0) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4976,c_270]) ).

tcf(c_5884,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( cons(hd(sk4),app(sk3,sk3)) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_4976,c_269]) ).

tcf(c_5885,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_4976,c_4683]) ).

tcf(c_5886,plain,
    ssList(cons(hd(sk4),app(sk3,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_5882,c_246,c_4358]) ).

tcf(c_5887,plain,
    cons(hd(sk4),app(sk3,sk3)) != sk3,
    inference(forward_subsumption_resolution,[status(thm)],[c_5885,c_4430,c_4358]) ).

tcf(c_5891,plain,
    cons(hd(sk4),app(sk3,sk3)) != nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_5880,c_4430,c_246,c_4358]) ).

tcf(c_5892,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk3,sk3)) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5884,c_246,c_4358]) ).

tcf(c_5896,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),sk3),X0) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5883,c_246,c_4358]) ).

tcf(c_5943,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk3 = nil )
      | ( hd(sk3) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk3))
      | ( cons(X0,X1) != sk3 ) ),
    inference(superposition,[status(thm)],[c_3359,c_265]) ).

tcf(c_5944,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(sk4) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ( cons(X0,X1) != sk4 ) ),
    inference(superposition,[status(thm)],[c_3365,c_265]) ).

tcf(c_5946,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(sk4) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(tl(sk4))
      | ( cons(X0,X1) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5944,c_4059]) ).

tcf(c_5986,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ( X0 = nil )
      | ( cons(hd(sk3),sk3) = nil )
      | ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( tl(X0) != sk3 )
      | ( hd(cons(hd(sk3),sk3)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_3240,c_273]) ).

tcf(c_5987,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),sk3) = nil )
      | ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( tl(X0) != sk3 )
      | ( hd(cons(hd(sk4),sk3)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_3246,c_273]) ).

tcf(c_5988,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ( X0 = nil )
      | ( cons(hd(sk3),sk4) = nil )
      | ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( tl(X0) != sk4 )
      | ( hd(cons(hd(sk3),sk4)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_3274,c_273]) ).

tcf(c_5989,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),sk4) = nil )
      | ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( tl(X0) != sk4 )
      | ( hd(cons(hd(sk4),sk4)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_3280,c_273]) ).

tcf(c_5990,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),nil) = nil )
      | ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(sk4),nil)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_4077,c_273]) ).

tcf(c_5991,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,sk3) = nil )
      | ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( hd(app(sk3,sk3)) != hd(X0) )
      | ( app(tl(sk3),sk3) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_4290,c_273]) ).

tcf(c_5992,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,sk4) = nil )
      | ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( hd(app(sk3,sk4)) != hd(X0) )
      | ( app(tl(sk3),sk4) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_4291,c_273]) ).

tcf(c_5993,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),sk4)) = nil )
      | ( app(sk3,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( hd(app(sk3,cons(hd(sk4),sk4))) != hd(X0) )
      | ( app(tl(sk3),cons(hd(sk4),sk4)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_4296,c_273]) ).

tcf(c_5994,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),sk3)) = nil )
      | ( app(sk3,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( hd(app(sk3,cons(hd(sk4),sk3))) != hd(X0) )
      | ( app(tl(sk3),cons(hd(sk4),sk3)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_4362,c_273]) ).

tcf(c_5995,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,sk3) = nil )
      | ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( hd(app(sk4,sk3)) != hd(X0) )
      | ( app(tl(sk4),sk3) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_5589,c_273]) ).

tcf(c_5996,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,sk4) = nil )
      | ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( hd(app(sk4,sk4)) != hd(X0) )
      | ( app(tl(sk4),sk4) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_5590,c_273]) ).

tcf(c_5998,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,sk4) = nil )
      | ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),sk4) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_5996,c_3949]) ).

tcf(c_6006,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,sk3) = nil )
      | ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),sk3) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_5995,c_3948]) ).

tcf(c_6014,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,sk4) = nil )
      | ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),sk4) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_5992,c_4034]) ).

tcf(c_6022,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,sk3) = nil )
      | ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),sk3) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_5991,c_4033]) ).

tcf(c_6030,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),nil) = nil )
      | ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( hd(X0) != hd(sk4) )
      | ( tl(X0) != nil ) ),
    inference(light_normalisation,[status(thm)],[c_5990,c_4074]) ).

tcf(c_6038,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),sk4) = nil )
      | ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( hd(X0) != hd(sk4) )
      | ( tl(X0) != sk4 ) ),
    inference(light_normalisation,[status(thm)],[c_5989,c_3537]) ).

tcf(c_6039,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ( hd(X0) != hd(sk4) )
      | ( tl(X0) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6038,c_4281,c_4223]) ).

tcf(c_6045,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),sk3) = nil )
      | ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( hd(X0) != hd(sk4) )
      | ( tl(X0) != sk3 ) ),
    inference(light_normalisation,[status(thm)],[c_5987,c_3488]) ).

tcf(c_6046,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ( hd(X0) != hd(sk4) )
      | ( tl(X0) != sk3 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6045,c_4430,c_4358]) ).

tcf(c_6068,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),sk3)) = nil )
      | ( app(sk3,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),cons(hd(sk4),sk3)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_5994,c_4363]) ).

tcf(c_6076,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),sk4)) = nil )
      | ( app(sk3,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),cons(hd(sk4),sk4)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_5993,c_4227]) ).

tcf(c_6088,plain,
    ! [X0: $i] :
      ( ssList(app(X0,sk4))
      | ~ ssList(sk4)
      | ~ ssList(X0) ),
    inference(instantiation,[status(thm)],[c_272]) ).

tcf(c_6137,plain,
    ! [X0: $i] :
      ( ssList(app(sk4,X0))
      | ~ ssList(sk4)
      | ~ ssList(X0) ),
    inference(instantiation,[status(thm)],[c_272]) ).

tcf(c_6155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( lt(X1,X3)
      | ~ ssItem(X3)
      | ~ ssItem(X1)
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(cons(X3,X4))
      | ~ ssList(app(X0,cons(X1,X2)))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
    inference(superposition,[status(thm)],[c_272,c_287]) ).

tcf(c_6156,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk3,cons(X0,X1)))
      | ~ strictorderedP(app(app(tl(sk4),cons(hd(sk4),nil)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_3088,c_287]) ).

tcf(c_6157,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(cons(hd(sk4),nil),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk4),nil)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_4818,c_287]) ).

tcf(c_6158,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(cons(hd(sk4),sk4),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk4),sk4)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_4067,c_287]) ).

tcf(c_6159,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(cons(hd(sk4),sk3),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk4),sk3)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_4068,c_287]) ).

tcf(c_6160,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk3),X1)
      | ( sk3 = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk3))
      | ~ ssList(app(app(X0,sk3),cons(X1,X2)))
      | ~ strictorderedP(app(app(X0,cons(hd(sk3),tl(sk3))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_3359,c_287]) ).

tcf(c_6161,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ ssList(app(app(X0,sk4),cons(X1,X2)))
      | ~ strictorderedP(app(app(X0,cons(hd(sk4),tl(sk4))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_3365,c_287]) ).

tcf(c_6162,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk3))
      | ( sk3 = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk3))
      | ~ ssList(app(app(X0,cons(X1,X2)),sk3))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_287]) ).

tcf(c_6163,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ ssList(app(app(X0,cons(X1,X2)),sk4))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_287]) ).

tcf(c_6164,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ strictorderedP(app(cons(hd(sk4),nil),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),nil),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_6157,c_4818]) ).

tcf(c_6165,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(cons(hd(sk4),nil),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),nil),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6164,c_259,c_4059]) ).

tcf(c_6171,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ strictorderedP(app(sk3,cons(X0,X1)))
      | ~ ssList(app(sk3,cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_6156,c_3088]) ).

tcf(c_6172,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(tl(sk4))
      | ~ strictorderedP(app(sk3,cons(X0,X1)))
      | ~ ssList(app(sk3,cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6171,c_259,c_4059]) ).

tcf(c_6188,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),sk3),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_6159,c_4068]) ).

tcf(c_6189,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),sk3),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6188,c_259,c_246,c_4059]) ).

tcf(c_6195,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),sk4),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_6158,c_4067]) ).

tcf(c_6196,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),sk4),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6195,c_259,c_247,c_4059]) ).

tcf(c_6202,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),sk4))
      | ~ ssList(app(app(X0,cons(X1,X2)),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_6163,c_3365]) ).

tcf(c_6203,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),sk4))
      | ~ ssList(app(app(X0,cons(X1,X2)),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6202,c_4059]) ).

tcf(c_6211,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ strictorderedP(app(app(X0,sk4),cons(X1,X2)))
      | ~ ssList(app(app(X0,sk4),cons(X1,X2))) ),
    inference(light_normalisation,[status(thm)],[c_6161,c_3365]) ).

tcf(c_6212,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ strictorderedP(app(app(X0,sk4),cons(X1,X2)))
      | ~ ssList(app(app(X0,sk4),cons(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6211,c_4059]) ).

tcf(c_6291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( leq(X1,X3)
      | ~ ssItem(X3)
      | ~ ssItem(X1)
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(cons(X3,X4))
      | ~ ssList(app(X0,cons(X1,X2)))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
    inference(superposition,[status(thm)],[c_272,c_300]) ).

tcf(c_6292,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk3,cons(X0,X1)))
      | ~ totalorderedP(app(app(tl(sk4),cons(hd(sk4),nil)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_3088,c_300]) ).

tcf(c_6293,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(cons(hd(sk4),nil),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk4),nil)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_4818,c_300]) ).

tcf(c_6294,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(cons(hd(sk4),sk4),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk4),sk4)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_4067,c_300]) ).

tcf(c_6295,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(cons(hd(sk4),sk3),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk4),sk3)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_4068,c_300]) ).

tcf(c_6296,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk3),X1)
      | ( sk3 = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk3))
      | ~ ssList(app(app(X0,sk3),cons(X1,X2)))
      | ~ totalorderedP(app(app(X0,cons(hd(sk3),tl(sk3))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_3359,c_300]) ).

tcf(c_6297,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ ssList(app(app(X0,sk4),cons(X1,X2)))
      | ~ totalorderedP(app(app(X0,cons(hd(sk4),tl(sk4))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_3365,c_300]) ).

tcf(c_6298,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk3))
      | ( sk3 = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk3))
      | ~ ssList(app(app(X0,cons(X1,X2)),sk3))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_300]) ).

tcf(c_6299,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ ssList(app(app(X0,cons(X1,X2)),sk4))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_300]) ).

tcf(c_6300,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ totalorderedP(app(cons(hd(sk4),nil),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),nil),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_6293,c_4818]) ).

tcf(c_6301,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(cons(hd(sk4),nil),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),nil),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6300,c_259,c_4059]) ).

tcf(c_6307,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ totalorderedP(app(sk3,cons(X0,X1)))
      | ~ ssList(app(sk3,cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_6292,c_3088]) ).

tcf(c_6308,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(tl(sk4))
      | ~ totalorderedP(app(sk3,cons(X0,X1)))
      | ~ ssList(app(sk3,cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6307,c_259,c_4059]) ).

tcf(c_6324,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),sk3),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_6295,c_4068]) ).

tcf(c_6325,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),sk3),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6324,c_259,c_246,c_4059]) ).

tcf(c_6331,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),sk4),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_6294,c_4067]) ).

tcf(c_6332,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),sk4),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6331,c_259,c_247,c_4059]) ).

tcf(c_6338,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),sk4))
      | ~ ssList(app(app(X0,cons(X1,X2)),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_6299,c_3365]) ).

tcf(c_6339,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),sk4))
      | ~ ssList(app(app(X0,cons(X1,X2)),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6338,c_4059]) ).

tcf(c_6347,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(sk4))
      | ~ totalorderedP(app(app(X0,sk4),cons(X1,X2)))
      | ~ ssList(app(app(X0,sk4),cons(X1,X2))) ),
    inference(light_normalisation,[status(thm)],[c_6297,c_3365]) ).

tcf(c_6348,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ totalorderedP(app(app(X0,sk4),cons(X1,X2)))
      | ~ ssList(app(app(X0,sk4),cons(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6347,c_4059]) ).

tcf(c_6382,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk3,sk3)),sk3),X0) = app(cons(hd(sk4),app(sk3,sk3)),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_4539]) ).

tcf(c_6383,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk4),app(sk3,sk3))),X0) = app(X1,app(cons(hd(sk4),app(sk3,sk3)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_271]) ).

tcf(c_6384,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk4),app(sk3,sk3)))) = app(cons(X1,X0),cons(hd(sk4),app(sk3,sk3))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_266]) ).

tcf(c_6385,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
      | ( app(tl(cons(hd(sk4),app(sk3,sk3))),X0) = tl(app(cons(hd(sk4),app(sk3,sk3)),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_274]) ).

tcf(c_6386,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
      | ( hd(app(cons(hd(sk4),app(sk3,sk3)),X0)) = hd(cons(hd(sk4),app(sk3,sk3))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_283]) ).

tcf(c_6387,plain,
    app(app(sk3,sk3),cons(hd(sk4),app(sk3,sk3))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_5886,c_5737]) ).

tcf(c_6388,plain,
    app(tl(sk4),cons(hd(sk4),app(sk3,sk3))) = tl(app(sk4,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_5886,c_4136]) ).

tcf(c_6389,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk3,sk3)),sk4)) = app(cons(X0,cons(hd(sk4),app(sk3,sk3))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_4462]) ).

tcf(c_6390,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk3,sk3)),sk3)) = app(cons(X0,cons(hd(sk4),app(sk3,sk3))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_4461]) ).

tcf(c_6391,plain,
    app(tl(sk3),cons(hd(sk4),app(sk3,sk3))) = tl(app(sk3,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_5886,c_4284]) ).

tcf(c_6392,plain,
    hd(app(sk3,cons(hd(sk4),app(sk3,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_4027]) ).

tcf(c_6393,plain,
    hd(app(sk4,cons(hd(sk4),app(sk3,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_3885]) ).

tcf(c_6394,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk4),app(sk3,sk3)))) = cons(X0,cons(hd(sk4),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3019]) ).

tcf(c_6395,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4),nil) = cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3452]) ).

tcf(c_6396,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3),nil) = cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3444]) ).

tcf(c_6397,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(tl(cons(hd(sk4),app(sk3,sk3))),nil) = tl(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3065]) ).

tcf(c_6398,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3215]) ).

tcf(c_6399,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3207]) ).

tcf(c_6400,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk4),app(sk3,sk3))) = cons(X0,cons(hd(sk4),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_253]) ).

tcf(c_6401,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))) = cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_5886,c_275]) ).

tcf(c_6402,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk4),app(sk3,sk3))),nil) = cons(X0,cons(hd(sk4),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3018]) ).

tcf(c_6403,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_5886,c_3191]) ).

tcf(c_6404,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_5886,c_3183]) ).

tcf(c_6405,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk4),app(sk3,sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_284]) ).

tcf(c_6406,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk4),app(sk3,sk3)))) = cons(hd(sk4),app(sk3,sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_276]) ).

tcf(c_6407,plain,
    app(cons(hd(sk4),app(sk3,sk3)),nil) = cons(hd(sk4),app(sk3,sk3)),
    inference(superposition,[status(thm)],[c_5886,c_258]) ).

tcf(c_6408,plain,
    app(nil,cons(hd(sk4),app(sk3,sk3))) = cons(hd(sk4),app(sk3,sk3)),
    inference(superposition,[status(thm)],[c_5886,c_257]) ).

tcf(c_6491,plain,
    ( ( sk3 = nil )
    | ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_246,c_275]) ).

tcf(c_6536,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),sk3) = cons(X0,sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_253]) ).

tcf(c_6565,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(app(sk3,sk3),X0) != app(sk3,sk3) ) ),
    inference(superposition,[status(thm)],[c_5825,c_270]) ).

tcf(c_6566,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(X0,nil) != app(sk3,sk3) ) ),
    inference(superposition,[status(thm)],[c_5825,c_269]) ).

tcf(c_6567,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(X0,nil) != app(sk3,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6566,c_259]) ).

tcf(c_6572,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(app(sk3,sk3),X0) != app(sk3,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6565,c_259]) ).

tcf(c_6580,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(sk3)
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_5817,c_255]) ).

tcf(c_6581,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_5817,c_254]) ).

tcf(c_6582,plain,
    ( ssList(app(sk3,app(sk3,sk3)))
    | ~ ssList(sk3)
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_5817,c_272]) ).

tcf(c_6583,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(app(sk3,sk3),X0) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_5817,c_270]) ).

tcf(c_6584,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,sk3)) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_5817,c_269]) ).

tcf(c_6585,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_5817,c_4683]) ).

tcf(c_6586,plain,
    ( ssList(app(sk3,app(sk3,sk3)))
    | ~ ssList(app(sk3,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6582,c_246]) ).

tcf(c_6592,plain,
    ( ( sk3 = nil )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6581,c_246]) ).

tcf(c_6596,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6580,c_246]) ).

tcf(c_6600,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,sk3)) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6584,c_246]) ).

tcf(c_6605,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(app(sk3,sk3),X0) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6583,c_246]) ).

tcf(c_6616,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,sk3)),sk3),X0) = app(app(sk3,app(sk3,sk3)),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4539]) ).

tcf(c_6617,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk3,sk3))),X0) = app(X1,app(app(sk3,app(sk3,sk3)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_271]) ).

tcf(c_6618,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk3,sk3)))) = app(cons(X1,X0),app(sk3,app(sk3,sk3))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_266]) ).

tcf(c_6619,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,sk3)) = nil )
      | ( app(tl(app(sk3,app(sk3,sk3))),X0) = tl(app(app(sk3,app(sk3,sk3)),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_274]) ).

tcf(c_6620,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,sk3)) = nil )
      | ( hd(app(app(sk3,app(sk3,sk3)),X0)) = hd(app(sk3,app(sk3,sk3))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_283]) ).

tcf(c_6621,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk3,sk3))) = app(sk3,app(sk3,app(sk3,app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_5737]) ).

tcf(c_6622,plain,
    ( ( app(tl(sk4),app(sk3,app(sk3,sk3))) = tl(app(sk4,app(sk3,app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4136]) ).

tcf(c_6623,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,sk3)),sk4)) = app(cons(X0,app(sk3,app(sk3,sk3))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4462]) ).

tcf(c_6624,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,sk3)),sk3)) = app(cons(X0,app(sk3,app(sk3,sk3))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4461]) ).

tcf(c_6625,plain,
    ( ( app(tl(sk3),app(sk3,app(sk3,sk3))) = tl(app(sk3,app(sk3,app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4284]) ).

tcf(c_6626,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4027]) ).

tcf(c_6627,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3885]) ).

tcf(c_6628,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk3,sk3)))) = cons(X0,app(sk3,app(sk3,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3019]) ).

tcf(c_6629,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk3))),sk4),nil) = cons(hd(app(sk3,app(sk3,sk3))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3452]) ).

tcf(c_6630,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk3))),sk3),nil) = cons(hd(app(sk3,app(sk3,sk3))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3444]) ).

tcf(c_6631,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(tl(app(sk3,app(sk3,sk3))),nil) = tl(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3065]) ).

tcf(c_6632,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),sk4)) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3215]) ).

tcf(c_6633,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),sk3)) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3207]) ).

tcf(c_6634,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk3,sk3))) = cons(X0,app(sk3,app(sk3,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_253]) ).

tcf(c_6635,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( cons(hd(app(sk3,app(sk3,sk3))),tl(app(sk3,app(sk3,sk3)))) = app(sk3,app(sk3,sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_275]) ).

tcf(c_6636,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk3,sk3))),nil) = cons(X0,app(sk3,app(sk3,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3018]) ).

tcf(c_6637,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk3))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3191]) ).

tcf(c_6638,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk3))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3183]) ).

tcf(c_6639,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_284]) ).

tcf(c_6640,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk3,sk3)))) = app(sk3,app(sk3,sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_276]) ).

tcf(c_6641,plain,
    ( ( app(app(sk3,app(sk3,sk3)),nil) = app(sk3,app(sk3,sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_258]) ).

tcf(c_6642,plain,
    ( ( app(nil,app(sk3,app(sk3,sk3))) = app(sk3,app(sk3,sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_257]) ).

tcf(c_6883,plain,
    cons(hd(sk3),tl(sk3)) = sk3,
    inference(global_subsumption_just,[status(thm)],[c_6491,c_247,c_259,c_1242,c_3359,c_3427,c_3439,c_3582,c_3703,c_3715]) ).

tcf(c_6887,plain,
    ( ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ( sk3 != nil ) ),
    inference(superposition,[status(thm)],[c_6883,c_256]) ).

tcf(c_6922,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),nil),sk3) = cons(hd(X0),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_6536]) ).

tcf(c_6929,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_5818,c_254]) ).

tcf(c_6930,plain,
    ( ssList(app(sk3,app(sk3,sk4)))
    | ~ ssList(sk4)
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_5818,c_272]) ).

tcf(c_6931,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(app(sk3,sk3),X0) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5818,c_270]) ).

tcf(c_6932,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,sk4)) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_5818,c_269]) ).

tcf(c_6933,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_5818,c_4679]) ).

tcf(c_6934,plain,
    ( ssList(app(sk3,app(sk3,sk4)))
    | ~ ssList(app(sk3,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6930,c_247]) ).

tcf(c_6940,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk4)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6929,c_1243,c_247]) ).

tcf(c_6943,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,sk4)) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6932,c_247]) ).

tcf(c_6948,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(app(sk3,sk3),X0) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6931,c_247]) ).

tcf(c_6983,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,sk4)),sk3),X0) = app(app(sk3,app(sk3,sk4)),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4539]) ).

tcf(c_6984,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk3,sk4))),X0) = app(X1,app(app(sk3,app(sk3,sk4)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_271]) ).

tcf(c_6985,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk3,sk4)))) = app(cons(X1,X0),app(sk3,app(sk3,sk4))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_266]) ).

tcf(c_6986,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,sk4)) = nil )
      | ( app(tl(app(sk3,app(sk3,sk4))),X0) = tl(app(app(sk3,app(sk3,sk4)),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_274]) ).

tcf(c_6987,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,sk4)) = nil )
      | ( hd(app(app(sk3,app(sk3,sk4)),X0)) = hd(app(sk3,app(sk3,sk4))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_283]) ).

tcf(c_6988,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk3,sk4))) = app(sk3,app(sk3,app(sk3,app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_5737]) ).

tcf(c_6989,plain,
    ( ( app(tl(sk4),app(sk3,app(sk3,sk4))) = tl(app(sk4,app(sk3,app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4136]) ).

tcf(c_6990,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,sk4)),sk4)) = app(cons(X0,app(sk3,app(sk3,sk4))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4462]) ).

tcf(c_6991,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,sk4)),sk3)) = app(cons(X0,app(sk3,app(sk3,sk4))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4461]) ).

tcf(c_6992,plain,
    ( ( app(tl(sk3),app(sk3,app(sk3,sk4))) = tl(app(sk3,app(sk3,app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4284]) ).

tcf(c_6993,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4027]) ).

tcf(c_6994,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3885]) ).

tcf(c_6995,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk3,sk4)))) = cons(X0,app(sk3,app(sk3,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3019]) ).

tcf(c_6996,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk4))),sk4),nil) = cons(hd(app(sk3,app(sk3,sk4))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3452]) ).

tcf(c_6997,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk4))),sk3),nil) = cons(hd(app(sk3,app(sk3,sk4))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3444]) ).

tcf(c_6998,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(tl(app(sk3,app(sk3,sk4))),nil) = tl(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3065]) ).

tcf(c_6999,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),sk4)) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3215]) ).

tcf(c_7000,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),sk3)) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3207]) ).

tcf(c_7001,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk3,sk4))) = cons(X0,app(sk3,app(sk3,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_253]) ).

tcf(c_7002,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( cons(hd(app(sk3,app(sk3,sk4))),tl(app(sk3,app(sk3,sk4)))) = app(sk3,app(sk3,sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_275]) ).

tcf(c_7003,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk3,sk4))),nil) = cons(X0,app(sk3,app(sk3,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3018]) ).

tcf(c_7004,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk4))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3191]) ).

tcf(c_7005,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk4))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3183]) ).

tcf(c_7006,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,sk4)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_284]) ).

tcf(c_7007,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk3,sk4)))) = app(sk3,app(sk3,sk4)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_276]) ).

tcf(c_7008,plain,
    ( ( app(app(sk3,app(sk3,sk4)),nil) = app(sk3,app(sk3,sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_258]) ).

tcf(c_7009,plain,
    ( ( app(nil,app(sk3,app(sk3,sk4))) = app(sk3,app(sk3,sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_257]) ).

tcf(c_7100,plain,
    sk3 != nil,
    inference(global_subsumption_just,[status(thm)],[c_6887,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715]) ).

tcf(c_7182,plain,
    app(app(sk4,sk3),sk3) = app(sk4,app(sk3,sk3)),
    inference(superposition,[status(thm)],[c_246,c_5738]) ).

tcf(c_7183,plain,
    app(app(sk4,sk3),sk4) = app(sk4,app(sk3,sk4)),
    inference(superposition,[status(thm)],[c_247,c_5738]) ).

tcf(c_7184,plain,
    app(app(sk4,sk3),nil) = app(sk4,app(sk3,nil)),
    inference(superposition,[status(thm)],[c_259,c_5738]) ).

tcf(c_7185,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(app(sk4,sk3),tl(X0)) = app(sk4,app(sk3,tl(X0))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_5738]) ).

tcf(c_7186,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk4,sk3),app(X1,X0)) = app(sk4,app(sk3,app(X1,X0))) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_5738]) ).

tcf(c_7187,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk4,sk3),cons(X1,X0)) = app(sk4,app(sk3,cons(X1,X0))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_5738]) ).

tcf(c_7188,plain,
    app(app(sk4,sk3),cons(hd(sk4),sk3)) = app(sk4,app(sk3,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_4358,c_5738]) ).

tcf(c_7189,plain,
    app(app(sk4,sk3),cons(hd(sk4),sk4)) = app(sk4,app(sk3,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_4223,c_5738]) ).

tcf(c_7190,plain,
    app(app(sk4,sk3),cons(hd(sk4),app(sk3,sk3))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_5886,c_5738]) ).

tcf(c_7191,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk3,sk3))) = app(sk4,app(sk3,app(sk3,app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_5738]) ).

tcf(c_7192,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk3,sk4))) = app(sk4,app(sk3,app(sk3,app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_5738]) ).

tcf(c_7193,plain,
    app(app(sk4,sk3),nil) = app(sk4,sk3),
    inference(light_normalisation,[status(thm)],[c_7184,c_3009]) ).

tcf(c_7237,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(sk3)
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_7182,c_255]) ).

tcf(c_7238,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_7182,c_254]) ).

tcf(c_7239,plain,
    ( ssList(app(sk4,app(sk3,sk3)))
    | ~ ssList(sk3)
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7182,c_272]) ).

tcf(c_7240,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(app(sk4,sk3),X0) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7182,c_270]) ).

tcf(c_7241,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,sk3)) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_7182,c_269]) ).

tcf(c_7242,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_7182,c_4683]) ).

tcf(c_7243,plain,
    ( ssList(app(sk4,app(sk3,sk3)))
    | ~ ssList(app(sk4,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7239,c_246]) ).

tcf(c_7249,plain,
    ( ( sk3 = nil )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7238,c_246]) ).

tcf(c_7253,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7237,c_246]) ).

tcf(c_7257,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,sk3)) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7241,c_246]) ).

tcf(c_7262,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(app(sk4,sk3),X0) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7240,c_246]) ).

tcf(c_7285,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,sk3)),sk3),X0) = app(app(sk4,app(sk3,sk3)),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4539]) ).

tcf(c_7286,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk3,sk3))),X0) = app(X1,app(app(sk4,app(sk3,sk3)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_271]) ).

tcf(c_7287,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk3,sk3)))) = app(cons(X1,X0),app(sk4,app(sk3,sk3))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_266]) ).

tcf(c_7288,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,sk3)) = nil )
      | ( app(tl(app(sk4,app(sk3,sk3))),X0) = tl(app(app(sk4,app(sk3,sk3)),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_274]) ).

tcf(c_7289,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,sk3)) = nil )
      | ( hd(app(app(sk4,app(sk3,sk3)),X0)) = hd(app(sk4,app(sk3,sk3))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_283]) ).

tcf(c_7290,plain,
    ( ( app(app(sk4,sk3),app(sk4,app(sk3,sk3))) = app(sk4,app(sk3,app(sk4,app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_5738]) ).

tcf(c_7291,plain,
    ( ( app(app(sk3,sk3),app(sk4,app(sk3,sk3))) = app(sk3,app(sk3,app(sk4,app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_5737]) ).

tcf(c_7292,plain,
    ( ( app(tl(sk4),app(sk4,app(sk3,sk3))) = tl(app(sk4,app(sk4,app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4136]) ).

tcf(c_7293,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,sk3)),sk4)) = app(cons(X0,app(sk4,app(sk3,sk3))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4462]) ).

tcf(c_7294,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,sk3)),sk3)) = app(cons(X0,app(sk4,app(sk3,sk3))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4461]) ).

tcf(c_7295,plain,
    ( ( app(tl(sk3),app(sk4,app(sk3,sk3))) = tl(app(sk3,app(sk4,app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4284]) ).

tcf(c_7296,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4027]) ).

tcf(c_7297,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3885]) ).

tcf(c_7298,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk3,sk3)))) = cons(X0,app(sk4,app(sk3,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3019]) ).

tcf(c_7299,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk3))),sk4),nil) = cons(hd(app(sk4,app(sk3,sk3))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3452]) ).

tcf(c_7300,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk3))),sk3),nil) = cons(hd(app(sk4,app(sk3,sk3))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3444]) ).

tcf(c_7301,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(tl(app(sk4,app(sk3,sk3))),nil) = tl(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3065]) ).

tcf(c_7302,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),sk4)) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3215]) ).

tcf(c_7303,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),sk3)) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3207]) ).

tcf(c_7304,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk3,sk3))) = cons(X0,app(sk4,app(sk3,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_253]) ).

tcf(c_7305,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( cons(hd(app(sk4,app(sk3,sk3))),tl(app(sk4,app(sk3,sk3)))) = app(sk4,app(sk3,sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_275]) ).

tcf(c_7306,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk3,sk3))),nil) = cons(X0,app(sk4,app(sk3,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3018]) ).

tcf(c_7307,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk3))),sk4)) = sk4 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3191]) ).

tcf(c_7308,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk3))),sk3)) = sk3 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3183]) ).

tcf(c_7309,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_284]) ).

tcf(c_7310,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk3,sk3)))) = app(sk4,app(sk3,sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_276]) ).

tcf(c_7311,plain,
    ( ( app(app(sk4,app(sk3,sk3)),nil) = app(sk4,app(sk3,sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_258]) ).

tcf(c_7312,plain,
    ( ( app(nil,app(sk4,app(sk3,sk3))) = app(sk4,app(sk3,sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_257]) ).

tcf(c_7534,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_4999,c_255]) ).

tcf(c_7535,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_4999,c_254]) ).

tcf(c_7536,plain,
    ( ssList(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_4999,c_272]) ).

tcf(c_7537,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(cons(hd(sk4),sk4),X0) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4999,c_270]) ).

tcf(c_7538,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( cons(hd(sk4),app(sk4,sk3)) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_4999,c_269]) ).

tcf(c_7539,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_4999,c_4683]) ).

tcf(c_7540,plain,
    ssList(cons(hd(sk4),app(sk4,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_7536,c_246,c_4223]) ).

tcf(c_7541,plain,
    cons(hd(sk4),app(sk4,sk3)) != sk3,
    inference(forward_subsumption_resolution,[status(thm)],[c_7539,c_4281,c_4223]) ).

tcf(c_7545,plain,
    cons(hd(sk4),app(sk4,sk3)) != nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_7534,c_4281,c_246,c_4223]) ).

tcf(c_7546,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk4,sk3)) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7538,c_246,c_4223]) ).

tcf(c_7550,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),sk4),X0) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7537,c_246,c_4223]) ).

tcf(c_7560,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ( app(sk3,X0) != nil ) ),
    inference(instantiation,[status(thm)],[c_255]) ).

tcf(c_7561,plain,
    ( ssItem(hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(sk3) ),
    inference(instantiation,[status(thm)],[c_286]) ).

tcf(c_7562,plain,
    ( ssList(tl(sk3))
    | ( sk3 = nil )
    | ~ ssList(sk3) ),
    inference(instantiation,[status(thm)],[c_278]) ).

tcf(c_7579,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk4,sk3)),sk3),X0) = app(cons(hd(sk4),app(sk4,sk3)),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_4539]) ).

tcf(c_7580,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk4),app(sk4,sk3))),X0) = app(X1,app(cons(hd(sk4),app(sk4,sk3)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_271]) ).

tcf(c_7581,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk4),app(sk4,sk3)))) = app(cons(X1,X0),cons(hd(sk4),app(sk4,sk3))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_266]) ).

tcf(c_7582,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
      | ( app(tl(cons(hd(sk4),app(sk4,sk3))),X0) = tl(app(cons(hd(sk4),app(sk4,sk3)),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_274]) ).

tcf(c_7583,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
      | ( hd(app(cons(hd(sk4),app(sk4,sk3)),X0)) = hd(cons(hd(sk4),app(sk4,sk3))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_283]) ).

tcf(c_7584,plain,
    app(app(sk4,sk3),cons(hd(sk4),app(sk4,sk3))) = app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_7540,c_5738]) ).

tcf(c_7585,plain,
    app(app(sk3,sk3),cons(hd(sk4),app(sk4,sk3))) = app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_7540,c_5737]) ).

tcf(c_7586,plain,
    app(tl(sk4),cons(hd(sk4),app(sk4,sk3))) = tl(app(sk4,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_7540,c_4136]) ).

tcf(c_7587,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk4,sk3)),sk4)) = app(cons(X0,cons(hd(sk4),app(sk4,sk3))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_4462]) ).

tcf(c_7588,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk4,sk3)),sk3)) = app(cons(X0,cons(hd(sk4),app(sk4,sk3))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_4461]) ).

tcf(c_7589,plain,
    app(tl(sk3),cons(hd(sk4),app(sk4,sk3))) = tl(app(sk3,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_7540,c_4284]) ).

tcf(c_7590,plain,
    hd(app(sk3,cons(hd(sk4),app(sk4,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_4027]) ).

tcf(c_7591,plain,
    hd(app(sk4,cons(hd(sk4),app(sk4,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_3885]) ).

tcf(c_7592,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk4),app(sk4,sk3)))) = cons(X0,cons(hd(sk4),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3019]) ).

tcf(c_7593,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4),nil) = cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3452]) ).

tcf(c_7594,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3),nil) = cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3444]) ).

tcf(c_7595,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(tl(cons(hd(sk4),app(sk4,sk3))),nil) = tl(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3065]) ).

tcf(c_7596,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4)) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3215]) ).

tcf(c_7597,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3)) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3207]) ).

tcf(c_7598,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk4),app(sk4,sk3))) = cons(X0,cons(hd(sk4),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_253]) ).

tcf(c_7599,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( cons(hd(cons(hd(sk4),app(sk4,sk3))),tl(cons(hd(sk4),app(sk4,sk3)))) = cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7540,c_275]) ).

tcf(c_7600,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk4),app(sk4,sk3))),nil) = cons(X0,cons(hd(sk4),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3018]) ).

tcf(c_7601,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_7540,c_3191]) ).

tcf(c_7602,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_7540,c_3183]) ).

tcf(c_7603,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk4),app(sk4,sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_284]) ).

tcf(c_7604,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk4),app(sk4,sk3)))) = cons(hd(sk4),app(sk4,sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_276]) ).

tcf(c_7605,plain,
    app(cons(hd(sk4),app(sk4,sk3)),nil) = cons(hd(sk4),app(sk4,sk3)),
    inference(superposition,[status(thm)],[c_7540,c_258]) ).

tcf(c_7606,plain,
    app(nil,cons(hd(sk4),app(sk4,sk3))) = cons(hd(sk4),app(sk4,sk3)),
    inference(superposition,[status(thm)],[c_7540,c_257]) ).

tcf(c_7727,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(app(sk4,sk3),X0) != app(sk4,sk3) ) ),
    inference(superposition,[status(thm)],[c_7193,c_270]) ).

tcf(c_7728,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(X0,nil) != app(sk4,sk3) ) ),
    inference(superposition,[status(thm)],[c_7193,c_269]) ).

tcf(c_7729,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(X0,nil) != app(sk4,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7728,c_259]) ).

tcf(c_7734,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(app(sk4,sk3),X0) != app(sk4,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7727,c_259]) ).

tcf(c_7749,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_7183,c_254]) ).

tcf(c_7750,plain,
    ( ssList(app(sk4,app(sk3,sk4)))
    | ~ ssList(sk4)
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7183,c_272]) ).

tcf(c_7751,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(app(sk4,sk3),X0) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_7183,c_270]) ).

tcf(c_7752,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,sk4)) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_7183,c_269]) ).

tcf(c_7753,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_7183,c_4679]) ).

tcf(c_7754,plain,
    ( ssList(app(sk4,app(sk3,sk4)))
    | ~ ssList(app(sk4,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7750,c_247]) ).

tcf(c_7760,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk4)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7749,c_1243,c_247]) ).

tcf(c_7763,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,sk4)) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7752,c_247]) ).

tcf(c_7768,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(app(sk4,sk3),X0) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7751,c_247]) ).

tcf(c_7805,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,sk4)),sk3),X0) = app(app(sk4,app(sk3,sk4)),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4539]) ).

tcf(c_7806,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk3,sk4))),X0) = app(X1,app(app(sk4,app(sk3,sk4)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_271]) ).

tcf(c_7807,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk3,sk4)))) = app(cons(X1,X0),app(sk4,app(sk3,sk4))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_266]) ).

tcf(c_7808,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,sk4)) = nil )
      | ( app(tl(app(sk4,app(sk3,sk4))),X0) = tl(app(app(sk4,app(sk3,sk4)),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_274]) ).

tcf(c_7809,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,sk4)) = nil )
      | ( hd(app(app(sk4,app(sk3,sk4)),X0)) = hd(app(sk4,app(sk3,sk4))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_283]) ).

tcf(c_7810,plain,
    ( ( app(app(sk4,sk3),app(sk4,app(sk3,sk4))) = app(sk4,app(sk3,app(sk4,app(sk3,sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_5738]) ).

tcf(c_7811,plain,
    ( ( app(app(sk3,sk3),app(sk4,app(sk3,sk4))) = app(sk3,app(sk3,app(sk4,app(sk3,sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_5737]) ).

tcf(c_7812,plain,
    ( ( app(tl(sk4),app(sk4,app(sk3,sk4))) = tl(app(sk4,app(sk4,app(sk3,sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4136]) ).

tcf(c_7813,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,sk4)),sk4)) = app(cons(X0,app(sk4,app(sk3,sk4))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4462]) ).

tcf(c_7814,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,sk4)),sk3)) = app(cons(X0,app(sk4,app(sk3,sk4))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4461]) ).

tcf(c_7815,plain,
    ( ( app(tl(sk3),app(sk4,app(sk3,sk4))) = tl(app(sk3,app(sk4,app(sk3,sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4284]) ).

tcf(c_7816,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,sk4)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4027]) ).

tcf(c_7817,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,sk4)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3885]) ).

tcf(c_7818,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk3,sk4)))) = cons(X0,app(sk4,app(sk3,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3019]) ).

tcf(c_7819,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk4))),sk4),nil) = cons(hd(app(sk4,app(sk3,sk4))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3452]) ).

tcf(c_7820,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk4))),sk3),nil) = cons(hd(app(sk4,app(sk3,sk4))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3444]) ).

tcf(c_7821,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(tl(app(sk4,app(sk3,sk4))),nil) = tl(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3065]) ).

tcf(c_7822,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),sk4)) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3215]) ).

tcf(c_7823,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),sk3)) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3207]) ).

tcf(c_7824,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk3,sk4))) = cons(X0,app(sk4,app(sk3,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_253]) ).

tcf(c_7825,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( cons(hd(app(sk4,app(sk3,sk4))),tl(app(sk4,app(sk3,sk4)))) = app(sk4,app(sk3,sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_275]) ).

tcf(c_7826,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk3,sk4))),nil) = cons(X0,app(sk4,app(sk3,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3018]) ).

tcf(c_7827,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk4))),sk4)) = sk4 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3191]) ).

tcf(c_7828,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk4))),sk3)) = sk3 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3183]) ).

tcf(c_7829,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,sk4)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_284]) ).

tcf(c_7830,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk3,sk4)))) = app(sk4,app(sk3,sk4)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_276]) ).

tcf(c_7831,plain,
    ( ( app(app(sk4,app(sk3,sk4)),nil) = app(sk4,app(sk3,sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_258]) ).

tcf(c_7832,plain,
    ( ( app(nil,app(sk4,app(sk3,sk4))) = app(sk4,app(sk3,sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_257]) ).

tcf(c_7963,plain,
    ( ( sk3 = nil )
    | ( app(cons(hd(sk3),nil),sk3) = cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_6922]) ).

tcf(c_7970,plain,
    app(cons(hd(sk3),nil),sk3) = cons(hd(sk3),sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_7963,c_7100]) ).

tcf(c_7999,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),sk4))))
      | ( cons(hd(sk4),cons(hd(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),sk4)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_5647,c_280]) ).

tcf(c_8000,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),sk4))))
      | ( cons(hd(sk4),cons(hd(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk4),sk4)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_5647,c_279]) ).

tcf(c_8019,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk4),sk3))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_4376]) ).

tcf(c_8020,plain,
    hd(cons(hd(sk4),cons(hd(sk4),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_4376]) ).

tcf(c_8047,plain,
    ! [X0: $i] :
      ( ( app(app(sk3,sk4),X0) = app(sk3,app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_4540]) ).

tcf(c_8048,plain,
    ! [X0: $i] :
      ( ( app(app(sk4,sk4),X0) = app(sk4,app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_4540]) ).

tcf(c_8049,plain,
    ! [X0: $i] :
      ( ( app(app(nil,sk4),X0) = app(nil,app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_4540]) ).

tcf(c_8050,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( app(app(tl(X0),sk4),X1) = app(tl(X0),app(sk4,X1)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4540]) ).

tcf(c_8051,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(app(app(X1,X0),sk4),X2) = app(app(X1,X0),app(sk4,X2)) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4540]) ).

tcf(c_8052,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(app(cons(X2,X0),sk4),X1) = app(cons(X2,X0),app(sk4,X1)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4540]) ).

tcf(c_8053,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),sk3),sk4),X0) = app(cons(hd(sk4),sk3),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_4540]) ).

tcf(c_8054,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),sk4),sk4),X0) = app(cons(hd(sk4),sk4),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_4540]) ).

tcf(c_8055,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk3,sk3)),sk4),X0) = app(cons(hd(sk4),app(sk3,sk3)),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_4540]) ).

tcf(c_8056,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,sk3)),sk4),X0) = app(app(sk3,app(sk3,sk3)),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4540]) ).

tcf(c_8057,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,sk4)),sk4),X0) = app(app(sk3,app(sk3,sk4)),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4540]) ).

tcf(c_8058,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,sk3)),sk4),X0) = app(app(sk4,app(sk3,sk3)),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4540]) ).

tcf(c_8059,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk4,sk3)),sk4),X0) = app(cons(hd(sk4),app(sk4,sk3)),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_4540]) ).

tcf(c_8060,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,sk4)),sk4),X0) = app(app(sk4,app(sk3,sk4)),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4540]) ).

tcf(c_8061,plain,
    ! [X0: $i] :
      ( ( app(nil,app(sk4,X0)) = app(sk4,X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_8049,c_3003]) ).

tcf(c_8068,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),app(sk4,sk4)),X0) = app(cons(hd(sk4),sk4),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_8054,c_5719]) ).

tcf(c_8071,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),app(sk3,sk4)),X0) = app(cons(hd(sk4),sk3),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_8053,c_5702]) ).

tcf(c_8158,plain,
    app(app(sk3,sk4),sk3) = app(sk3,app(sk4,sk3)),
    inference(superposition,[status(thm)],[c_246,c_8047]) ).

tcf(c_8159,plain,
    app(app(sk3,sk4),sk4) = app(sk3,app(sk4,sk4)),
    inference(superposition,[status(thm)],[c_247,c_8047]) ).

tcf(c_8160,plain,
    app(app(sk3,sk4),nil) = app(sk3,app(sk4,nil)),
    inference(superposition,[status(thm)],[c_259,c_8047]) ).

tcf(c_8161,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(app(sk3,sk4),tl(X0)) = app(sk3,app(sk4,tl(X0))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_8047]) ).

tcf(c_8162,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk3,sk4),app(X1,X0)) = app(sk3,app(sk4,app(X1,X0))) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_8047]) ).

tcf(c_8163,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk3,sk4),cons(X1,X0)) = app(sk3,app(sk4,cons(X1,X0))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_8047]) ).

tcf(c_8164,plain,
    app(app(sk3,sk4),cons(hd(sk4),sk3)) = app(sk3,app(sk4,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_4358,c_8047]) ).

tcf(c_8165,plain,
    app(app(sk3,sk4),cons(hd(sk4),sk4)) = app(sk3,app(sk4,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_4223,c_8047]) ).

tcf(c_8166,plain,
    app(app(sk3,sk4),cons(hd(sk4),app(sk3,sk3))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_5886,c_8047]) ).

tcf(c_8167,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk3,sk3))) = app(sk3,app(sk4,app(sk3,app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_8047]) ).

tcf(c_8168,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk3,sk4))) = app(sk3,app(sk4,app(sk3,app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_8047]) ).

tcf(c_8169,plain,
    ( ( app(app(sk3,sk4),app(sk4,app(sk3,sk3))) = app(sk3,app(sk4,app(sk4,app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_8047]) ).

tcf(c_8170,plain,
    app(app(sk3,sk4),cons(hd(sk4),app(sk4,sk3))) = app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_7540,c_8047]) ).

tcf(c_8171,plain,
    ( ( app(app(sk3,sk4),app(sk4,app(sk3,sk4))) = app(sk3,app(sk4,app(sk4,app(sk3,sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_8047]) ).

tcf(c_8172,plain,
    app(app(sk3,sk4),nil) = app(sk3,sk4),
    inference(light_normalisation,[status(thm)],[c_8160,c_3010]) ).

tcf(c_8246,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(sk3)
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_8158,c_255]) ).

tcf(c_8247,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_8158,c_254]) ).

tcf(c_8248,plain,
    ( ssList(app(sk3,app(sk4,sk3)))
    | ~ ssList(sk3)
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8158,c_272]) ).

tcf(c_8249,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(app(sk3,sk4),X0) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_8158,c_270]) ).

tcf(c_8250,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,sk3)) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_8158,c_269]) ).

tcf(c_8251,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_8158,c_4683]) ).

tcf(c_8252,plain,
    ( ssList(app(sk3,app(sk4,sk3)))
    | ~ ssList(app(sk3,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8248,c_246]) ).

tcf(c_8258,plain,
    ( ( sk3 = nil )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8247,c_246]) ).

tcf(c_8262,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8246,c_246]) ).

tcf(c_8266,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,sk3)) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8250,c_246]) ).

tcf(c_8271,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(app(sk3,sk4),X0) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8249,c_246]) ).

tcf(c_8290,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,sk3)),sk4),X0) = app(app(sk3,app(sk4,sk3)),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4540]) ).

tcf(c_8291,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,sk3)),sk3),X0) = app(app(sk3,app(sk4,sk3)),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4539]) ).

tcf(c_8292,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk4,sk3))),X0) = app(X1,app(app(sk3,app(sk4,sk3)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_271]) ).

tcf(c_8293,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk4,sk3)))) = app(cons(X1,X0),app(sk3,app(sk4,sk3))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_266]) ).

tcf(c_8294,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,sk3)) = nil )
      | ( app(tl(app(sk3,app(sk4,sk3))),X0) = tl(app(app(sk3,app(sk4,sk3)),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_274]) ).

tcf(c_8295,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,sk3)) = nil )
      | ( hd(app(app(sk3,app(sk4,sk3)),X0)) = hd(app(sk3,app(sk4,sk3))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_283]) ).

tcf(c_8296,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk4,sk3))) = app(sk3,app(sk4,app(sk3,app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_8047]) ).

tcf(c_8297,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk4,sk3))) = app(sk4,app(sk3,app(sk3,app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_5738]) ).

tcf(c_8298,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk4,sk3))) = app(sk3,app(sk3,app(sk3,app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_5737]) ).

tcf(c_8299,plain,
    ( ( app(tl(sk4),app(sk3,app(sk4,sk3))) = tl(app(sk4,app(sk3,app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4136]) ).

tcf(c_8300,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,sk3)),sk4)) = app(cons(X0,app(sk3,app(sk4,sk3))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4462]) ).

tcf(c_8301,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,sk3)),sk3)) = app(cons(X0,app(sk3,app(sk4,sk3))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4461]) ).

tcf(c_8302,plain,
    ( ( app(tl(sk3),app(sk3,app(sk4,sk3))) = tl(app(sk3,app(sk3,app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4284]) ).

tcf(c_8303,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4027]) ).

tcf(c_8304,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3885]) ).

tcf(c_8305,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk4,sk3)))) = cons(X0,app(sk3,app(sk4,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3019]) ).

tcf(c_8306,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk3))),sk4),nil) = cons(hd(app(sk3,app(sk4,sk3))),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3452]) ).

tcf(c_8307,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk3))),sk3),nil) = cons(hd(app(sk3,app(sk4,sk3))),sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3444]) ).

tcf(c_8308,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(tl(app(sk3,app(sk4,sk3))),nil) = tl(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3065]) ).

tcf(c_8309,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),sk4)) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3215]) ).

tcf(c_8310,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),sk3)) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3207]) ).

tcf(c_8311,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk4,sk3))) = cons(X0,app(sk3,app(sk4,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_253]) ).

tcf(c_8312,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( cons(hd(app(sk3,app(sk4,sk3))),tl(app(sk3,app(sk4,sk3)))) = app(sk3,app(sk4,sk3)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_275]) ).

tcf(c_8313,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk4,sk3))),nil) = cons(X0,app(sk3,app(sk4,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3018]) ).

tcf(c_8314,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk3))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3191]) ).

tcf(c_8315,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk3))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3183]) ).

tcf(c_8316,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_284]) ).

tcf(c_8317,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk4,sk3)))) = app(sk3,app(sk4,sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_276]) ).

tcf(c_8318,plain,
    ( ( app(app(sk3,app(sk4,sk3)),nil) = app(sk3,app(sk4,sk3)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_258]) ).

tcf(c_8319,plain,
    ( ( app(nil,app(sk3,app(sk4,sk3))) = app(sk3,app(sk4,sk3)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_257]) ).

tcf(c_8533,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_8159,c_254]) ).

tcf(c_8534,plain,
    ( ssList(app(sk3,app(sk4,sk4)))
    | ~ ssList(sk4)
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8159,c_272]) ).

tcf(c_8535,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(app(sk3,sk4),X0) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_8159,c_270]) ).

tcf(c_8536,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,sk4)) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_8159,c_269]) ).

tcf(c_8537,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_8159,c_4679]) ).

tcf(c_8538,plain,
    ( ssList(app(sk3,app(sk4,sk4)))
    | ~ ssList(app(sk3,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8534,c_247]) ).

tcf(c_8544,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk4)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8533,c_1243,c_247]) ).

tcf(c_8547,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,sk4)) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8536,c_247]) ).

tcf(c_8552,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(app(sk3,sk4),X0) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8535,c_247]) ).

tcf(c_8580,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,sk4)),sk4),X0) = app(app(sk3,app(sk4,sk4)),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4540]) ).

tcf(c_8581,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,sk4)),sk3),X0) = app(app(sk3,app(sk4,sk4)),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4539]) ).

tcf(c_8582,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk4,sk4))),X0) = app(X1,app(app(sk3,app(sk4,sk4)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_271]) ).

tcf(c_8583,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk4,sk4)))) = app(cons(X1,X0),app(sk3,app(sk4,sk4))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_266]) ).

tcf(c_8584,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,sk4)) = nil )
      | ( app(tl(app(sk3,app(sk4,sk4))),X0) = tl(app(app(sk3,app(sk4,sk4)),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_274]) ).

tcf(c_8585,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,sk4)) = nil )
      | ( hd(app(app(sk3,app(sk4,sk4)),X0)) = hd(app(sk3,app(sk4,sk4))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_283]) ).

tcf(c_8586,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk4,sk4))) = app(sk3,app(sk4,app(sk3,app(sk4,sk4)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_8047]) ).

tcf(c_8587,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk4,sk4))) = app(sk4,app(sk3,app(sk3,app(sk4,sk4)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_5738]) ).

tcf(c_8588,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk4,sk4))) = app(sk3,app(sk3,app(sk3,app(sk4,sk4)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_5737]) ).

tcf(c_8589,plain,
    ( ( app(tl(sk4),app(sk3,app(sk4,sk4))) = tl(app(sk4,app(sk3,app(sk4,sk4)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4136]) ).

tcf(c_8590,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,sk4)),sk4)) = app(cons(X0,app(sk3,app(sk4,sk4))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4462]) ).

tcf(c_8591,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,sk4)),sk3)) = app(cons(X0,app(sk3,app(sk4,sk4))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4461]) ).

tcf(c_8592,plain,
    ( ( app(tl(sk3),app(sk3,app(sk4,sk4))) = tl(app(sk3,app(sk3,app(sk4,sk4)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4284]) ).

tcf(c_8593,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4027]) ).

tcf(c_8594,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3885]) ).

tcf(c_8595,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk4,sk4)))) = cons(X0,app(sk3,app(sk4,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3019]) ).

tcf(c_8596,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk4))),sk4),nil) = cons(hd(app(sk3,app(sk4,sk4))),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3452]) ).

tcf(c_8597,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk4))),sk3),nil) = cons(hd(app(sk3,app(sk4,sk4))),sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3444]) ).

tcf(c_8598,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(tl(app(sk3,app(sk4,sk4))),nil) = tl(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3065]) ).

tcf(c_8599,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),sk4)) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3215]) ).

tcf(c_8600,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),sk3)) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3207]) ).

tcf(c_8601,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk4,sk4))) = cons(X0,app(sk3,app(sk4,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_253]) ).

tcf(c_8602,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( cons(hd(app(sk3,app(sk4,sk4))),tl(app(sk3,app(sk4,sk4)))) = app(sk3,app(sk4,sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_275]) ).

tcf(c_8603,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk4,sk4))),nil) = cons(X0,app(sk3,app(sk4,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3018]) ).

tcf(c_8604,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk4))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3191]) ).

tcf(c_8605,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk4))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3183]) ).

tcf(c_8606,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,sk4)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_284]) ).

tcf(c_8607,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk4,sk4)))) = app(sk3,app(sk4,sk4)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_276]) ).

tcf(c_8608,plain,
    ( ( app(app(sk3,app(sk4,sk4)),nil) = app(sk3,app(sk4,sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_258]) ).

tcf(c_8609,plain,
    ( ( app(nil,app(sk3,app(sk4,sk4))) = app(sk3,app(sk4,sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_257]) ).

tcf(c_8805,plain,
    ( ssList(app(tl(sk4),cons(hd(sk4),sk3)))
    | ( app(sk4,cons(hd(sk4),sk3)) = nil )
    | ~ ssList(app(sk4,cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_5595,c_278]) ).

tcf(c_8806,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),sk3)) = nil )
      | ( app(sk4,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( hd(app(sk4,cons(hd(sk4),sk3))) != hd(X0) )
      | ( app(tl(sk4),cons(hd(sk4),sk3)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_5595,c_273]) ).

tcf(c_8810,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),sk3)) = nil )
      | ( app(sk4,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),cons(hd(sk4),sk3)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_8806,c_4364]) ).

tcf(c_8825,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(app(sk3,sk4),X0) != app(sk3,sk4) ) ),
    inference(superposition,[status(thm)],[c_8172,c_270]) ).

tcf(c_8826,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(X0,nil) != app(sk3,sk4) ) ),
    inference(superposition,[status(thm)],[c_8172,c_269]) ).

tcf(c_8827,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(X0,nil) != app(sk3,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8826,c_259]) ).

tcf(c_8832,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(app(sk3,sk4),X0) != app(sk3,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8825,c_259]) ).

tcf(c_8846,plain,
    app(nil,app(sk3,sk3)) = app(sk3,sk3),
    inference(superposition,[status(thm)],[c_246,c_5745]) ).

tcf(c_8847,plain,
    app(nil,app(sk3,sk4)) = app(sk3,sk4),
    inference(superposition,[status(thm)],[c_247,c_5745]) ).

tcf(c_8848,plain,
    app(nil,app(sk3,nil)) = app(sk3,nil),
    inference(superposition,[status(thm)],[c_259,c_5745]) ).

tcf(c_8849,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(nil,app(sk3,tl(X0))) = app(sk3,tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_5745]) ).

tcf(c_8850,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(nil,app(sk3,app(X1,X0))) = app(sk3,app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_5745]) ).

tcf(c_8851,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(nil,app(sk3,cons(X1,X0))) = app(sk3,cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_5745]) ).

tcf(c_8852,plain,
    app(nil,app(sk3,cons(hd(sk4),sk3))) = app(sk3,cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4358,c_5745]) ).

tcf(c_8853,plain,
    app(nil,app(sk3,cons(hd(sk4),sk4))) = app(sk3,cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4223,c_5745]) ).

tcf(c_8854,plain,
    app(nil,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = app(sk3,cons(hd(sk4),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_5886,c_5745]) ).

tcf(c_8855,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk3,sk3)))) = app(sk3,app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_5745]) ).

tcf(c_8856,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk3,sk4)))) = app(sk3,app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_5745]) ).

tcf(c_8857,plain,
    ( ( app(nil,app(sk3,app(sk4,app(sk3,sk3)))) = app(sk3,app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_5745]) ).

tcf(c_8858,plain,
    app(nil,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = app(sk3,cons(hd(sk4),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_7540,c_5745]) ).

tcf(c_8859,plain,
    ( ( app(nil,app(sk3,app(sk4,app(sk3,sk4)))) = app(sk3,app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_5745]) ).

tcf(c_8860,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk4,sk3)))) = app(sk3,app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_5745]) ).

tcf(c_8861,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk4,sk4)))) = app(sk3,app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_5745]) ).

tcf(c_9012,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(nil,X0) != app(sk3,sk3) ) ),
    inference(superposition,[status(thm)],[c_8846,c_270]) ).

tcf(c_9013,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(X0,app(sk3,sk3)) != app(sk3,sk3) ) ),
    inference(superposition,[status(thm)],[c_8846,c_269]) ).

tcf(c_9014,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(X0,app(sk3,sk3)) != app(sk3,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9013,c_259]) ).

tcf(c_9019,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(nil,X0) != app(sk3,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9012,c_259]) ).

tcf(c_9031,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(nil,X0) != app(sk3,sk4) ) ),
    inference(superposition,[status(thm)],[c_8847,c_270]) ).

tcf(c_9032,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(X0,app(sk3,sk4)) != app(sk3,sk4) ) ),
    inference(superposition,[status(thm)],[c_8847,c_269]) ).

tcf(c_9033,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(X0,app(sk3,sk4)) != app(sk3,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9032,c_259]) ).

tcf(c_9038,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(nil,X0) != app(sk3,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9031,c_259]) ).

tcf(c_9044,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),sk3))))
      | ( cons(hd(sk4),cons(hd(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),sk3)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_8020,c_280]) ).

tcf(c_9045,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),sk3))))
      | ( cons(hd(sk4),cons(hd(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk4),sk3)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_8020,c_279]) ).

tcf(c_9060,plain,
    ( ssItem(hd(sk3))
    | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_6392,c_286]) ).

tcf(c_9061,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
      | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_6392,c_280]) ).

tcf(c_9062,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
      | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_6392,c_279]) ).

tcf(c_9095,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
      | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_6393,c_280]) ).

tcf(c_9096,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
      | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_6393,c_279]) ).

tcf(c_9136,plain,
    ( ssItem(hd(sk3))
    | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_7590,c_286]) ).

tcf(c_9137,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
      | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_7590,c_280]) ).

tcf(c_9138,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
      | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_7590,c_279]) ).

tcf(c_9160,plain,
    app(app(sk4,sk4),sk3) = app(sk4,app(sk4,sk3)),
    inference(superposition,[status(thm)],[c_246,c_8048]) ).

tcf(c_9161,plain,
    app(app(sk4,sk4),sk4) = app(sk4,app(sk4,sk4)),
    inference(superposition,[status(thm)],[c_247,c_8048]) ).

tcf(c_9162,plain,
    app(app(sk4,sk4),nil) = app(sk4,app(sk4,nil)),
    inference(superposition,[status(thm)],[c_259,c_8048]) ).

tcf(c_9163,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(app(sk4,sk4),tl(X0)) = app(sk4,app(sk4,tl(X0))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_8048]) ).

tcf(c_9164,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk4,sk4),app(X1,X0)) = app(sk4,app(sk4,app(X1,X0))) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_8048]) ).

tcf(c_9165,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk4,sk4),cons(X1,X0)) = app(sk4,app(sk4,cons(X1,X0))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_8048]) ).

tcf(c_9166,plain,
    app(app(sk4,sk4),cons(hd(sk4),sk3)) = app(sk4,app(sk4,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_4358,c_8048]) ).

tcf(c_9167,plain,
    app(app(sk4,sk4),cons(hd(sk4),sk4)) = app(sk4,app(sk4,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_4223,c_8048]) ).

tcf(c_9168,plain,
    app(app(sk4,sk4),cons(hd(sk4),app(sk3,sk3))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_5886,c_8048]) ).

tcf(c_9169,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk3,sk3))) = app(sk4,app(sk4,app(sk3,app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_8048]) ).

tcf(c_9170,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk3,sk4))) = app(sk4,app(sk4,app(sk3,app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_8048]) ).

tcf(c_9171,plain,
    ( ( app(app(sk4,sk4),app(sk4,app(sk3,sk3))) = app(sk4,app(sk4,app(sk4,app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_8048]) ).

tcf(c_9172,plain,
    app(app(sk4,sk4),cons(hd(sk4),app(sk4,sk3))) = app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_7540,c_8048]) ).

tcf(c_9173,plain,
    ( ( app(app(sk4,sk4),app(sk4,app(sk3,sk4))) = app(sk4,app(sk4,app(sk4,app(sk3,sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_8048]) ).

tcf(c_9174,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk4,sk3))) = app(sk4,app(sk4,app(sk3,app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_8048]) ).

tcf(c_9175,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk4,sk4))) = app(sk4,app(sk4,app(sk3,app(sk4,sk4)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_8048]) ).

tcf(c_9176,plain,
    app(app(sk4,sk4),nil) = app(sk4,sk4),
    inference(light_normalisation,[status(thm)],[c_9162,c_3010]) ).

tcf(c_9213,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != nil ) ),
    inference(superposition,[status(thm)],[c_7970,c_254]) ).

tcf(c_9214,plain,
    ( ssList(cons(hd(sk3),sk3))
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(superposition,[status(thm)],[c_7970,c_272]) ).

tcf(c_9215,plain,
    ( ssList(cons(hd(sk3),sk3))
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9214,c_246]) ).

tcf(c_9218,plain,
    ( ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9213,c_7100,c_246]) ).

tcf(c_9223,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(sk3)
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_9160,c_255]) ).

tcf(c_9224,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_9160,c_254]) ).

tcf(c_9225,plain,
    ( ssList(app(sk4,app(sk4,sk3)))
    | ~ ssList(sk3)
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9160,c_272]) ).

tcf(c_9226,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(app(sk4,sk4),X0) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_9160,c_270]) ).

tcf(c_9227,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,sk3)) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_9160,c_269]) ).

tcf(c_9228,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_9160,c_4683]) ).

tcf(c_9229,plain,
    ( ssList(app(sk4,app(sk4,sk3)))
    | ~ ssList(app(sk4,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9225,c_246]) ).

tcf(c_9235,plain,
    ( ( sk3 = nil )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9224,c_246]) ).

tcf(c_9239,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9223,c_246]) ).

tcf(c_9243,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,sk3)) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9227,c_246]) ).

tcf(c_9248,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(app(sk4,sk4),X0) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9226,c_246]) ).

tcf(c_9259,plain,
    ( ssList(cons(hd(sk3),sk3))
    | ~ ssList(nil)
    | ~ ssItem(hd(sk3)) ),
    inference(superposition,[status(thm)],[c_268,c_9215]) ).

tcf(c_9260,plain,
    ( ssList(cons(hd(sk3),sk3))
    | ~ ssItem(hd(sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9259,c_259]) ).

tcf(c_9272,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,sk3)),sk4),X0) = app(app(sk4,app(sk4,sk3)),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4540]) ).

tcf(c_9273,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,sk3)),sk3),X0) = app(app(sk4,app(sk4,sk3)),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4539]) ).

tcf(c_9274,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk4,sk3))),X0) = app(X1,app(app(sk4,app(sk4,sk3)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_271]) ).

tcf(c_9275,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk4,sk3)))) = app(cons(X1,X0),app(sk4,app(sk4,sk3))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_266]) ).

tcf(c_9276,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,sk3)) = nil )
      | ( app(tl(app(sk4,app(sk4,sk3))),X0) = tl(app(app(sk4,app(sk4,sk3)),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_274]) ).

tcf(c_9277,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,sk3)) = nil )
      | ( hd(app(app(sk4,app(sk4,sk3)),X0)) = hd(app(sk4,app(sk4,sk3))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_283]) ).

tcf(c_9278,plain,
    ( ( app(app(sk4,sk4),app(sk4,app(sk4,sk3))) = app(sk4,app(sk4,app(sk4,app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_8048]) ).

tcf(c_9279,plain,
    ( ( app(nil,app(sk3,app(sk4,app(sk4,sk3)))) = app(sk3,app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_5745]) ).

tcf(c_9280,plain,
    ( ( app(app(sk3,sk4),app(sk4,app(sk4,sk3))) = app(sk3,app(sk4,app(sk4,app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_8047]) ).

tcf(c_9281,plain,
    ( ( app(app(sk4,sk3),app(sk4,app(sk4,sk3))) = app(sk4,app(sk3,app(sk4,app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_5738]) ).

tcf(c_9282,plain,
    ( ( app(app(sk3,sk3),app(sk4,app(sk4,sk3))) = app(sk3,app(sk3,app(sk4,app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_5737]) ).

tcf(c_9283,plain,
    ( ( app(tl(sk4),app(sk4,app(sk4,sk3))) = tl(app(sk4,app(sk4,app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4136]) ).

tcf(c_9284,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,sk3)),sk4)) = app(cons(X0,app(sk4,app(sk4,sk3))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4462]) ).

tcf(c_9285,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,sk3)),sk3)) = app(cons(X0,app(sk4,app(sk4,sk3))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4461]) ).

tcf(c_9286,plain,
    ( ( app(tl(sk3),app(sk4,app(sk4,sk3))) = tl(app(sk3,app(sk4,app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4284]) ).

tcf(c_9287,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4027]) ).

tcf(c_9288,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3885]) ).

tcf(c_9289,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk4,sk3)))) = cons(X0,app(sk4,app(sk4,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3019]) ).

tcf(c_9290,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk3))),sk4),nil) = cons(hd(app(sk4,app(sk4,sk3))),sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3452]) ).

tcf(c_9291,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk3))),sk3),nil) = cons(hd(app(sk4,app(sk4,sk3))),sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3444]) ).

tcf(c_9292,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(tl(app(sk4,app(sk4,sk3))),nil) = tl(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3065]) ).

tcf(c_9293,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),sk4)) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3215]) ).

tcf(c_9294,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),sk3)) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3207]) ).

tcf(c_9295,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk4,sk3))) = cons(X0,app(sk4,app(sk4,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_253]) ).

tcf(c_9296,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( cons(hd(app(sk4,app(sk4,sk3))),tl(app(sk4,app(sk4,sk3)))) = app(sk4,app(sk4,sk3)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_275]) ).

tcf(c_9297,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk4,sk3))),nil) = cons(X0,app(sk4,app(sk4,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3018]) ).

tcf(c_9298,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk3))),sk4)) = sk4 )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3191]) ).

tcf(c_9299,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk3))),sk3)) = sk3 )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3183]) ).

tcf(c_9300,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_284]) ).

tcf(c_9301,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk4,sk3)))) = app(sk4,app(sk4,sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_276]) ).

tcf(c_9302,plain,
    ( ( app(app(sk4,app(sk4,sk3)),nil) = app(sk4,app(sk4,sk3)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_258]) ).

tcf(c_9303,plain,
    ( ( app(nil,app(sk4,app(sk4,sk3))) = app(sk4,app(sk4,sk3)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_257]) ).

tcf(c_9508,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_9161,c_254]) ).

tcf(c_9509,plain,
    ( ssList(app(sk4,app(sk4,sk4)))
    | ~ ssList(sk4)
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9161,c_272]) ).

tcf(c_9510,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(app(sk4,sk4),X0) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9161,c_270]) ).

tcf(c_9511,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,sk4)) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_9161,c_269]) ).

tcf(c_9512,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_9161,c_4679]) ).

tcf(c_9513,plain,
    ( ssList(app(sk4,app(sk4,sk4)))
    | ~ ssList(app(sk4,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9509,c_247]) ).

tcf(c_9519,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk4)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9508,c_1243,c_247]) ).

tcf(c_9522,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,sk4)) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9511,c_247]) ).

tcf(c_9527,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(app(sk4,sk4),X0) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9510,c_247]) ).

tcf(c_9541,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,sk4)),sk4),X0) = app(app(sk4,app(sk4,sk4)),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4540]) ).

tcf(c_9542,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,sk4)),sk3),X0) = app(app(sk4,app(sk4,sk4)),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4539]) ).

tcf(c_9543,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk4,sk4))),X0) = app(X1,app(app(sk4,app(sk4,sk4)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_271]) ).

tcf(c_9544,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk4,sk4)))) = app(cons(X1,X0),app(sk4,app(sk4,sk4))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_266]) ).

tcf(c_9545,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,sk4)) = nil )
      | ( app(tl(app(sk4,app(sk4,sk4))),X0) = tl(app(app(sk4,app(sk4,sk4)),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_274]) ).

tcf(c_9546,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,sk4)) = nil )
      | ( hd(app(app(sk4,app(sk4,sk4)),X0)) = hd(app(sk4,app(sk4,sk4))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_283]) ).

tcf(c_9547,plain,
    ( ( app(app(sk4,sk4),app(sk4,app(sk4,sk4))) = app(sk4,app(sk4,app(sk4,app(sk4,sk4)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_8048]) ).

tcf(c_9548,plain,
    ( ( app(nil,app(sk3,app(sk4,app(sk4,sk4)))) = app(sk3,app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_5745]) ).

tcf(c_9549,plain,
    ( ( app(app(sk3,sk4),app(sk4,app(sk4,sk4))) = app(sk3,app(sk4,app(sk4,app(sk4,sk4)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_8047]) ).

tcf(c_9550,plain,
    ( ( app(app(sk4,sk3),app(sk4,app(sk4,sk4))) = app(sk4,app(sk3,app(sk4,app(sk4,sk4)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_5738]) ).

tcf(c_9551,plain,
    ( ( app(app(sk3,sk3),app(sk4,app(sk4,sk4))) = app(sk3,app(sk3,app(sk4,app(sk4,sk4)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_5737]) ).

tcf(c_9552,plain,
    ( ( app(tl(sk4),app(sk4,app(sk4,sk4))) = tl(app(sk4,app(sk4,app(sk4,sk4)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4136]) ).

tcf(c_9553,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,sk4)),sk4)) = app(cons(X0,app(sk4,app(sk4,sk4))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4462]) ).

tcf(c_9554,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,sk4)),sk3)) = app(cons(X0,app(sk4,app(sk4,sk4))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4461]) ).

tcf(c_9555,plain,
    ( ( app(tl(sk3),app(sk4,app(sk4,sk4))) = tl(app(sk3,app(sk4,app(sk4,sk4)))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4284]) ).

tcf(c_9556,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,sk4)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4027]) ).

tcf(c_9557,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,sk4)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3885]) ).

tcf(c_9558,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk4,sk4)))) = cons(X0,app(sk4,app(sk4,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3019]) ).

tcf(c_9559,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk4))),sk4),nil) = cons(hd(app(sk4,app(sk4,sk4))),sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3452]) ).

tcf(c_9560,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk4))),sk3),nil) = cons(hd(app(sk4,app(sk4,sk4))),sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3444]) ).

tcf(c_9561,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(tl(app(sk4,app(sk4,sk4))),nil) = tl(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3065]) ).

tcf(c_9562,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),sk4)) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3215]) ).

tcf(c_9563,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),sk3)) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3207]) ).

tcf(c_9564,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk4,sk4))) = cons(X0,app(sk4,app(sk4,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_253]) ).

tcf(c_9565,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( cons(hd(app(sk4,app(sk4,sk4))),tl(app(sk4,app(sk4,sk4)))) = app(sk4,app(sk4,sk4)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_275]) ).

tcf(c_9566,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk4,sk4))),nil) = cons(X0,app(sk4,app(sk4,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3018]) ).

tcf(c_9567,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk4))),sk4)) = sk4 )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3191]) ).

tcf(c_9568,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk4))),sk3)) = sk3 )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3183]) ).

tcf(c_9569,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,sk4)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_284]) ).

tcf(c_9570,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk4,sk4)))) = app(sk4,app(sk4,sk4)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_276]) ).

tcf(c_9571,plain,
    ( ( app(app(sk4,app(sk4,sk4)),nil) = app(sk4,app(sk4,sk4)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_258]) ).

tcf(c_9572,plain,
    ( ( app(nil,app(sk4,app(sk4,sk4))) = app(sk4,app(sk4,sk4)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_257]) ).

tcf(c_9820,plain,
    ( ( app(sk3,app(sk3,sk3)) != nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(global_subsumption_just,[status(thm)],[c_6592,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_6592]) ).

tcf(c_9821,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != nil ) ),
    inference(renaming,[status(thm)],[c_9820]) ).

tcf(c_9826,plain,
    ( ( app(sk4,app(sk3,sk3)) != nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(global_subsumption_just,[status(thm)],[c_7249,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7249]) ).

tcf(c_9827,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != nil ) ),
    inference(renaming,[status(thm)],[c_9826]) ).

tcf(c_9833,plain,
    ( ssList(app(tl(sk4),cons(hd(sk4),sk4)))
    | ( app(sk4,cons(hd(sk4),sk4)) = nil )
    | ~ ssList(app(sk4,cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_5596,c_278]) ).

tcf(c_9834,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),sk4)) = nil )
      | ( app(sk4,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( hd(app(sk4,cons(hd(sk4),sk4))) != hd(X0) )
      | ( app(tl(sk4),cons(hd(sk4),sk4)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_5596,c_273]) ).

tcf(c_9838,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),sk4)) = nil )
      | ( app(sk4,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),cons(hd(sk4),sk4)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_9834,c_4228]) ).

tcf(c_9853,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(app(sk4,sk4),X0) != app(sk4,sk4) ) ),
    inference(superposition,[status(thm)],[c_9176,c_270]) ).

tcf(c_9854,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(X0,nil) != app(sk4,sk4) ) ),
    inference(superposition,[status(thm)],[c_9176,c_269]) ).

tcf(c_9855,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(X0,nil) != app(sk4,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9854,c_259]) ).

tcf(c_9860,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(app(sk4,sk4),X0) != app(sk4,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9853,c_259]) ).

tcf(c_9870,plain,
    app(nil,app(sk4,sk3)) = app(sk4,sk3),
    inference(superposition,[status(thm)],[c_246,c_8061]) ).

tcf(c_9871,plain,
    app(nil,app(sk4,sk4)) = app(sk4,sk4),
    inference(superposition,[status(thm)],[c_247,c_8061]) ).

tcf(c_9872,plain,
    app(nil,app(sk4,nil)) = app(sk4,nil),
    inference(superposition,[status(thm)],[c_259,c_8061]) ).

tcf(c_9873,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(nil,app(sk4,tl(X0))) = app(sk4,tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_8061]) ).

tcf(c_9874,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(nil,app(sk4,app(X1,X0))) = app(sk4,app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_8061]) ).

tcf(c_9875,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(nil,app(sk4,cons(X1,X0))) = app(sk4,cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_8061]) ).

tcf(c_9876,plain,
    app(nil,app(sk4,cons(hd(sk4),sk3))) = app(sk4,cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4358,c_8061]) ).

tcf(c_9877,plain,
    app(nil,app(sk4,cons(hd(sk4),sk4))) = app(sk4,cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4223,c_8061]) ).

tcf(c_9878,plain,
    app(nil,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = app(sk4,cons(hd(sk4),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_5886,c_8061]) ).

tcf(c_9879,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk3,sk3)))) = app(sk4,app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_8061]) ).

tcf(c_9880,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk3,sk4)))) = app(sk4,app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_8061]) ).

tcf(c_9881,plain,
    ( ( app(nil,app(sk4,app(sk4,app(sk3,sk3)))) = app(sk4,app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_8061]) ).

tcf(c_9882,plain,
    app(nil,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = app(sk4,cons(hd(sk4),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_7540,c_8061]) ).

tcf(c_9883,plain,
    ( ( app(nil,app(sk4,app(sk4,app(sk3,sk4)))) = app(sk4,app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_8061]) ).

tcf(c_9884,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk4,sk3)))) = app(sk4,app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_8061]) ).

tcf(c_9885,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk4,sk4)))) = app(sk4,app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_8061]) ).

tcf(c_9886,plain,
    ( ( app(nil,app(sk4,app(sk4,app(sk4,sk3)))) = app(sk4,app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_8061]) ).

tcf(c_9887,plain,
    ( ( app(nil,app(sk4,app(sk4,app(sk4,sk4)))) = app(sk4,app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_8061]) ).

tcf(c_9968,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(nil,X0) != app(sk4,sk3) ) ),
    inference(superposition,[status(thm)],[c_9870,c_270]) ).

tcf(c_9969,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(X0,app(sk4,sk3)) != app(sk4,sk3) ) ),
    inference(superposition,[status(thm)],[c_9870,c_269]) ).

tcf(c_9970,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(X0,app(sk4,sk3)) != app(sk4,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9969,c_259]) ).

tcf(c_9975,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(nil,X0) != app(sk4,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9968,c_259]) ).

tcf(c_10086,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(nil,X0) != app(sk4,sk4) ) ),
    inference(superposition,[status(thm)],[c_9871,c_270]) ).

tcf(c_10087,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(X0,app(sk4,sk4)) != app(sk4,sk4) ) ),
    inference(superposition,[status(thm)],[c_9871,c_269]) ).

tcf(c_10088,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(X0,app(sk4,sk4)) != app(sk4,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10087,c_259]) ).

tcf(c_10093,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(nil,X0) != app(sk4,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10086,c_259]) ).

tcf(c_10099,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
      | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_7591,c_280]) ).

tcf(c_10100,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
      | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_7591,c_279]) ).

tcf(c_10117,plain,
    ssItem(hd(sk3)),
    inference(global_subsumption_just,[status(thm)],[c_4051,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7561]) ).

tcf(c_10119,plain,
    ( ~ ssList(tl(sk3))
    | ( tl(sk3) != sk3 ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_3733,c_10117]) ).

tcf(c_10122,plain,
    hd(cons(hd(sk3),cons(hd(sk4),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_4376]) ).

tcf(c_10123,plain,
    cons(hd(sk3),app(sk4,sk4)) = app(cons(hd(sk3),sk4),sk4),
    inference(superposition,[status(thm)],[c_10117,c_5010]) ).

tcf(c_10124,plain,
    cons(hd(sk3),app(sk3,sk4)) = app(cons(hd(sk3),sk3),sk4),
    inference(superposition,[status(thm)],[c_10117,c_5009]) ).

tcf(c_10125,plain,
    hd(cons(hd(sk3),cons(hd(sk4),sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_4240]) ).

tcf(c_10126,plain,
    cons(hd(sk3),app(sk4,sk3)) = app(cons(hd(sk3),sk4),sk3),
    inference(superposition,[status(thm)],[c_10117,c_4929]) ).

tcf(c_10127,plain,
    cons(hd(sk3),app(sk3,sk3)) = app(cons(hd(sk3),sk3),sk3),
    inference(superposition,[status(thm)],[c_10117,c_4928]) ).

tcf(c_10128,plain,
    app(nil,cons(hd(sk3),nil)) = cons(hd(sk3),nil),
    inference(superposition,[status(thm)],[c_10117,c_3820]) ).

tcf(c_10129,plain,
    app(nil,cons(hd(sk3),sk4)) = cons(hd(sk3),sk4),
    inference(superposition,[status(thm)],[c_10117,c_3819]) ).

tcf(c_10130,plain,
    app(nil,cons(hd(sk3),sk3)) = cons(hd(sk3),sk3),
    inference(superposition,[status(thm)],[c_10117,c_3818]) ).

tcf(c_10131,plain,
    app(cons(hd(sk3),nil),nil) = cons(hd(sk3),nil),
    inference(superposition,[status(thm)],[c_10117,c_3310]) ).

tcf(c_10132,plain,
    app(cons(hd(sk3),nil),sk4) = cons(hd(sk3),sk4),
    inference(superposition,[status(thm)],[c_10117,c_3388]) ).

tcf(c_10133,plain,
    app(cons(hd(sk3),nil),sk3) = cons(hd(sk3),sk3),
    inference(superposition,[status(thm)],[c_10117,c_3387]) ).

tcf(c_10136,plain,
    hd(cons(hd(sk3),nil)) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_3152]) ).

tcf(c_10137,plain,
    hd(cons(hd(sk3),sk4)) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_3151]) ).

tcf(c_10138,plain,
    hd(cons(hd(sk3),sk3)) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_3150]) ).

tcf(c_10139,plain,
    tl(cons(hd(sk3),nil)) = nil,
    inference(superposition,[status(thm)],[c_10117,c_3117]) ).

tcf(c_10140,plain,
    tl(cons(hd(sk3),sk4)) = sk4,
    inference(superposition,[status(thm)],[c_10117,c_3116]) ).

tcf(c_10141,plain,
    tl(cons(hd(sk3),sk3)) = sk3,
    inference(superposition,[status(thm)],[c_10117,c_3115]) ).

tcf(c_10144,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),nil) = nil )
      | ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(sk3),nil)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_10139,c_273]) ).

tcf(c_10145,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),nil) = nil )
      | ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( hd(X0) != hd(sk3) )
      | ( tl(X0) != nil ) ),
    inference(light_normalisation,[status(thm)],[c_10144,c_10136]) ).

tcf(c_10153,plain,
    ( ( app(sk3,app(sk4,sk3)) != nil )
    | ~ ssList(app(sk3,sk4)) ),
    inference(global_subsumption_just,[status(thm)],[c_8258,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_8258]) ).

tcf(c_10154,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != nil ) ),
    inference(renaming,[status(thm)],[c_10153]) ).

tcf(c_10159,plain,
    ( ( app(sk4,app(sk4,sk3)) != nil )
    | ~ ssList(app(sk4,sk4)) ),
    inference(global_subsumption_just,[status(thm)],[c_9235,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_9235]) ).

tcf(c_10160,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != nil ) ),
    inference(renaming,[status(thm)],[c_10159]) ).

tcf(c_10171,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_5892]) ).

tcf(c_10173,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4999,c_5892]) ).

tcf(c_10177,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),sk4) )
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10173,c_4223]) ).

tcf(c_10183,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_5702,c_254]) ).

tcf(c_10184,plain,
    ( ssList(cons(hd(sk4),app(sk3,sk4)))
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_5702,c_272]) ).

tcf(c_10185,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(cons(hd(sk4),sk3),X0) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5702,c_270]) ).

tcf(c_10186,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk3))
      | ( cons(hd(sk4),app(sk3,sk4)) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_5702,c_269]) ).

tcf(c_10187,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_5702,c_4679]) ).

tcf(c_10188,plain,
    ssList(cons(hd(sk4),app(sk3,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_10184,c_247,c_4358]) ).

tcf(c_10189,plain,
    cons(hd(sk4),app(sk3,sk4)) != sk4,
    inference(forward_subsumption_resolution,[status(thm)],[c_10187,c_4430,c_4358]) ).

tcf(c_10190,plain,
    cons(hd(sk4),app(sk3,sk4)) != nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_10183,c_1243,c_247,c_4358]) ).

tcf(c_10191,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk3,sk4)) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10186,c_247,c_4358]) ).

tcf(c_10195,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),sk3),X0) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10185,c_247,c_4358]) ).

tcf(c_10201,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk3,sk4)),sk4),X0) = app(cons(hd(sk4),app(sk3,sk4)),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_4540]) ).

tcf(c_10202,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk3,sk4)),sk3),X0) = app(cons(hd(sk4),app(sk3,sk4)),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_4539]) ).

tcf(c_10203,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk4),app(sk3,sk4))),X0) = app(X1,app(cons(hd(sk4),app(sk3,sk4)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_271]) ).

tcf(c_10204,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk4),app(sk3,sk4)))) = app(cons(X1,X0),cons(hd(sk4),app(sk3,sk4))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_266]) ).

tcf(c_10205,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
      | ( app(tl(cons(hd(sk4),app(sk3,sk4))),X0) = tl(app(cons(hd(sk4),app(sk3,sk4)),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_274]) ).

tcf(c_10206,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
      | ( hd(app(cons(hd(sk4),app(sk3,sk4)),X0)) = hd(cons(hd(sk4),app(sk3,sk4))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_283]) ).

tcf(c_10207,plain,
    app(nil,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = app(sk4,cons(hd(sk4),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_10188,c_8061]) ).

tcf(c_10208,plain,
    app(app(sk4,sk4),cons(hd(sk4),app(sk3,sk4))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_10188,c_8048]) ).

tcf(c_10209,plain,
    app(nil,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = app(sk3,cons(hd(sk4),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_10188,c_5745]) ).

tcf(c_10210,plain,
    app(app(sk3,sk4),cons(hd(sk4),app(sk3,sk4))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_10188,c_8047]) ).

tcf(c_10211,plain,
    app(app(sk4,sk3),cons(hd(sk4),app(sk3,sk4))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_10188,c_5738]) ).

tcf(c_10212,plain,
    app(app(sk3,sk3),cons(hd(sk4),app(sk3,sk4))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_10188,c_5737]) ).

tcf(c_10213,plain,
    app(tl(sk4),cons(hd(sk4),app(sk3,sk4))) = tl(app(sk4,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_10188,c_4136]) ).

tcf(c_10214,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk3,sk4)),sk4)) = app(cons(X0,cons(hd(sk4),app(sk3,sk4))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_4462]) ).

tcf(c_10215,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk3,sk4)),sk3)) = app(cons(X0,cons(hd(sk4),app(sk3,sk4))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_4461]) ).

tcf(c_10216,plain,
    app(tl(sk3),cons(hd(sk4),app(sk3,sk4))) = tl(app(sk3,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_10188,c_4284]) ).

tcf(c_10217,plain,
    hd(app(sk3,cons(hd(sk4),app(sk3,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_4027]) ).

tcf(c_10218,plain,
    hd(app(sk4,cons(hd(sk4),app(sk3,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_3885]) ).

tcf(c_10219,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk4),app(sk3,sk4)))) = cons(X0,cons(hd(sk4),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3019]) ).

tcf(c_10220,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4),nil) = cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3452]) ).

tcf(c_10221,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3),nil) = cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3444]) ).

tcf(c_10222,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(tl(cons(hd(sk4),app(sk3,sk4))),nil) = tl(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3065]) ).

tcf(c_10223,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4)) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3215]) ).

tcf(c_10224,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3)) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3207]) ).

tcf(c_10225,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk4),app(sk3,sk4))) = cons(X0,cons(hd(sk4),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_253]) ).

tcf(c_10226,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( cons(hd(cons(hd(sk4),app(sk3,sk4))),tl(cons(hd(sk4),app(sk3,sk4)))) = cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10188,c_275]) ).

tcf(c_10227,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk4),app(sk3,sk4))),nil) = cons(X0,cons(hd(sk4),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3018]) ).

tcf(c_10228,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_10188,c_3191]) ).

tcf(c_10229,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_10188,c_3183]) ).

tcf(c_10230,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk4),app(sk3,sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_284]) ).

tcf(c_10231,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk4),app(sk3,sk4)))) = cons(hd(sk4),app(sk3,sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_276]) ).

tcf(c_10232,plain,
    app(cons(hd(sk4),app(sk3,sk4)),nil) = cons(hd(sk4),app(sk3,sk4)),
    inference(superposition,[status(thm)],[c_10188,c_258]) ).

tcf(c_10233,plain,
    app(nil,cons(hd(sk4),app(sk3,sk4))) = cons(hd(sk4),app(sk3,sk4)),
    inference(superposition,[status(thm)],[c_10188,c_257]) ).

tcf(c_10347,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),sk4) = nil )
      | ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( tl(X0) != sk4 )
      | ( hd(cons(hd(sk3),sk4)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_10140,c_273]) ).

tcf(c_10348,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),sk4) = nil )
      | ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( hd(X0) != hd(sk3) )
      | ( tl(X0) != sk4 ) ),
    inference(light_normalisation,[status(thm)],[c_10347,c_10137]) ).

tcf(c_10358,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),sk3) = nil )
      | ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( tl(X0) != sk3 )
      | ( hd(cons(hd(sk3),sk3)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_10141,c_273]) ).

tcf(c_10359,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),sk3) = nil )
      | ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( hd(X0) != hd(sk3) )
      | ( tl(X0) != sk3 ) ),
    inference(light_normalisation,[status(thm)],[c_10358,c_10138]) ).

tcf(c_10368,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),nil)))
      | ( cons(hd(sk3),nil) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),nil))
      | ~ ssList(cons(hd(sk3),nil)) ),
    inference(superposition,[status(thm)],[c_10136,c_280]) ).

tcf(c_10369,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),nil)))
      | ( cons(hd(sk3),nil) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),nil))
      | ~ ssList(cons(hd(sk3),nil)) ),
    inference(superposition,[status(thm)],[c_10136,c_279]) ).

tcf(c_10385,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),sk4)))
      | ( cons(hd(sk3),sk4) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),sk4))
      | ~ ssList(cons(hd(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_10137,c_280]) ).

tcf(c_10386,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),sk4)))
      | ( cons(hd(sk3),sk4) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),sk4))
      | ~ ssList(cons(hd(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_10137,c_279]) ).

tcf(c_10407,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_3752,c_5896]) ).

tcf(c_10409,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5702,c_5896]) ).

tcf(c_10410,plain,
    ( ( sk3 = nil )
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10407,c_259]) ).

tcf(c_10413,plain,
    ( ( sk3 = sk4 )
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10409,c_247]) ).

tcf(c_10430,plain,
    ( ( cons(hd(sk4),sk4) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_7546]) ).

tcf(c_10431,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4976,c_7546]) ).

tcf(c_10443,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_3788,c_7550]) ).

tcf(c_10445,plain,
    ( ( sk3 = nil )
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10443,c_259]) ).

tcf(c_10454,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_10191]) ).

tcf(c_10469,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_3752,c_10195]) ).

tcf(c_10470,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_4976,c_10195]) ).

tcf(c_10472,plain,
    cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk4),sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_10469,c_1243,c_259]) ).

tcf(c_10482,plain,
    ( ( cons(hd(sk4),nil) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),nil))
    | ( app(sk3,app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_6600]) ).

tcf(c_10483,plain,
    ( ( cons(hd(sk4),sk3) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4976,c_6600]) ).

tcf(c_10484,plain,
    ( ( cons(hd(sk4),sk4) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4999,c_6600]) ).

tcf(c_10486,plain,
    ( ( app(sk3,sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7182,c_6600]) ).

tcf(c_10487,plain,
    ( ( app(sk3,sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_8158,c_6600]) ).

tcf(c_10488,plain,
    ( ( app(sk3,sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_9160,c_6600]) ).

tcf(c_10505,plain,
    ( ( cons(hd(sk4),sk4) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( cons(hd(sk4),app(sk4,sk3)) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10484,c_4223]) ).

tcf(c_10509,plain,
    ( ( cons(hd(sk4),sk3) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10483,c_4358]) ).

tcf(c_10585,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != app(sk3,sk3) ) ),
    inference(superposition,[status(thm)],[c_5825,c_6605]) ).

tcf(c_10587,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5818,c_6605]) ).

tcf(c_10588,plain,
    ( ( sk3 = nil )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != app(sk3,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10585,c_259]) ).

tcf(c_10592,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10587,c_247]) ).

tcf(c_10599,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_5719,c_254]) ).

tcf(c_10600,plain,
    ( ssList(cons(hd(sk4),app(sk4,sk4)))
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_5719,c_272]) ).

tcf(c_10601,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(cons(hd(sk4),sk4),X0) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5719,c_270]) ).

tcf(c_10602,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),sk4))
      | ( cons(hd(sk4),app(sk4,sk4)) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_5719,c_269]) ).

tcf(c_10603,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5719,c_10191]) ).

tcf(c_10604,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_5719,c_4679]) ).

tcf(c_10605,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5719,c_7550]) ).

tcf(c_10606,plain,
    ssList(cons(hd(sk4),app(sk4,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_10600,c_247,c_4223]) ).

tcf(c_10607,plain,
    ( ( sk3 = sk4 )
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10605,c_247]) ).

tcf(c_10610,plain,
    cons(hd(sk4),app(sk4,sk4)) != sk4,
    inference(forward_subsumption_resolution,[status(thm)],[c_10604,c_4281,c_4223]) ).

tcf(c_10611,plain,
    cons(hd(sk4),app(sk4,sk4)) != nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_10599,c_1243,c_247,c_4223]) ).

tcf(c_10612,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),sk4) )
    | ( cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10603,c_4223]) ).

tcf(c_10615,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk4,sk4)) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10602,c_247,c_4223]) ).

tcf(c_10619,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),sk4),X0) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10601,c_247,c_4223]) ).

tcf(c_10667,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk4,sk4)),sk4),X0) = app(cons(hd(sk4),app(sk4,sk4)),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_4540]) ).

tcf(c_10668,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk4,sk4)),sk3),X0) = app(cons(hd(sk4),app(sk4,sk4)),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_4539]) ).

tcf(c_10669,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk4),app(sk4,sk4))),X0) = app(X1,app(cons(hd(sk4),app(sk4,sk4)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_271]) ).

tcf(c_10670,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk4),app(sk4,sk4)))) = app(cons(X1,X0),cons(hd(sk4),app(sk4,sk4))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_266]) ).

tcf(c_10671,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
      | ( app(tl(cons(hd(sk4),app(sk4,sk4))),X0) = tl(app(cons(hd(sk4),app(sk4,sk4)),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_274]) ).

tcf(c_10672,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
      | ( hd(app(cons(hd(sk4),app(sk4,sk4)),X0)) = hd(cons(hd(sk4),app(sk4,sk4))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_283]) ).

tcf(c_10673,plain,
    app(nil,app(sk4,cons(hd(sk4),app(sk4,sk4)))) = app(sk4,cons(hd(sk4),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_10606,c_8061]) ).

tcf(c_10674,plain,
    app(app(sk4,sk4),cons(hd(sk4),app(sk4,sk4))) = app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_10606,c_8048]) ).

tcf(c_10675,plain,
    app(nil,app(sk3,cons(hd(sk4),app(sk4,sk4)))) = app(sk3,cons(hd(sk4),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_10606,c_5745]) ).

tcf(c_10676,plain,
    app(app(sk3,sk4),cons(hd(sk4),app(sk4,sk4))) = app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_10606,c_8047]) ).

tcf(c_10677,plain,
    app(app(sk4,sk3),cons(hd(sk4),app(sk4,sk4))) = app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_10606,c_5738]) ).

tcf(c_10678,plain,
    app(app(sk3,sk3),cons(hd(sk4),app(sk4,sk4))) = app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_10606,c_5737]) ).

tcf(c_10679,plain,
    app(tl(sk4),cons(hd(sk4),app(sk4,sk4))) = tl(app(sk4,cons(hd(sk4),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_10606,c_4136]) ).

tcf(c_10680,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk4,sk4)),sk4)) = app(cons(X0,cons(hd(sk4),app(sk4,sk4))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_4462]) ).

tcf(c_10681,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk4,sk4)),sk3)) = app(cons(X0,cons(hd(sk4),app(sk4,sk4))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_4461]) ).

tcf(c_10682,plain,
    app(tl(sk3),cons(hd(sk4),app(sk4,sk4))) = tl(app(sk3,cons(hd(sk4),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_10606,c_4284]) ).

tcf(c_10683,plain,
    hd(app(sk3,cons(hd(sk4),app(sk4,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_4027]) ).

tcf(c_10684,plain,
    hd(app(sk4,cons(hd(sk4),app(sk4,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_3885]) ).

tcf(c_10685,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk4),app(sk4,sk4)))) = cons(X0,cons(hd(sk4),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3019]) ).

tcf(c_10686,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk4))),sk4),nil) = cons(hd(cons(hd(sk4),app(sk4,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3452]) ).

tcf(c_10687,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk4))),sk3),nil) = cons(hd(cons(hd(sk4),app(sk4,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3444]) ).

tcf(c_10688,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(tl(cons(hd(sk4),app(sk4,sk4))),nil) = tl(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3065]) ).

tcf(c_10689,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),sk4)) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3215]) ).

tcf(c_10690,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),sk3)) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3207]) ).

tcf(c_10691,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk4),app(sk4,sk4))) = cons(X0,cons(hd(sk4),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_253]) ).

tcf(c_10692,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( cons(hd(cons(hd(sk4),app(sk4,sk4))),tl(cons(hd(sk4),app(sk4,sk4)))) = cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10606,c_275]) ).

tcf(c_10693,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk4),app(sk4,sk4))),nil) = cons(X0,cons(hd(sk4),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3018]) ).

tcf(c_10694,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk4))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_10606,c_3191]) ).

tcf(c_10695,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk4))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_10606,c_3183]) ).

tcf(c_10696,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk4),app(sk4,sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_284]) ).

tcf(c_10697,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk4),app(sk4,sk4)))) = cons(hd(sk4),app(sk4,sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_276]) ).

tcf(c_10698,plain,
    app(cons(hd(sk4),app(sk4,sk4)),nil) = cons(hd(sk4),app(sk4,sk4)),
    inference(superposition,[status(thm)],[c_10606,c_258]) ).

tcf(c_10699,plain,
    app(nil,cons(hd(sk4),app(sk4,sk4))) = cons(hd(sk4),app(sk4,sk4)),
    inference(superposition,[status(thm)],[c_10606,c_257]) ).

tcf(c_10870,plain,
    ( ( sk3 = nil )
    | ( app(nil,tl(sk3)) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_3066]) ).

tcf(c_10871,plain,
    ( ( sk4 = nil )
    | ( app(nil,tl(sk4)) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_3066]) ).

tcf(c_10873,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(nil,tl(tl(X0))) = tl(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3066]) ).

tcf(c_10874,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(nil,tl(app(X1,X0))) = tl(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3066]) ).

tcf(c_10875,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(nil,tl(cons(X1,X0))) = tl(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3066]) ).

tcf(c_10876,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(nil,tl(cons(hd(sk4),sk3))) = tl(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3066]) ).

tcf(c_10877,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(nil,tl(cons(hd(sk4),sk4))) = tl(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3066]) ).

tcf(c_10878,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(nil,tl(cons(hd(sk4),app(sk3,sk3)))) = tl(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3066]) ).

tcf(c_10879,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(nil,tl(app(sk3,app(sk3,sk3)))) = tl(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3066]) ).

tcf(c_10880,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(nil,tl(app(sk3,app(sk3,sk4)))) = tl(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3066]) ).

tcf(c_10881,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(nil,tl(app(sk4,app(sk3,sk3)))) = tl(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3066]) ).

tcf(c_10882,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(nil,tl(cons(hd(sk4),app(sk4,sk3)))) = tl(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3066]) ).

tcf(c_10883,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(nil,tl(app(sk4,app(sk3,sk4)))) = tl(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3066]) ).

tcf(c_10884,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(nil,tl(app(sk3,app(sk4,sk3)))) = tl(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3066]) ).

tcf(c_10885,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(nil,tl(app(sk3,app(sk4,sk4)))) = tl(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3066]) ).

tcf(c_10886,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(nil,tl(app(sk4,app(sk4,sk3)))) = tl(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3066]) ).

tcf(c_10887,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(nil,tl(app(sk4,app(sk4,sk4)))) = tl(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3066]) ).

tcf(c_10888,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(nil,tl(cons(hd(sk4),app(sk3,sk4)))) = tl(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3066]) ).

tcf(c_10889,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(nil,tl(cons(hd(sk4),app(sk4,sk4)))) = tl(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3066]) ).

tcf(c_10890,plain,
    app(nil,tl(sk4)) = tl(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_10871,c_1243]) ).

tcf(c_10907,plain,
    app(nil,tl(cons(hd(sk4),app(sk4,sk4)))) = tl(cons(hd(sk4),app(sk4,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_10889,c_10611]) ).

tcf(c_10908,plain,
    app(nil,tl(cons(hd(sk4),app(sk3,sk4)))) = tl(cons(hd(sk4),app(sk3,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_10888,c_10190]) ).

tcf(c_10909,plain,
    app(nil,tl(cons(hd(sk4),app(sk4,sk3)))) = tl(cons(hd(sk4),app(sk4,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_10882,c_7545]) ).

tcf(c_10910,plain,
    app(nil,tl(cons(hd(sk4),app(sk3,sk3)))) = tl(cons(hd(sk4),app(sk3,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_10878,c_5891]) ).

tcf(c_10944,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ( app(nil,X0) != tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_10890,c_270]) ).

tcf(c_10945,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ( app(X0,tl(sk4)) != tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_10890,c_269]) ).

tcf(c_10946,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ( app(X0,tl(sk4)) != tl(sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10945,c_259]) ).

tcf(c_10951,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ( app(nil,X0) != tl(sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10944,c_259]) ).

tcf(c_10957,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),sk3)))
      | ( cons(hd(sk3),sk3) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),sk3))
      | ~ ssList(cons(hd(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_10138,c_280]) ).

tcf(c_10958,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),sk3)))
      | ( cons(hd(sk3),sk3) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),sk3))
      | ~ ssList(cons(hd(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_10138,c_279]) ).

tcf(c_10973,plain,
    tl(sk3) != sk3,
    inference(global_subsumption_just,[status(thm)],[c_10119,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_3733,c_7562,c_7561]) ).

tcf(c_10975,plain,
    app(nil,tl(sk3)) = tl(sk3),
    inference(global_subsumption_just,[status(thm)],[c_10870,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_10870]) ).

tcf(c_10985,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ( app(nil,X0) != tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_10975,c_270]) ).

tcf(c_10986,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ( app(X0,tl(sk3)) != tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_10975,c_269]) ).

tcf(c_10987,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ( app(X0,tl(sk3)) != tl(sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10986,c_259]) ).

tcf(c_10992,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ( app(nil,X0) != tl(sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10985,c_259]) ).

tcf(c_11130,plain,
    ( ( cons(hd(sk4),sk4) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk4),app(sk4,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_10615]) ).

tcf(c_11131,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5702,c_10615]) ).

tcf(c_11143,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk4),app(sk4,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_3788,c_10619]) ).

tcf(c_11144,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_4999,c_10619]) ).

tcf(c_11146,plain,
    cons(hd(sk4),app(sk4,sk4)) != cons(hd(sk4),sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_11143,c_1243,c_259]) ).

tcf(c_11156,plain,
    ( ( cons(hd(sk4),nil) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),nil))
    | ( app(sk3,app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_6943]) ).

tcf(c_11157,plain,
    ( ( cons(hd(sk4),sk3) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5702,c_6943]) ).

tcf(c_11158,plain,
    ( ( cons(hd(sk4),sk4) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk4)) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5719,c_6943]) ).

tcf(c_11160,plain,
    ( ( app(sk3,sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_7183,c_6943]) ).

tcf(c_11161,plain,
    ( ( app(sk3,sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk4)) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_8159,c_6943]) ).

tcf(c_11162,plain,
    ( ( app(sk3,sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9161,c_6943]) ).

tcf(c_11179,plain,
    ( ( cons(hd(sk4),sk4) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( cons(hd(sk4),app(sk4,sk4)) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11158,c_4223]) ).

tcf(c_11183,plain,
    ( ( cons(hd(sk4),sk3) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11157,c_4358]) ).

tcf(c_11195,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk4)) != app(sk3,sk3) ) ),
    inference(superposition,[status(thm)],[c_5825,c_6948]) ).

tcf(c_11196,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5817,c_6948]) ).

tcf(c_11198,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk4)) != app(sk3,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11195,c_1243,c_259]) ).

tcf(c_11210,plain,
    ( ( cons(hd(sk4),nil) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),nil))
    | ( app(sk4,app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_7257]) ).

tcf(c_11211,plain,
    ( ( cons(hd(sk4),sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4976,c_7257]) ).

tcf(c_11212,plain,
    ( ( cons(hd(sk4),sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4999,c_7257]) ).

tcf(c_11215,plain,
    ( ( app(sk3,sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_8158,c_7257]) ).

tcf(c_11216,plain,
    ( ( app(sk4,sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_9160,c_7257]) ).

tcf(c_11229,plain,
    ( ( cons(hd(sk4),sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( cons(hd(sk4),app(sk4,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11212,c_4223]) ).

tcf(c_11233,plain,
    ( ( cons(hd(sk4),sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11211,c_4358]) ).

tcf(c_11239,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_5823,c_255]) ).

tcf(c_11240,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_5823,c_254]) ).

tcf(c_11241,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_5823,c_272]) ).

tcf(c_11242,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != app(app(sk3,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_5823,c_270]) ).

tcf(c_11243,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != app(X0,cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_5823,c_269]) ).

tcf(c_11244,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(app(sk3,sk3),cons(hd(sk4),sk3)),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_5823,c_300]) ).

tcf(c_11245,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(app(sk3,sk3),cons(hd(sk4),sk3)),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_5823,c_287]) ).

tcf(c_11246,plain,
    ( ( cons(hd(sk4),sk3) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5823,c_6948]) ).

tcf(c_11247,plain,
    ( ( cons(hd(sk4),sk3) = sk3 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_5823,c_6605]) ).

tcf(c_11248,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11241,c_4358]) ).

tcf(c_11255,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11240,c_4430,c_4358]) ).

tcf(c_11258,plain,
    ( ( cons(hd(sk4),sk3) = sk3 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11247,c_4358]) ).

tcf(c_11262,plain,
    ( ( cons(hd(sk4),sk3) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11246,c_4358]) ).

tcf(c_11266,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != app(X0,cons(hd(sk4),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11243,c_4358]) ).

tcf(c_11271,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) != app(app(sk3,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11242,c_4358]) ).

tcf(c_11276,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_11245,c_5823]) ).

tcf(c_11277,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11276,c_246,c_4059]) ).

tcf(c_11284,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_11244,c_5823]) ).

tcf(c_11285,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11284,c_246,c_4059]) ).

tcf(c_11342,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4),X0) = app(app(sk3,app(sk3,cons(hd(sk4),sk3))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4540]) ).

tcf(c_11343,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk3),X0) = app(app(sk3,app(sk3,cons(hd(sk4),sk3))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4539]) ).

tcf(c_11344,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk3,cons(hd(sk4),sk3)))),X0) = app(X1,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_271]) ).

tcf(c_11345,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = app(cons(X1,X0),app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_266]) ).

tcf(c_11346,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))),X0) = tl(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_274]) ).

tcf(c_11347,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ( hd(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_283]) ).

tcf(c_11348,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))) = tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3066]) ).

tcf(c_11349,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_8061]) ).

tcf(c_11350,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk3,cons(hd(sk4),sk3)))) = app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_8048]) ).

tcf(c_11351,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_5745]) ).

tcf(c_11352,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk3,cons(hd(sk4),sk3)))) = app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_8047]) ).

tcf(c_11353,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))) = app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_5738]) ).

tcf(c_11354,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))) = app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_5737]) ).

tcf(c_11355,plain,
    ( ( app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),sk3)))) = tl(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4136]) ).

tcf(c_11356,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4462]) ).

tcf(c_11357,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk3)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4461]) ).

tcf(c_11358,plain,
    ( ( app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))) = tl(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4284]) ).

tcf(c_11359,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4027]) ).

tcf(c_11360,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3885]) ).

tcf(c_11361,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3019]) ).

tcf(c_11362,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3452]) ).

tcf(c_11363,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3444]) ).

tcf(c_11364,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil) = tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3065]) ).

tcf(c_11365,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4)) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3215]) ).

tcf(c_11366,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3)) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3207]) ).

tcf(c_11367,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk3,cons(hd(sk4),sk3)))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_253]) ).

tcf(c_11368,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))) = app(sk3,app(sk3,cons(hd(sk4),sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_275]) ).

tcf(c_11369,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3018]) ).

tcf(c_11370,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3191]) ).

tcf(c_11371,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3183]) ).

tcf(c_11372,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_284]) ).

tcf(c_11373,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = app(sk3,app(sk3,cons(hd(sk4),sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_276]) ).

tcf(c_11374,plain,
    ( ( app(app(sk3,app(sk3,cons(hd(sk4),sk3))),nil) = app(sk3,app(sk3,cons(hd(sk4),sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_258]) ).

tcf(c_11375,plain,
    ( ( app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3)))) = app(sk3,app(sk3,cons(hd(sk4),sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_257]) ).

tcf(c_11534,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( tl(cons(hd(tl(X0)),nil)) = nil )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3199]) ).

tcf(c_11535,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( tl(cons(hd(app(X1,X0)),nil)) = nil )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3199]) ).

tcf(c_11536,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( tl(cons(hd(cons(X1,X0)),nil)) = nil )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3199]) ).

tcf(c_11537,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk3)),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_4358,c_3199]) ).

tcf(c_11538,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk4)),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_4223,c_3199]) ).

tcf(c_11539,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_5886,c_3199]) ).

tcf(c_11540,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk3))),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3199]) ).

tcf(c_11541,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk4))),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3199]) ).

tcf(c_11542,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk3))),nil)) = nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3199]) ).

tcf(c_11543,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_7540,c_3199]) ).

tcf(c_11544,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk4))),nil)) = nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3199]) ).

tcf(c_11545,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk3))),nil)) = nil )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3199]) ).

tcf(c_11546,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk4))),nil)) = nil )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3199]) ).

tcf(c_11547,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk3))),nil)) = nil )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3199]) ).

tcf(c_11548,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk4))),nil)) = nil )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3199]) ).

tcf(c_11549,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_10188,c_3199]) ).

tcf(c_11550,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_10606,c_3199]) ).

tcf(c_11551,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3199]) ).

tcf(c_11558,plain,
    tl(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil)) = nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_11550,c_10611]) ).

tcf(c_11559,plain,
    tl(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil)) = nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_11549,c_10190]) ).

tcf(c_11560,plain,
    tl(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil)) = nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_11543,c_7545]) ).

tcf(c_11561,plain,
    tl(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil)) = nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_11539,c_5891]) ).

tcf(c_11625,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk4),app(sk3,sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_6405]) ).

tcf(c_11626,plain,
    hd(cons(hd(sk4),cons(hd(sk4),app(sk3,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_6405]) ).

tcf(c_11627,plain,
    hd(cons(hd(sk3),cons(hd(sk4),app(sk3,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_6405]) ).

tcf(c_11635,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk4),app(sk4,sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_7603]) ).

tcf(c_11636,plain,
    hd(cons(hd(sk4),cons(hd(sk4),app(sk4,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_7603]) ).

tcf(c_11637,plain,
    hd(cons(hd(sk3),cons(hd(sk4),app(sk4,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_7603]) ).

tcf(c_11642,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),sk3))))
      | ( cons(hd(sk3),cons(hd(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),sk3)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_10122,c_280]) ).

tcf(c_11643,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),sk3))))
      | ( cons(hd(sk3),cons(hd(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk4),sk3)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_10122,c_279]) ).

tcf(c_11659,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),sk4))))
      | ( cons(hd(sk3),cons(hd(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),sk4)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_10125,c_280]) ).

tcf(c_11660,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),sk4))))
      | ( cons(hd(sk3),cons(hd(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk4),sk4)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_10125,c_279]) ).

tcf(c_11675,plain,
    ! [X0: $i] :
      ( ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk3))
      | ( app(cons(hd(sk3),nil),X0) != sk3 )
      | ( app(app(X0,cons(hd(sk3),nil)),nil) != sk4 ) ),
    inference(superposition,[status(thm)],[c_10128,c_249]) ).

tcf(c_11684,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),nil) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_10128,c_270]) ).

tcf(c_11685,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(X0,cons(hd(sk3),nil)) != cons(hd(sk3),nil) ) ),
    inference(superposition,[status(thm)],[c_10128,c_269]) ).

tcf(c_11686,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(cons(hd(sk3),nil),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk3),nil)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10128,c_300]) ).

tcf(c_11687,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(cons(hd(sk3),nil),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk3),nil)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10128,c_287]) ).

tcf(c_11688,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(X0,cons(hd(sk3),nil)) != cons(hd(sk3),nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11685,c_259]) ).

tcf(c_11693,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),nil) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11684,c_259]) ).

tcf(c_11698,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ( app(cons(hd(sk3),nil),X0) != sk3 )
      | ( app(app(X0,cons(hd(sk3),nil)),nil) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11675,c_259,c_10117]) ).

tcf(c_11702,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ strictorderedP(app(cons(hd(sk3),nil),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),nil),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_11687,c_10128]) ).

tcf(c_11703,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(cons(hd(sk3),nil),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),nil),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11702,c_259,c_10117]) ).

tcf(c_11709,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ totalorderedP(app(cons(hd(sk3),nil),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),nil),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_11686,c_10128]) ).

tcf(c_11710,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(cons(hd(sk3),nil),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),nil),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11709,c_259,c_10117]) ).

tcf(c_11744,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != app(sk4,sk3) ) ),
    inference(superposition,[status(thm)],[c_7193,c_7262]) ).

tcf(c_11746,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_7183,c_7262]) ).

tcf(c_11747,plain,
    ( ( sk3 = nil )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != app(sk4,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11744,c_259]) ).

tcf(c_11751,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11746,c_247]) ).

tcf(c_11769,plain,
    ( ( cons(hd(sk4),nil) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),nil))
    | ( app(sk4,app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_7763]) ).

tcf(c_11770,plain,
    ( ( cons(hd(sk4),sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5702,c_7763]) ).

tcf(c_11771,plain,
    ( ( cons(hd(sk4),sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5719,c_7763]) ).

tcf(c_11774,plain,
    ( ( app(sk3,sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_8159,c_7763]) ).

tcf(c_11775,plain,
    ( ( app(sk4,sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9161,c_7763]) ).

tcf(c_11788,plain,
    ( ( cons(hd(sk4),sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( cons(hd(sk4),app(sk4,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11771,c_4223]) ).

tcf(c_11792,plain,
    ( ( cons(hd(sk4),sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11770,c_4358]) ).

tcf(c_11858,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk4)) != app(sk4,sk3) ) ),
    inference(superposition,[status(thm)],[c_7193,c_7768]) ).

tcf(c_11859,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_7182,c_7768]) ).

tcf(c_11861,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk4)) != app(sk4,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11858,c_1243,c_259]) ).

tcf(c_11873,plain,
    ( ( cons(hd(sk4),nil) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ( app(sk3,app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_8266]) ).

tcf(c_11874,plain,
    ( ( cons(hd(sk4),sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4976,c_8266]) ).

tcf(c_11875,plain,
    ( ( cons(hd(sk4),sk4) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4999,c_8266]) ).

tcf(c_11879,plain,
    ( ( app(sk3,sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_9160,c_8266]) ).

tcf(c_11888,plain,
    ( ( cons(hd(sk4),sk4) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11875,c_4223]) ).

tcf(c_11892,plain,
    ( ( cons(hd(sk4),sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( cons(hd(sk4),app(sk3,sk3)) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11874,c_4358]) ).

tcf(c_11920,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != app(sk3,sk4) ) ),
    inference(superposition,[status(thm)],[c_8172,c_8271]) ).

tcf(c_11922,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_8159,c_8271]) ).

tcf(c_11923,plain,
    ( ( sk3 = nil )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != app(sk3,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11920,c_259]) ).

tcf(c_11927,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11922,c_247]) ).

tcf(c_11981,plain,
    ( ( cons(hd(sk4),nil) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ( app(sk3,app(sk4,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_8547]) ).

tcf(c_11982,plain,
    ( ( cons(hd(sk4),sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5702,c_8547]) ).

tcf(c_11983,plain,
    ( ( cons(hd(sk4),sk4) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk4)) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5719,c_8547]) ).

tcf(c_11987,plain,
    ( ( app(sk3,sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9161,c_8547]) ).

tcf(c_11996,plain,
    ( ( cons(hd(sk4),sk4) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( cons(hd(sk4),app(sk4,sk4)) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11983,c_4223]) ).

tcf(c_12000,plain,
    ( ( cons(hd(sk4),sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( cons(hd(sk4),app(sk3,sk4)) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11982,c_4358]) ).

tcf(c_12006,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_5824,c_255]) ).

tcf(c_12007,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_5824,c_254]) ).

tcf(c_12008,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_5824,c_272]) ).

tcf(c_12009,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != app(app(sk3,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_5824,c_270]) ).

tcf(c_12010,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != app(X0,cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_5824,c_269]) ).

tcf(c_12011,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(app(sk3,sk3),cons(hd(sk4),sk4)),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_5824,c_300]) ).

tcf(c_12012,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(app(sk3,sk3),cons(hd(sk4),sk4)),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_5824,c_287]) ).

tcf(c_12013,plain,
    ( ( cons(hd(sk4),sk4) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5824,c_6948]) ).

tcf(c_12014,plain,
    ( ( cons(hd(sk4),sk4) = sk3 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_5824,c_6605]) ).

tcf(c_12015,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12008,c_4223]) ).

tcf(c_12022,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12007,c_4281,c_4223]) ).

tcf(c_12025,plain,
    ( ( cons(hd(sk4),sk4) = sk3 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12014,c_4223]) ).

tcf(c_12029,plain,
    ( ( cons(hd(sk4),sk4) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12013,c_4223]) ).

tcf(c_12033,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != app(X0,cons(hd(sk4),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12010,c_4223]) ).

tcf(c_12038,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) != app(app(sk3,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12009,c_4223]) ).

tcf(c_12043,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_12012,c_5824]) ).

tcf(c_12044,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12043,c_247,c_4059]) ).

tcf(c_12051,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_12011,c_5824]) ).

tcf(c_12052,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12051,c_247,c_4059]) ).

tcf(c_12087,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4),X0) = app(app(sk3,app(sk3,cons(hd(sk4),sk4))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4540]) ).

tcf(c_12088,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk3),X0) = app(app(sk3,app(sk3,cons(hd(sk4),sk4))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4539]) ).

tcf(c_12089,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk3,cons(hd(sk4),sk4)))),X0) = app(X1,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_271]) ).

tcf(c_12090,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = app(cons(X1,X0),app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_266]) ).

tcf(c_12091,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))),X0) = tl(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_274]) ).

tcf(c_12092,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ( hd(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_283]) ).

tcf(c_12093,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3199]) ).

tcf(c_12094,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))) = tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3066]) ).

tcf(c_12095,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_8061]) ).

tcf(c_12096,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk3,cons(hd(sk4),sk4)))) = app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_8048]) ).

tcf(c_12097,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_5745]) ).

tcf(c_12098,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk3,cons(hd(sk4),sk4)))) = app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_8047]) ).

tcf(c_12099,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))) = app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_5738]) ).

tcf(c_12100,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))) = app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_5737]) ).

tcf(c_12101,plain,
    ( ( app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),sk4)))) = tl(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4136]) ).

tcf(c_12102,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4462]) ).

tcf(c_12103,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk3)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4461]) ).

tcf(c_12104,plain,
    ( ( app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))) = tl(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4284]) ).

tcf(c_12105,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4027]) ).

tcf(c_12106,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3885]) ).

tcf(c_12107,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3019]) ).

tcf(c_12108,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3452]) ).

tcf(c_12109,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3444]) ).

tcf(c_12110,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil) = tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3065]) ).

tcf(c_12111,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4)) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3215]) ).

tcf(c_12112,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3)) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3207]) ).

tcf(c_12113,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk3,cons(hd(sk4),sk4)))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_253]) ).

tcf(c_12114,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))) = app(sk3,app(sk3,cons(hd(sk4),sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_275]) ).

tcf(c_12115,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3018]) ).

tcf(c_12116,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3191]) ).

tcf(c_12117,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3183]) ).

tcf(c_12118,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_284]) ).

tcf(c_12119,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = app(sk3,app(sk3,cons(hd(sk4),sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_276]) ).

tcf(c_12120,plain,
    ( ( app(app(sk3,app(sk3,cons(hd(sk4),sk4))),nil) = app(sk3,app(sk3,cons(hd(sk4),sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_258]) ).

tcf(c_12121,plain,
    ( ( app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4)))) = app(sk3,app(sk3,cons(hd(sk4),sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_257]) ).

tcf(c_12330,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk4),app(sk3,sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_10230]) ).

tcf(c_12331,plain,
    hd(cons(hd(sk4),cons(hd(sk4),app(sk3,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_10230]) ).

tcf(c_12332,plain,
    hd(cons(hd(sk3),cons(hd(sk4),app(sk3,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_10230]) ).

tcf(c_12340,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk4),app(sk4,sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_10696]) ).

tcf(c_12341,plain,
    hd(cons(hd(sk4),cons(hd(sk4),app(sk4,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_10696]) ).

tcf(c_12342,plain,
    hd(cons(hd(sk3),cons(hd(sk4),app(sk4,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_10696]) ).

tcf(c_12352,plain,
    ! [X0: $i] :
      ( ( app(app(sk3,X0),nil) = app(sk3,X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_3049]) ).

tcf(c_12353,plain,
    ! [X0: $i] :
      ( ( app(app(sk4,X0),nil) = app(sk4,X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_3049]) ).

tcf(c_12354,plain,
    ! [X0: $i] :
      ( ( app(app(nil,X0),nil) = app(nil,X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_3049]) ).

tcf(c_12355,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( app(app(tl(X0),X1),nil) = app(tl(X0),X1) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3049]) ).

tcf(c_12356,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(app(app(X1,X0),X2),nil) = app(app(X1,X0),X2) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3049]) ).

tcf(c_12357,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(app(cons(X2,X0),X1),nil) = app(cons(X2,X0),X1) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3049]) ).

tcf(c_12358,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),sk3),X0),nil) = app(cons(hd(sk4),sk3),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3049]) ).

tcf(c_12359,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),sk4),X0),nil) = app(cons(hd(sk4),sk4),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3049]) ).

tcf(c_12360,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk3,sk3)),X0),nil) = app(cons(hd(sk4),app(sk3,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3049]) ).

tcf(c_12361,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,sk3)),X0),nil) = app(app(sk3,app(sk3,sk3)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3049]) ).

tcf(c_12362,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,sk4)),X0),nil) = app(app(sk3,app(sk3,sk4)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3049]) ).

tcf(c_12363,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,sk3)),X0),nil) = app(app(sk4,app(sk3,sk3)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3049]) ).

tcf(c_12364,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk4,sk3)),X0),nil) = app(cons(hd(sk4),app(sk4,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3049]) ).

tcf(c_12365,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,sk4)),X0),nil) = app(app(sk4,app(sk3,sk4)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3049]) ).

tcf(c_12366,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,sk3)),X0),nil) = app(app(sk3,app(sk4,sk3)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3049]) ).

tcf(c_12367,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,sk4)),X0),nil) = app(app(sk3,app(sk4,sk4)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3049]) ).

tcf(c_12368,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,sk3)),X0),nil) = app(app(sk4,app(sk4,sk3)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3049]) ).

tcf(c_12369,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,sk4)),X0),nil) = app(app(sk4,app(sk4,sk4)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3049]) ).

tcf(c_12370,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk3,sk4)),X0),nil) = app(cons(hd(sk4),app(sk3,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3049]) ).

tcf(c_12371,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk4,sk4)),X0),nil) = app(cons(hd(sk4),app(sk4,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3049]) ).

tcf(c_12372,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0),nil) = app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3049]) ).

tcf(c_12373,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0),nil) = app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3049]) ).

tcf(c_12607,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( cons(hd(sk3),sk4) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_10129,c_270]) ).

tcf(c_12608,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( app(X0,cons(hd(sk3),sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10129,c_269]) ).

tcf(c_12609,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(cons(hd(sk3),sk4),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk3),sk4)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10129,c_300]) ).

tcf(c_12610,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(cons(hd(sk3),sk4),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk3),sk4)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10129,c_287]) ).

tcf(c_12611,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( app(X0,cons(hd(sk3),sk4)) != cons(hd(sk3),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12608,c_259]) ).

tcf(c_12616,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( cons(hd(sk3),sk4) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12607,c_259]) ).

tcf(c_12621,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),sk4),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_12610,c_10129]) ).

tcf(c_12622,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),sk4),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12621,c_259,c_247,c_10117]) ).

tcf(c_12628,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),sk4),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_12609,c_10129]) ).

tcf(c_12629,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),sk4),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12628,c_259,c_247,c_10117]) ).

tcf(c_12645,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( cons(hd(sk3),sk3) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_10130,c_270]) ).

tcf(c_12646,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( app(X0,cons(hd(sk3),sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10130,c_269]) ).

tcf(c_12647,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(cons(hd(sk3),sk3),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk3),sk3)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10130,c_300]) ).

tcf(c_12648,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(cons(hd(sk3),sk3),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk3),sk3)),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10130,c_287]) ).

tcf(c_12649,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( app(X0,cons(hd(sk3),sk3)) != cons(hd(sk3),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12646,c_259]) ).

tcf(c_12654,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( cons(hd(sk3),sk3) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12645,c_259]) ).

tcf(c_12659,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),sk3),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_12648,c_10130]) ).

tcf(c_12660,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),sk3),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12659,c_259,c_246,c_10117]) ).

tcf(c_12666,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),sk3),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_12647,c_10130]) ).

tcf(c_12667,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),sk3),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12666,c_259,c_246,c_10117]) ).

tcf(c_12689,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(cons(hd(sk3),nil),X0) != cons(hd(sk3),nil) ) ),
    inference(superposition,[status(thm)],[c_10131,c_270]) ).

tcf(c_12690,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),nil) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_10131,c_269]) ).

tcf(c_12691,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),nil) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12690,c_259]) ).

tcf(c_12696,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(cons(hd(sk3),nil),X0) != cons(hd(sk3),nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12689,c_259]) ).

tcf(c_12724,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk4) != nil ) ),
    inference(superposition,[status(thm)],[c_10132,c_254]) ).

tcf(c_12725,plain,
    ( ssList(cons(hd(sk3),sk4))
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(superposition,[status(thm)],[c_10132,c_272]) ).

tcf(c_12726,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(cons(hd(sk3),nil),X0) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_270]) ).

tcf(c_12727,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),sk4) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_269]) ).

tcf(c_12728,plain,
    ( ( cons(hd(sk3),nil) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( app(sk3,app(sk4,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_8547]) ).

tcf(c_12729,plain,
    ( ( cons(hd(sk3),nil) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ( app(sk4,app(sk3,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_7763]) ).

tcf(c_12730,plain,
    ( ( cons(hd(sk3),nil) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ( app(sk3,app(sk3,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_6943]) ).

tcf(c_12731,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk4),app(sk4,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_10615]) ).

tcf(c_12732,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_10191]) ).

tcf(c_12733,plain,
    ( ( cons(hd(sk3),nil) = nil )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk4) != sk4 ) ),
    inference(superposition,[status(thm)],[c_10132,c_4679]) ).

tcf(c_12734,plain,
    ( ssList(cons(hd(sk3),sk4))
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12725,c_247]) ).

tcf(c_12740,plain,
    ( ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk4) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12724,c_1243,c_247]) ).

tcf(c_12749,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),sk4) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12727,c_247]) ).

tcf(c_12754,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(cons(hd(sk3),nil),X0) != cons(hd(sk3),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12726,c_247]) ).

tcf(c_12795,plain,
    ( ssList(cons(hd(sk3),sk4))
    | ~ ssList(nil)
    | ~ ssItem(hd(sk3)) ),
    inference(superposition,[status(thm)],[c_268,c_12734]) ).

tcf(c_12796,plain,
    ssList(cons(hd(sk3),sk4)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12795,c_259,c_10117]) ).

tcf(c_12803,plain,
    app(app(sk3,nil),nil) = app(sk3,nil),
    inference(superposition,[status(thm)],[c_259,c_12352]) ).

tcf(c_12804,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(app(sk3,tl(X0)),nil) = app(sk3,tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_12352]) ).

tcf(c_12805,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk3,app(X1,X0)),nil) = app(sk3,app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_12352]) ).

tcf(c_12806,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk3,cons(X1,X0)),nil) = app(sk3,cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_12352]) ).

tcf(c_12807,plain,
    app(app(sk3,cons(hd(sk4),sk3)),nil) = app(sk3,cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4358,c_12352]) ).

tcf(c_12808,plain,
    app(app(sk3,cons(hd(sk4),sk4)),nil) = app(sk3,cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4223,c_12352]) ).

tcf(c_12809,plain,
    app(app(sk3,cons(hd(sk4),app(sk3,sk3))),nil) = app(sk3,cons(hd(sk4),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_5886,c_12352]) ).

tcf(c_12810,plain,
    ( ( app(app(sk3,app(sk3,app(sk3,sk3))),nil) = app(sk3,app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_12352]) ).

tcf(c_12811,plain,
    ( ( app(app(sk3,app(sk3,app(sk3,sk4))),nil) = app(sk3,app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_12352]) ).

tcf(c_12812,plain,
    ( ( app(app(sk3,app(sk4,app(sk3,sk3))),nil) = app(sk3,app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_12352]) ).

tcf(c_12813,plain,
    app(app(sk3,cons(hd(sk4),app(sk4,sk3))),nil) = app(sk3,cons(hd(sk4),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_7540,c_12352]) ).

tcf(c_12814,plain,
    ( ( app(app(sk3,app(sk4,app(sk3,sk4))),nil) = app(sk3,app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_12352]) ).

tcf(c_12815,plain,
    ( ( app(app(sk3,app(sk3,app(sk4,sk3))),nil) = app(sk3,app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_12352]) ).

tcf(c_12816,plain,
    ( ( app(app(sk3,app(sk3,app(sk4,sk4))),nil) = app(sk3,app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_12352]) ).

tcf(c_12817,plain,
    ( ( app(app(sk3,app(sk4,app(sk4,sk3))),nil) = app(sk3,app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_12352]) ).

tcf(c_12818,plain,
    ( ( app(app(sk3,app(sk4,app(sk4,sk4))),nil) = app(sk3,app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_12352]) ).

tcf(c_12819,plain,
    app(app(sk3,cons(hd(sk4),app(sk3,sk4))),nil) = app(sk3,cons(hd(sk4),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_10188,c_12352]) ).

tcf(c_12820,plain,
    app(app(sk3,cons(hd(sk4),app(sk4,sk4))),nil) = app(sk3,cons(hd(sk4),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_10606,c_12352]) ).

tcf(c_12821,plain,
    ( ( app(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_12352]) ).

tcf(c_12822,plain,
    ( ( app(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_12352]) ).

tcf(c_12879,plain,
    app(app(sk4,nil),nil) = app(sk4,nil),
    inference(superposition,[status(thm)],[c_259,c_12353]) ).

tcf(c_12880,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(app(sk4,tl(X0)),nil) = app(sk4,tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_12353]) ).

tcf(c_12881,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk4,app(X1,X0)),nil) = app(sk4,app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_12353]) ).

tcf(c_12882,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sk4,cons(X1,X0)),nil) = app(sk4,cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_12353]) ).

tcf(c_12883,plain,
    app(app(sk4,cons(hd(sk4),sk3)),nil) = app(sk4,cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4358,c_12353]) ).

tcf(c_12884,plain,
    app(app(sk4,cons(hd(sk4),sk4)),nil) = app(sk4,cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4223,c_12353]) ).

tcf(c_12885,plain,
    app(app(sk4,cons(hd(sk4),app(sk3,sk3))),nil) = app(sk4,cons(hd(sk4),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_5886,c_12353]) ).

tcf(c_12886,plain,
    ( ( app(app(sk4,app(sk3,app(sk3,sk3))),nil) = app(sk4,app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_12353]) ).

tcf(c_12887,plain,
    ( ( app(app(sk4,app(sk3,app(sk3,sk4))),nil) = app(sk4,app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_12353]) ).

tcf(c_12888,plain,
    ( ( app(app(sk4,app(sk4,app(sk3,sk3))),nil) = app(sk4,app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_12353]) ).

tcf(c_12889,plain,
    app(app(sk4,cons(hd(sk4),app(sk4,sk3))),nil) = app(sk4,cons(hd(sk4),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_7540,c_12353]) ).

tcf(c_12890,plain,
    ( ( app(app(sk4,app(sk4,app(sk3,sk4))),nil) = app(sk4,app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_12353]) ).

tcf(c_12891,plain,
    ( ( app(app(sk4,app(sk3,app(sk4,sk3))),nil) = app(sk4,app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_12353]) ).

tcf(c_12892,plain,
    ( ( app(app(sk4,app(sk3,app(sk4,sk4))),nil) = app(sk4,app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_12353]) ).

tcf(c_12893,plain,
    ( ( app(app(sk4,app(sk4,app(sk4,sk3))),nil) = app(sk4,app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_12353]) ).

tcf(c_12894,plain,
    ( ( app(app(sk4,app(sk4,app(sk4,sk4))),nil) = app(sk4,app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_12353]) ).

tcf(c_12895,plain,
    app(app(sk4,cons(hd(sk4),app(sk3,sk4))),nil) = app(sk4,cons(hd(sk4),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_10188,c_12353]) ).

tcf(c_12896,plain,
    app(app(sk4,cons(hd(sk4),app(sk4,sk4))),nil) = app(sk4,cons(hd(sk4),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_10606,c_12353]) ).

tcf(c_12897,plain,
    ( ( app(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_12353]) ).

tcf(c_12898,plain,
    ( ( app(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_12353]) ).

tcf(c_13043,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk4)) != app(sk3,sk4) ) ),
    inference(superposition,[status(thm)],[c_8172,c_8552]) ).

tcf(c_13044,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_8158,c_8552]) ).

tcf(c_13046,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk4)) != app(sk3,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13043,c_1243,c_259]) ).

tcf(c_13058,plain,
    ( ( cons(hd(sk4),nil) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ( app(sk4,app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_9243]) ).

tcf(c_13059,plain,
    ( ( cons(hd(sk4),sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4976,c_9243]) ).

tcf(c_13060,plain,
    ( ( cons(hd(sk4),sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4999,c_9243]) ).

tcf(c_13069,plain,
    ( ( cons(hd(sk4),sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13060,c_4223]) ).

tcf(c_13073,plain,
    ( ( cons(hd(sk4),sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( cons(hd(sk4),app(sk3,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13059,c_4358]) ).

tcf(c_13085,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != app(sk4,sk4) ) ),
    inference(superposition,[status(thm)],[c_9176,c_9248]) ).

tcf(c_13087,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9161,c_9248]) ).

tcf(c_13088,plain,
    ( ( sk3 = nil )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != app(sk4,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13085,c_259]) ).

tcf(c_13092,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13087,c_247]) ).

tcf(c_13104,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_6387,c_255]) ).

tcf(c_13105,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_6387,c_254]) ).

tcf(c_13106,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_6387,c_272]) ).

tcf(c_13107,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(app(sk3,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_6387,c_270]) ).

tcf(c_13108,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(X0,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_6387,c_269]) ).

tcf(c_13109,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(app(sk3,sk3),cons(hd(sk4),app(sk3,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_6387,c_300]) ).

tcf(c_13110,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(app(sk3,sk3),cons(hd(sk4),app(sk3,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_6387,c_287]) ).

tcf(c_13111,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_6387,c_6948]) ).

tcf(c_13112,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_6387,c_6605]) ).

tcf(c_13113,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk3,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13106,c_5886]) ).

tcf(c_13120,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13105,c_5891,c_5886]) ).

tcf(c_13123,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13112,c_5887,c_5886]) ).

tcf(c_13126,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13111,c_5886]) ).

tcf(c_13130,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(X0,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13108,c_5886]) ).

tcf(c_13135,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(app(sk3,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13107,c_5886]) ).

tcf(c_13140,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_13110,c_6387]) ).

tcf(c_13141,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13140,c_4059]) ).

tcf(c_13148,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_13109,c_6387]) ).

tcf(c_13149,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13148,c_4059]) ).

tcf(c_13160,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),sk4),X0),nil) = app(cons(hd(sk3),sk4),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3049]) ).

tcf(c_13161,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),sk4),sk4),X0) = app(cons(hd(sk3),sk4),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_4540]) ).

tcf(c_13162,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),sk4),sk3),X0) = app(cons(hd(sk3),sk4),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_4539]) ).

tcf(c_13163,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk3),sk4)),X0) = app(X1,app(cons(hd(sk3),sk4),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_271]) ).

tcf(c_13164,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk3),sk4))) = app(cons(X1,X0),cons(hd(sk3),sk4)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_266]) ).

tcf(c_13165,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = nil )
      | ( app(tl(cons(hd(sk3),sk4)),X0) = tl(app(cons(hd(sk3),sk4),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_274]) ).

tcf(c_13166,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = nil )
      | ( hd(app(cons(hd(sk3),sk4),X0)) = hd(cons(hd(sk3),sk4)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_283]) ).

tcf(c_13167,plain,
    app(app(sk4,cons(hd(sk3),sk4)),nil) = app(sk4,cons(hd(sk3),sk4)),
    inference(superposition,[status(thm)],[c_12796,c_12353]) ).

tcf(c_13168,plain,
    app(app(sk3,cons(hd(sk3),sk4)),nil) = app(sk3,cons(hd(sk3),sk4)),
    inference(superposition,[status(thm)],[c_12796,c_12352]) ).

tcf(c_13169,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk4)),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_12796,c_3199]) ).

tcf(c_13170,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(nil,tl(cons(hd(sk3),sk4))) = tl(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3066]) ).

tcf(c_13171,plain,
    app(nil,app(sk4,cons(hd(sk3),sk4))) = app(sk4,cons(hd(sk3),sk4)),
    inference(superposition,[status(thm)],[c_12796,c_8061]) ).

tcf(c_13172,plain,
    app(app(sk4,sk4),cons(hd(sk3),sk4)) = app(sk4,app(sk4,cons(hd(sk3),sk4))),
    inference(superposition,[status(thm)],[c_12796,c_8048]) ).

tcf(c_13173,plain,
    app(nil,app(sk3,cons(hd(sk3),sk4))) = app(sk3,cons(hd(sk3),sk4)),
    inference(superposition,[status(thm)],[c_12796,c_5745]) ).

tcf(c_13174,plain,
    app(app(sk3,sk4),cons(hd(sk3),sk4)) = app(sk3,app(sk4,cons(hd(sk3),sk4))),
    inference(superposition,[status(thm)],[c_12796,c_8047]) ).

tcf(c_13175,plain,
    app(app(sk4,sk3),cons(hd(sk3),sk4)) = app(sk4,app(sk3,cons(hd(sk3),sk4))),
    inference(superposition,[status(thm)],[c_12796,c_5738]) ).

tcf(c_13176,plain,
    app(app(sk3,sk3),cons(hd(sk3),sk4)) = app(sk3,app(sk3,cons(hd(sk3),sk4))),
    inference(superposition,[status(thm)],[c_12796,c_5737]) ).

tcf(c_13177,plain,
    app(tl(sk4),cons(hd(sk3),sk4)) = tl(app(sk4,cons(hd(sk3),sk4))),
    inference(superposition,[status(thm)],[c_12796,c_4136]) ).

tcf(c_13178,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),sk4),sk4)) = app(cons(X0,cons(hd(sk3),sk4)),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_4462]) ).

tcf(c_13179,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),sk4),sk3)) = app(cons(X0,cons(hd(sk3),sk4)),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_4461]) ).

tcf(c_13180,plain,
    app(tl(sk3),cons(hd(sk3),sk4)) = tl(app(sk3,cons(hd(sk3),sk4))),
    inference(superposition,[status(thm)],[c_12796,c_4284]) ).

tcf(c_13181,plain,
    hd(app(sk3,cons(hd(sk3),sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_4027]) ).

tcf(c_13182,plain,
    hd(app(sk4,cons(hd(sk3),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_3885]) ).

tcf(c_13183,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk3),sk4))) = cons(X0,cons(hd(sk3),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3019]) ).

tcf(c_13184,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk4)),sk4),nil) = cons(hd(cons(hd(sk3),sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3452]) ).

tcf(c_13185,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk4)),sk3),nil) = cons(hd(cons(hd(sk3),sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3444]) ).

tcf(c_13186,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(tl(cons(hd(sk3),sk4)),nil) = tl(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3065]) ).

tcf(c_13187,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),sk4)) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3215]) ).

tcf(c_13188,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),sk3)) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3207]) ).

tcf(c_13189,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk3),sk4)) = cons(X0,cons(hd(sk3),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_253]) ).

tcf(c_13190,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( cons(hd(cons(hd(sk3),sk4)),tl(cons(hd(sk3),sk4))) = cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_275]) ).

tcf(c_13191,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk3),sk4)),nil) = cons(X0,cons(hd(sk3),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3018]) ).

tcf(c_13192,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk4)),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_12796,c_3191]) ).

tcf(c_13193,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk4)),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_12796,c_3183]) ).

tcf(c_13194,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk3),sk4))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_284]) ).

tcf(c_13195,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk3),sk4))) = cons(hd(sk3),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_276]) ).

tcf(c_13214,plain,
    ! [X0: $i] :
      ( ( cons(X0,cons(hd(sk3),app(sk4,sk3))) = app(cons(X0,cons(hd(sk3),sk4)),sk3) )
      | ~ ssItem(X0) ),
    inference(light_normalisation,[status(thm)],[c_13179,c_10126]) ).

tcf(c_13217,plain,
    ! [X0: $i] :
      ( ( cons(X0,cons(hd(sk3),app(sk4,sk4))) = app(cons(X0,cons(hd(sk3),sk4)),sk4) )
      | ~ ssItem(X0) ),
    inference(light_normalisation,[status(thm)],[c_13178,c_10123]) ).

tcf(c_13221,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),app(sk4,sk3)),X0) = app(cons(hd(sk3),sk4),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_13162,c_10126]) ).

tcf(c_13224,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),app(sk4,sk4)),X0) = app(cons(hd(sk3),sk4),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_13161,c_10123]) ).

tcf(c_13230,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = nil )
      | ( hd(app(cons(hd(sk3),sk4),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_13166,c_10137]) ).

tcf(c_13242,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = nil )
      | ( tl(app(cons(hd(sk3),sk4),X0)) = app(sk4,X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_13165,c_10140]) ).

tcf(c_13370,plain,
    app(app(nil,sk3),nil) = app(nil,sk3),
    inference(superposition,[status(thm)],[c_246,c_12354]) ).

tcf(c_13371,plain,
    app(app(nil,sk4),nil) = app(nil,sk4),
    inference(superposition,[status(thm)],[c_247,c_12354]) ).

tcf(c_13372,plain,
    app(app(nil,nil),nil) = app(nil,nil),
    inference(superposition,[status(thm)],[c_259,c_12354]) ).

tcf(c_13373,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(app(nil,tl(X0)),nil) = app(nil,tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_12354]) ).

tcf(c_13374,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(nil,app(X1,X0)),nil) = app(nil,app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_12354]) ).

tcf(c_13375,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(nil,cons(X1,X0)),nil) = app(nil,cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_12354]) ).

tcf(c_13376,plain,
    app(app(nil,cons(hd(sk4),sk3)),nil) = app(nil,cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4358,c_12354]) ).

tcf(c_13377,plain,
    app(app(nil,cons(hd(sk3),sk4)),nil) = app(nil,cons(hd(sk3),sk4)),
    inference(superposition,[status(thm)],[c_12796,c_12354]) ).

tcf(c_13378,plain,
    app(app(nil,cons(hd(sk4),sk4)),nil) = app(nil,cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4223,c_12354]) ).

tcf(c_13379,plain,
    app(app(nil,cons(hd(sk4),app(sk3,sk3))),nil) = app(nil,cons(hd(sk4),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_5886,c_12354]) ).

tcf(c_13380,plain,
    ( ( app(app(nil,app(sk3,app(sk3,sk3))),nil) = app(nil,app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_12354]) ).

tcf(c_13381,plain,
    ( ( app(app(nil,app(sk3,app(sk3,sk4))),nil) = app(nil,app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_12354]) ).

tcf(c_13382,plain,
    ( ( app(app(nil,app(sk4,app(sk3,sk3))),nil) = app(nil,app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_12354]) ).

tcf(c_13383,plain,
    app(app(nil,cons(hd(sk4),app(sk4,sk3))),nil) = app(nil,cons(hd(sk4),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_7540,c_12354]) ).

tcf(c_13384,plain,
    ( ( app(app(nil,app(sk4,app(sk3,sk4))),nil) = app(nil,app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_12354]) ).

tcf(c_13385,plain,
    ( ( app(app(nil,app(sk3,app(sk4,sk3))),nil) = app(nil,app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_12354]) ).

tcf(c_13386,plain,
    ( ( app(app(nil,app(sk3,app(sk4,sk4))),nil) = app(nil,app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_12354]) ).

tcf(c_13387,plain,
    ( ( app(app(nil,app(sk4,app(sk4,sk3))),nil) = app(nil,app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_12354]) ).

tcf(c_13388,plain,
    ( ( app(app(nil,app(sk4,app(sk4,sk4))),nil) = app(nil,app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_12354]) ).

tcf(c_13389,plain,
    app(app(nil,cons(hd(sk4),app(sk3,sk4))),nil) = app(nil,cons(hd(sk4),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_10188,c_12354]) ).

tcf(c_13390,plain,
    app(app(nil,cons(hd(sk4),app(sk4,sk4))),nil) = app(nil,cons(hd(sk4),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_10606,c_12354]) ).

tcf(c_13391,plain,
    ( ( app(app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil) = app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_12354]) ).

tcf(c_13392,plain,
    ( ( app(app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil) = app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_12354]) ).

tcf(c_13438,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk3),sk4))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_13194]) ).

tcf(c_13439,plain,
    hd(cons(hd(sk4),cons(hd(sk3),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_13194]) ).

tcf(c_13440,plain,
    hd(cons(hd(sk3),cons(hd(sk3),sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_13194]) ).

tcf(c_13452,plain,
    ! [X0: $i] :
      ( ( app(nil,app(nil,X0)) = app(nil,X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_3050]) ).

tcf(c_13453,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( app(nil,app(tl(X0),X1)) = app(tl(X0),X1) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3050]) ).

tcf(c_13454,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(nil,app(app(X1,X0),X2)) = app(app(X1,X0),X2) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3050]) ).

tcf(c_13455,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(nil,app(cons(X2,X0),X1)) = app(cons(X2,X0),X1) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3050]) ).

tcf(c_13456,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk4),sk3),X0)) = app(cons(hd(sk4),sk3),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3050]) ).

tcf(c_13457,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk3),sk4),X0)) = app(cons(hd(sk3),sk4),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3050]) ).

tcf(c_13458,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk4),sk4),X0)) = app(cons(hd(sk4),sk4),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3050]) ).

tcf(c_13459,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk4),app(sk3,sk3)),X0)) = app(cons(hd(sk4),app(sk3,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3050]) ).

tcf(c_13460,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk3,sk3)),X0)) = app(app(sk3,app(sk3,sk3)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3050]) ).

tcf(c_13461,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk3,sk4)),X0)) = app(app(sk3,app(sk3,sk4)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3050]) ).

tcf(c_13462,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk3,sk3)),X0)) = app(app(sk4,app(sk3,sk3)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3050]) ).

tcf(c_13463,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk4),app(sk4,sk3)),X0)) = app(cons(hd(sk4),app(sk4,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3050]) ).

tcf(c_13464,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk3,sk4)),X0)) = app(app(sk4,app(sk3,sk4)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3050]) ).

tcf(c_13465,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk4,sk3)),X0)) = app(app(sk3,app(sk4,sk3)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3050]) ).

tcf(c_13466,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk4,sk4)),X0)) = app(app(sk3,app(sk4,sk4)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3050]) ).

tcf(c_13467,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk4,sk3)),X0)) = app(app(sk4,app(sk4,sk3)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3050]) ).

tcf(c_13468,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk4,sk4)),X0)) = app(app(sk4,app(sk4,sk4)),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3050]) ).

tcf(c_13469,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk4),app(sk3,sk4)),X0)) = app(cons(hd(sk4),app(sk3,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3050]) ).

tcf(c_13470,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk4),app(sk4,sk4)),X0)) = app(cons(hd(sk4),app(sk4,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3050]) ).

tcf(c_13471,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)) = app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3050]) ).

tcf(c_13472,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)) = app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3050]) ).

tcf(c_13671,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),sk4))))
      | ( app(sk3,cons(hd(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),sk4)))
      | ~ ssList(app(sk3,cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13181,c_280]) ).

tcf(c_13672,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),sk4))))
      | ( app(sk3,cons(hd(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),sk4)))
      | ~ ssList(app(sk3,cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13181,c_279]) ).

tcf(c_13688,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),sk4))))
      | ( app(sk4,cons(hd(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),sk4)))
      | ~ ssList(app(sk4,cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13182,c_280]) ).

tcf(c_13689,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),sk4))))
      | ( app(sk4,cons(hd(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),sk4)))
      | ~ ssList(app(sk4,cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13182,c_279]) ).

tcf(c_13706,plain,
    ( ( cons(hd(sk3),nil) = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != nil ) ),
    inference(superposition,[status(thm)],[c_10133,c_255]) ).

tcf(c_13707,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != nil ) ),
    inference(superposition,[status(thm)],[c_10133,c_254]) ).

tcf(c_13708,plain,
    ( ssList(cons(hd(sk3),sk3))
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(superposition,[status(thm)],[c_10133,c_272]) ).

tcf(c_13709,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(cons(hd(sk3),nil),X0) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10133,c_270]) ).

tcf(c_13710,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),sk3) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_10133,c_269]) ).

tcf(c_13711,plain,
    ( ( cons(hd(sk3),nil) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( app(sk4,app(sk4,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10133,c_9243]) ).

tcf(c_13712,plain,
    ( ( cons(hd(sk3),nil) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( app(sk3,app(sk4,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10133,c_8266]) ).

tcf(c_13713,plain,
    ( ( cons(hd(sk3),nil) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ( app(sk4,app(sk3,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10133,c_7257]) ).

tcf(c_13714,plain,
    ( ( cons(hd(sk3),nil) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ( app(sk3,app(sk3,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10133,c_6600]) ).

tcf(c_13715,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10133,c_7546]) ).

tcf(c_13716,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10133,c_5892]) ).

tcf(c_13717,plain,
    ( ( cons(hd(sk3),nil) = nil )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != sk3 ) ),
    inference(superposition,[status(thm)],[c_10133,c_4683]) ).

tcf(c_13718,plain,
    ( ssList(cons(hd(sk3),sk3))
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13708,c_246]) ).

tcf(c_13724,plain,
    ( ( sk3 = nil )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13707,c_246]) ).

tcf(c_13728,plain,
    ( ( cons(hd(sk3),nil) = nil )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13706,c_246]) ).

tcf(c_13738,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),sk3) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13710,c_246]) ).

tcf(c_13743,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(cons(hd(sk3),nil),X0) != cons(hd(sk3),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13709,c_246]) ).

tcf(c_13784,plain,
    ssList(cons(hd(sk3),sk3)),
    inference(global_subsumption_just,[status(thm)],[c_13718,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7561,c_9260]) ).

tcf(c_13786,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk3),sk3),X0)) = app(cons(hd(sk3),sk3),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3050]) ).

tcf(c_13787,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),sk3),X0),nil) = app(cons(hd(sk3),sk3),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3049]) ).

tcf(c_13788,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),sk3),sk4),X0) = app(cons(hd(sk3),sk3),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_4540]) ).

tcf(c_13789,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),sk3),sk3),X0) = app(cons(hd(sk3),sk3),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_4539]) ).

tcf(c_13790,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk3),sk3)),X0) = app(X1,app(cons(hd(sk3),sk3),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_271]) ).

tcf(c_13791,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk3),sk3))) = app(cons(X1,X0),cons(hd(sk3),sk3)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_266]) ).

tcf(c_13792,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = nil )
      | ( app(tl(cons(hd(sk3),sk3)),X0) = tl(app(cons(hd(sk3),sk3),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_274]) ).

tcf(c_13793,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = nil )
      | ( hd(app(cons(hd(sk3),sk3),X0)) = hd(cons(hd(sk3),sk3)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_283]) ).

tcf(c_13794,plain,
    app(app(nil,cons(hd(sk3),sk3)),nil) = app(nil,cons(hd(sk3),sk3)),
    inference(superposition,[status(thm)],[c_13784,c_12354]) ).

tcf(c_13795,plain,
    app(app(sk4,cons(hd(sk3),sk3)),nil) = app(sk4,cons(hd(sk3),sk3)),
    inference(superposition,[status(thm)],[c_13784,c_12353]) ).

tcf(c_13796,plain,
    app(app(sk3,cons(hd(sk3),sk3)),nil) = app(sk3,cons(hd(sk3),sk3)),
    inference(superposition,[status(thm)],[c_13784,c_12352]) ).

tcf(c_13797,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk3)),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_13784,c_3199]) ).

tcf(c_13798,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(nil,tl(cons(hd(sk3),sk3))) = tl(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3066]) ).

tcf(c_13799,plain,
    app(nil,app(sk4,cons(hd(sk3),sk3))) = app(sk4,cons(hd(sk3),sk3)),
    inference(superposition,[status(thm)],[c_13784,c_8061]) ).

tcf(c_13800,plain,
    app(app(sk4,sk4),cons(hd(sk3),sk3)) = app(sk4,app(sk4,cons(hd(sk3),sk3))),
    inference(superposition,[status(thm)],[c_13784,c_8048]) ).

tcf(c_13801,plain,
    app(nil,app(sk3,cons(hd(sk3),sk3))) = app(sk3,cons(hd(sk3),sk3)),
    inference(superposition,[status(thm)],[c_13784,c_5745]) ).

tcf(c_13802,plain,
    app(app(sk3,sk4),cons(hd(sk3),sk3)) = app(sk3,app(sk4,cons(hd(sk3),sk3))),
    inference(superposition,[status(thm)],[c_13784,c_8047]) ).

tcf(c_13803,plain,
    app(app(sk4,sk3),cons(hd(sk3),sk3)) = app(sk4,app(sk3,cons(hd(sk3),sk3))),
    inference(superposition,[status(thm)],[c_13784,c_5738]) ).

tcf(c_13804,plain,
    app(app(sk3,sk3),cons(hd(sk3),sk3)) = app(sk3,app(sk3,cons(hd(sk3),sk3))),
    inference(superposition,[status(thm)],[c_13784,c_5737]) ).

tcf(c_13805,plain,
    app(tl(sk4),cons(hd(sk3),sk3)) = tl(app(sk4,cons(hd(sk3),sk3))),
    inference(superposition,[status(thm)],[c_13784,c_4136]) ).

tcf(c_13806,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),sk3),sk4)) = app(cons(X0,cons(hd(sk3),sk3)),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_4462]) ).

tcf(c_13807,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),sk3),sk3)) = app(cons(X0,cons(hd(sk3),sk3)),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_4461]) ).

tcf(c_13808,plain,
    app(tl(sk3),cons(hd(sk3),sk3)) = tl(app(sk3,cons(hd(sk3),sk3))),
    inference(superposition,[status(thm)],[c_13784,c_4284]) ).

tcf(c_13809,plain,
    hd(app(sk3,cons(hd(sk3),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_4027]) ).

tcf(c_13810,plain,
    hd(app(sk4,cons(hd(sk3),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_3885]) ).

tcf(c_13811,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk3),sk3))) = cons(X0,cons(hd(sk3),sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3019]) ).

tcf(c_13812,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk3)),sk4),nil) = cons(hd(cons(hd(sk3),sk3)),sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3452]) ).

tcf(c_13813,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk3)),sk3),nil) = cons(hd(cons(hd(sk3),sk3)),sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3444]) ).

tcf(c_13814,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(tl(cons(hd(sk3),sk3)),nil) = tl(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3065]) ).

tcf(c_13815,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),sk4)) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3215]) ).

tcf(c_13816,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),sk3)) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3207]) ).

tcf(c_13817,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk3),sk3)) = cons(X0,cons(hd(sk3),sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_253]) ).

tcf(c_13818,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( cons(hd(cons(hd(sk3),sk3)),tl(cons(hd(sk3),sk3))) = cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_275]) ).

tcf(c_13819,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk3),sk3)),nil) = cons(X0,cons(hd(sk3),sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3018]) ).

tcf(c_13820,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk3)),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_13784,c_3191]) ).

tcf(c_13821,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk3)),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_13784,c_3183]) ).

tcf(c_13822,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk3),sk3))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_284]) ).

tcf(c_13823,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk3),sk3))) = cons(hd(sk3),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_276]) ).

tcf(c_13845,plain,
    ! [X0: $i] :
      ( ( cons(X0,cons(hd(sk3),app(sk3,sk3))) = app(cons(X0,cons(hd(sk3),sk3)),sk3) )
      | ~ ssItem(X0) ),
    inference(light_normalisation,[status(thm)],[c_13807,c_10127]) ).

tcf(c_13848,plain,
    ! [X0: $i] :
      ( ( cons(X0,cons(hd(sk3),app(sk3,sk4))) = app(cons(X0,cons(hd(sk3),sk3)),sk4) )
      | ~ ssItem(X0) ),
    inference(light_normalisation,[status(thm)],[c_13806,c_10124]) ).

tcf(c_13852,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),app(sk3,sk3)),X0) = app(cons(hd(sk3),sk3),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_13789,c_10127]) ).

tcf(c_13855,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),app(sk3,sk4)),X0) = app(cons(hd(sk3),sk3),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_13788,c_10124]) ).

tcf(c_13861,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = nil )
      | ( hd(app(cons(hd(sk3),sk3),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_13793,c_10138]) ).

tcf(c_13873,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = nil )
      | ( tl(app(cons(hd(sk3),sk3),X0)) = app(sk3,X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_13792,c_10141]) ).

tcf(c_13952,plain,
    ( ( cons(hd(sk3),sk3) != nil )
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(global_subsumption_just,[status(thm)],[c_13724,c_9218]) ).

tcf(c_13953,plain,
    ( ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != nil ) ),
    inference(renaming,[status(thm)],[c_13952]) ).

tcf(c_13966,plain,
    ( ( cons(hd(sk4),nil) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ( app(sk4,app(sk4,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_9522]) ).

tcf(c_13967,plain,
    ( ( cons(hd(sk4),sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5702,c_9522]) ).

tcf(c_13968,plain,
    ( ( cons(hd(sk4),sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5719,c_9522]) ).

tcf(c_13973,plain,
    ( ( cons(hd(sk3),nil) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( app(sk4,app(sk4,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_9522]) ).

tcf(c_13982,plain,
    ( ( cons(hd(sk4),sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( cons(hd(sk4),app(sk4,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13968,c_4223]) ).

tcf(c_13986,plain,
    ( ( cons(hd(sk4),sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( cons(hd(sk4),app(sk3,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13967,c_4358]) ).

tcf(c_13998,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk4)) != app(sk4,sk4) ) ),
    inference(superposition,[status(thm)],[c_9176,c_9527]) ).

tcf(c_13999,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9160,c_9527]) ).

tcf(c_14001,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk4)) != app(sk4,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13998,c_1243,c_259]) ).

tcf(c_14022,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),sk3) != app(X0,sk3) ) ),
    inference(global_subsumption_just,[status(thm)],[c_4702,c_247,c_259,c_1242,c_3439,c_3715,c_4702]) ).

tcf(c_14032,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4976,c_14022]) ).

tcf(c_14033,plain,
    ( ( cons(hd(sk4),sk4) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4999,c_14022]) ).

tcf(c_14034,plain,
    ( ( cons(hd(sk4),nil) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_5817,c_14022]) ).

tcf(c_14035,plain,
    ( ( cons(hd(sk4),nil) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_7182,c_14022]) ).

tcf(c_14036,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_10133,c_14022]) ).

tcf(c_14037,plain,
    ( ( cons(hd(sk4),nil) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_8158,c_14022]) ).

tcf(c_14038,plain,
    ( ( cons(hd(sk4),nil) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_9160,c_14022]) ).

tcf(c_14054,plain,
    ( ( cons(hd(sk4),sk4) = cons(hd(sk4),nil) )
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14033,c_4223]) ).

tcf(c_14057,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),nil) )
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14032,c_4358]) ).

tcf(c_14075,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),sk4) != app(X0,sk4) ) ),
    inference(global_subsumption_just,[status(thm)],[c_4707,c_247,c_259,c_1242,c_3439,c_3715,c_4707]) ).

tcf(c_14085,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_5702,c_14075]) ).

tcf(c_14087,plain,
    ( ( cons(hd(sk4),nil) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_5818,c_14075]) ).

tcf(c_14088,plain,
    ( ( cons(hd(sk4),nil) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_7183,c_14075]) ).

tcf(c_14089,plain,
    ( ( cons(hd(sk4),nil) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_8159,c_14075]) ).

tcf(c_14090,plain,
    ( ( cons(hd(sk4),nil) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_9161,c_14075]) ).

tcf(c_14091,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk4) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_14075]) ).

tcf(c_14107,plain,
    ( ( cons(hd(sk4),sk3) = cons(hd(sk4),nil) )
    | ( cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14085,c_4358]) ).

tcf(c_14143,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),nil),X0) != cons(hd(sk4),sk3) ) ),
    inference(global_subsumption_just,[status(thm)],[c_5172,c_247,c_259,c_1242,c_3439,c_3715,c_5172]) ).

tcf(c_14152,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk4),sk3) != cons(hd(sk4),nil) ) ),
    inference(superposition,[status(thm)],[c_4069,c_14143]) ).

tcf(c_14153,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ( cons(hd(sk4),sk3) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_14143]) ).

tcf(c_14155,plain,
    ( ( sk3 = sk4 )
    | ( cons(hd(sk4),sk3) != cons(hd(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14153,c_247]) ).

tcf(c_14158,plain,
    ( ( sk3 = nil )
    | ( cons(hd(sk4),sk3) != cons(hd(sk4),nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14152,c_259]) ).

tcf(c_14180,plain,
    ( ssList(app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))
    | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_6388,c_278]) ).

tcf(c_14181,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = nil )
      | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3))))
      | ( hd(app(sk4,cons(hd(sk4),app(sk3,sk3)))) != hd(X0) )
      | ( app(tl(sk4),cons(hd(sk4),app(sk3,sk3))) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_6388,c_273]) ).

tcf(c_14185,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = nil )
      | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3))))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),cons(hd(sk4),app(sk3,sk3))) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_14181,c_6393]) ).

tcf(c_14197,plain,
    app(nil,app(nil,sk3)) = app(nil,sk3),
    inference(superposition,[status(thm)],[c_246,c_13452]) ).

tcf(c_14198,plain,
    app(nil,app(nil,sk4)) = app(nil,sk4),
    inference(superposition,[status(thm)],[c_247,c_13452]) ).

tcf(c_14199,plain,
    app(nil,app(nil,nil)) = app(nil,nil),
    inference(superposition,[status(thm)],[c_259,c_13452]) ).

tcf(c_14200,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(nil,app(nil,tl(X0))) = app(nil,tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_13452]) ).

tcf(c_14201,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(nil,app(nil,app(X1,X0))) = app(nil,app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_13452]) ).

tcf(c_14202,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(nil,app(nil,cons(X1,X0))) = app(nil,cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_13452]) ).

tcf(c_14203,plain,
    app(nil,app(nil,cons(hd(sk3),sk3))) = app(nil,cons(hd(sk3),sk3)),
    inference(superposition,[status(thm)],[c_13784,c_13452]) ).

tcf(c_14204,plain,
    app(nil,app(nil,cons(hd(sk4),sk3))) = app(nil,cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4358,c_13452]) ).

tcf(c_14205,plain,
    app(nil,app(nil,cons(hd(sk3),sk4))) = app(nil,cons(hd(sk3),sk4)),
    inference(superposition,[status(thm)],[c_12796,c_13452]) ).

tcf(c_14206,plain,
    app(nil,app(nil,cons(hd(sk4),sk4))) = app(nil,cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4223,c_13452]) ).

tcf(c_14207,plain,
    app(nil,app(nil,cons(hd(sk4),app(sk3,sk3)))) = app(nil,cons(hd(sk4),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_5886,c_13452]) ).

tcf(c_14208,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk3,sk3)))) = app(nil,app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_13452]) ).

tcf(c_14209,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk3,sk4)))) = app(nil,app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_13452]) ).

tcf(c_14210,plain,
    ( ( app(nil,app(nil,app(sk4,app(sk3,sk3)))) = app(nil,app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_13452]) ).

tcf(c_14211,plain,
    app(nil,app(nil,cons(hd(sk4),app(sk4,sk3)))) = app(nil,cons(hd(sk4),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_7540,c_13452]) ).

tcf(c_14212,plain,
    ( ( app(nil,app(nil,app(sk4,app(sk3,sk4)))) = app(nil,app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_13452]) ).

tcf(c_14213,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk4,sk3)))) = app(nil,app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_13452]) ).

tcf(c_14214,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk4,sk4)))) = app(nil,app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_13452]) ).

tcf(c_14215,plain,
    ( ( app(nil,app(nil,app(sk4,app(sk4,sk3)))) = app(nil,app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_13452]) ).

tcf(c_14216,plain,
    ( ( app(nil,app(nil,app(sk4,app(sk4,sk4)))) = app(nil,app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_13452]) ).

tcf(c_14217,plain,
    app(nil,app(nil,cons(hd(sk4),app(sk3,sk4)))) = app(nil,cons(hd(sk4),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_10188,c_13452]) ).

tcf(c_14218,plain,
    app(nil,app(nil,cons(hd(sk4),app(sk4,sk4)))) = app(nil,cons(hd(sk4),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_10606,c_13452]) ).

tcf(c_14219,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_13452]) ).

tcf(c_14220,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_13452]) ).

tcf(c_14345,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk3),sk3))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_13822]) ).

tcf(c_14346,plain,
    hd(cons(hd(sk4),cons(hd(sk3),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_13822]) ).

tcf(c_14347,plain,
    hd(cons(hd(sk3),cons(hd(sk3),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_13822]) ).

tcf(c_14360,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),nil)) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3423]) ).

tcf(c_14361,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),nil)) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3423]) ).

tcf(c_14362,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),nil)) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3423]) ).

tcf(c_14363,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),nil)) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3423]) ).

tcf(c_14364,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),nil)) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3423]) ).

tcf(c_14365,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),nil)) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3423]) ).

tcf(c_14366,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),nil)) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3423]) ).

tcf(c_14367,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil)) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3423]) ).

tcf(c_14368,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),nil)) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3423]) ).

tcf(c_14369,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),nil)) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3423]) ).

tcf(c_14370,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),nil)) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3423]) ).

tcf(c_14371,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil)) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3423]) ).

tcf(c_14372,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),nil)) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3423]) ).

tcf(c_14373,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),nil)) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3423]) ).

tcf(c_14374,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),nil)) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3423]) ).

tcf(c_14375,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),nil)) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3423]) ).

tcf(c_14376,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),nil)) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3423]) ).

tcf(c_14377,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil)) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3423]) ).

tcf(c_14378,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil)) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3423]) ).

tcf(c_14379,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil)) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3423]) ).

tcf(c_14380,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil)) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3423]) ).

tcf(c_14397,plain,
    hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil)) = hd(cons(hd(sk4),app(sk4,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_14378,c_10611]) ).

tcf(c_14398,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil)) = hd(cons(hd(sk4),app(sk3,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_14377,c_10190]) ).

tcf(c_14399,plain,
    hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil)) = hd(cons(hd(sk4),app(sk4,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_14371,c_7545]) ).

tcf(c_14400,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil)) = hd(cons(hd(sk4),app(sk3,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_14367,c_5891]) ).

tcf(c_14539,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),sk3))))
      | ( app(sk3,cons(hd(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),sk3)))
      | ~ ssList(app(sk3,cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_13809,c_280]) ).

tcf(c_14540,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),sk3))))
      | ( app(sk3,cons(hd(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),sk3)))
      | ~ ssList(app(sk3,cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_13809,c_279]) ).

tcf(c_14554,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),sk3))))
      | ( app(sk4,cons(hd(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),sk3)))
      | ~ ssList(app(sk4,cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_13810,c_280]) ).

tcf(c_14555,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),sk3))))
      | ( app(sk4,cons(hd(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),sk3)))
      | ~ ssList(app(sk4,cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_13810,c_279]) ).

tcf(c_14569,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),sk4))))
      | ( cons(hd(sk4),cons(hd(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),sk4)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13439,c_280]) ).

tcf(c_14570,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),sk4))))
      | ( cons(hd(sk4),cons(hd(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk3),sk4)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13439,c_279]) ).

tcf(c_14586,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),sk4))))
      | ( cons(hd(sk3),cons(hd(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),sk4)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13440,c_280]) ).

tcf(c_14587,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),sk4))))
      | ( cons(hd(sk3),cons(hd(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk3),sk4)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13440,c_279]) ).

tcf(c_14602,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),nil),X0) != cons(hd(sk4),sk4) ) ),
    inference(global_subsumption_just,[status(thm)],[c_5177,c_247,c_259,c_1242,c_3439,c_3715,c_5177]) ).

tcf(c_14611,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk4),sk4) != cons(hd(sk4),nil) ) ),
    inference(superposition,[status(thm)],[c_4069,c_14602]) ).

tcf(c_14613,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ( cons(hd(sk4),sk3) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4071,c_14602]) ).

tcf(c_14615,plain,
    cons(hd(sk4),sk4) != cons(hd(sk4),nil),
    inference(forward_subsumption_resolution,[status(thm)],[c_14611,c_1243,c_259]) ).

tcf(c_14624,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk4) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_12749]) ).

tcf(c_14625,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk4),app(sk3,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_5702,c_12749]) ).

tcf(c_14626,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk4),app(sk4,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_5719,c_12749]) ).

tcf(c_14646,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10133,c_12754]) ).

tcf(c_14647,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk4) != cons(hd(sk3),nil) ) ),
    inference(superposition,[status(thm)],[c_10131,c_12754]) ).

tcf(c_14649,plain,
    ( ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk4) != cons(hd(sk3),nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14647,c_1243,c_259]) ).

tcf(c_14652,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != cons(hd(sk3),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14646,c_246]) ).

tcf(c_14670,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_13738]) ).

tcf(c_14671,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_4976,c_13738]) ).

tcf(c_14672,plain,
    ( ( cons(hd(sk3),nil) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_4999,c_13738]) ).

tcf(c_14693,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != cons(hd(sk3),nil) ) ),
    inference(superposition,[status(thm)],[c_10131,c_13743]) ).

tcf(c_14694,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10132,c_13743]) ).

tcf(c_14696,plain,
    ( ( sk3 = nil )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),sk3) != cons(hd(sk3),nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14693,c_259]) ).

tcf(c_14710,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(cons(hd(sk4),sk3))
      | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_6189]) ).

tcf(c_14711,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(cons(hd(sk4),sk3),sk3))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_6189]) ).

tcf(c_14712,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(cons(hd(sk4),sk3),sk4))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_6189]) ).

tcf(c_14713,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14710,c_4358]) ).

tcf(c_14719,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(cons(hd(sk4),app(sk3,sk4)))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4))) ),
    inference(light_normalisation,[status(thm)],[c_14712,c_3365,c_5702]) ).

tcf(c_14720,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(cons(hd(sk4),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14719,c_4059,c_10188]) ).

tcf(c_14724,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_14711,c_4976]) ).

tcf(c_14725,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14724,c_10117,c_5886]) ).

tcf(c_14741,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(cons(hd(sk4),sk4))
      | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_6196]) ).

tcf(c_14742,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(cons(hd(sk4),sk4),sk3))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_6196]) ).

tcf(c_14743,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(cons(hd(sk4),sk4),sk4))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_6196]) ).

tcf(c_14744,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14741,c_4223]) ).

tcf(c_14750,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(cons(hd(sk4),app(sk4,sk4)))
    | ~ ssList(cons(hd(sk4),app(sk4,sk4))) ),
    inference(light_normalisation,[status(thm)],[c_14743,c_3365,c_5719]) ).

tcf(c_14751,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(cons(hd(sk4),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14750,c_4059,c_10606]) ).

tcf(c_14755,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_14742,c_4999]) ).

tcf(c_14756,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14755,c_10117,c_7540]) ).

tcf(c_14763,plain,
    ( ssList(app(tl(sk3),cons(hd(sk4),app(sk3,sk3))))
    | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_6391,c_278]) ).

tcf(c_14764,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = nil )
      | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3))))
      | ( hd(app(sk3,cons(hd(sk4),app(sk3,sk3)))) != hd(X0) )
      | ( app(tl(sk3),cons(hd(sk4),app(sk3,sk3))) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_6391,c_273]) ).

tcf(c_14768,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = nil )
      | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3))))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),cons(hd(sk4),app(sk3,sk3))) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_14764,c_6392]) ).

tcf(c_14784,plain,
    ( ( sk3 = nil )
    | ( hd(app(sk4,tl(sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_246,c_3951]) ).

tcf(c_14785,plain,
    ( ( sk4 = nil )
    | ( hd(app(sk4,tl(sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_3951]) ).

tcf(c_14787,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk4,tl(tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3951]) ).

tcf(c_14788,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk4,tl(app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3951]) ).

tcf(c_14789,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk4,tl(cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3951]) ).

tcf(c_14790,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk3),sk3)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3951]) ).

tcf(c_14791,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk4),sk3)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3951]) ).

tcf(c_14792,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk3),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3951]) ).

tcf(c_14793,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3951]) ).

tcf(c_14794,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3951]) ).

tcf(c_14795,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3951]) ).

tcf(c_14796,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3951]) ).

tcf(c_14797,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3951]) ).

tcf(c_14798,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3951]) ).

tcf(c_14799,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3951]) ).

tcf(c_14800,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3951]) ).

tcf(c_14801,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3951]) ).

tcf(c_14802,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3951]) ).

tcf(c_14803,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3951]) ).

tcf(c_14804,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3951]) ).

tcf(c_14805,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3951]) ).

tcf(c_14806,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3951]) ).

tcf(c_14807,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3951]) ).

tcf(c_14808,plain,
    hd(app(sk4,tl(sk4))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_14785,c_1243]) ).

tcf(c_14819,plain,
    hd(app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_14805,c_10611]) ).

tcf(c_14820,plain,
    hd(app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_14804,c_10190]) ).

tcf(c_14821,plain,
    hd(app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_14798,c_7545]) ).

tcf(c_14822,plain,
    hd(app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_14794,c_5891]) ).

tcf(c_14905,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,tl(sk4))))
      | ( app(sk4,tl(sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,tl(sk4)))
      | ~ ssList(app(sk4,tl(sk4))) ),
    inference(superposition,[status(thm)],[c_14808,c_280]) ).

tcf(c_14906,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,tl(sk4))))
      | ( app(sk4,tl(sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,tl(sk4)))
      | ~ ssList(app(sk4,tl(sk4))) ),
    inference(superposition,[status(thm)],[c_14808,c_279]) ).

tcf(c_14921,plain,
    hd(app(sk4,tl(sk3))) = hd(sk4),
    inference(global_subsumption_just,[status(thm)],[c_14784,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_14784]) ).

tcf(c_14924,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,tl(sk3))))
      | ( app(sk4,tl(sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,tl(sk3)))
      | ~ ssList(app(sk4,tl(sk3))) ),
    inference(superposition,[status(thm)],[c_14921,c_280]) ).

tcf(c_14925,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,tl(sk3))))
      | ( app(sk4,tl(sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,tl(sk3)))
      | ~ ssList(app(sk4,tl(sk3))) ),
    inference(superposition,[status(thm)],[c_14921,c_279]) ).

tcf(c_14941,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),sk3))))
      | ( cons(hd(sk4),cons(hd(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),sk3)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_14346,c_280]) ).

tcf(c_14942,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),sk3))))
      | ( cons(hd(sk4),cons(hd(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk3),sk3)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_14346,c_279]) ).

tcf(c_14956,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),sk3))))
      | ( cons(hd(sk3),cons(hd(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),sk3)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_14347,c_280]) ).

tcf(c_14957,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),sk3))))
      | ( cons(hd(sk3),cons(hd(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk3),sk3)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_14347,c_279]) ).

tcf(c_14980,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
      | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_10217,c_280]) ).

tcf(c_14981,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
      | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_10217,c_279]) ).

tcf(c_15046,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(cons(hd(sk4),sk3))
      | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_6325]) ).

tcf(c_15047,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(cons(hd(sk4),sk3),sk3))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_6325]) ).

tcf(c_15048,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(cons(hd(sk4),sk3),sk4))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_6325]) ).

tcf(c_15049,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15046,c_4358]) ).

tcf(c_15055,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4)))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4))) ),
    inference(light_normalisation,[status(thm)],[c_15048,c_3365,c_5702]) ).

tcf(c_15056,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15055,c_4059,c_10188]) ).

tcf(c_15060,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_15047,c_4976]) ).

tcf(c_15061,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15060,c_10117,c_5886]) ).

tcf(c_15086,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(cons(hd(sk4),sk4))
      | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_6332]) ).

tcf(c_15087,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(cons(hd(sk4),sk4),sk3))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_6332]) ).

tcf(c_15088,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(cons(hd(sk4),sk4),sk4))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_6332]) ).

tcf(c_15089,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15086,c_4223]) ).

tcf(c_15095,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk4)))
    | ~ ssList(cons(hd(sk4),app(sk4,sk4))) ),
    inference(light_normalisation,[status(thm)],[c_15088,c_3365,c_5719]) ).

tcf(c_15096,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15095,c_4059,c_10606]) ).

tcf(c_15100,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_15087,c_4999]) ).

tcf(c_15101,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15100,c_10117,c_7540]) ).

tcf(c_15117,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(cons(hd(sk3),sk4))
      | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_12622]) ).

tcf(c_15118,plain,
    ( lt(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(cons(hd(sk3),sk4),sk3))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_12622]) ).

tcf(c_15119,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(cons(hd(sk3),sk4),sk4))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_12622]) ).

tcf(c_15120,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15117,c_12796]) ).

tcf(c_15126,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(cons(hd(sk3),app(sk4,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk4,sk4))) ),
    inference(light_normalisation,[status(thm)],[c_15119,c_3365,c_10123]) ).

tcf(c_15127,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(cons(hd(sk3),app(sk4,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15126,c_4059]) ).

tcf(c_15132,plain,
    ( lt(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk3),app(sk4,sk3)))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_15118,c_10126]) ).

tcf(c_15133,plain,
    ( lt(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk3),app(sk4,sk3)))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15132,c_10117]) ).

tcf(c_15193,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(cons(hd(sk3),sk4))
      | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_12629]) ).

tcf(c_15194,plain,
    ( leq(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(cons(hd(sk3),sk4),sk3))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_12629]) ).

tcf(c_15195,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(cons(hd(sk3),sk4),sk4))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_12629]) ).

tcf(c_15196,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15193,c_12796]) ).

tcf(c_15202,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(cons(hd(sk3),app(sk4,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk4,sk4))) ),
    inference(light_normalisation,[status(thm)],[c_15195,c_3365,c_10123]) ).

tcf(c_15203,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(cons(hd(sk3),app(sk4,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15202,c_4059]) ).

tcf(c_15208,plain,
    ( leq(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk3),app(sk4,sk3)))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_15194,c_10126]) ).

tcf(c_15209,plain,
    ( leq(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk3),app(sk4,sk3)))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15208,c_10117]) ).

tcf(c_15226,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(cons(hd(sk3),sk3))
      | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_12660]) ).

tcf(c_15227,plain,
    ( lt(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(cons(hd(sk3),sk3),sk3))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_12660]) ).

tcf(c_15228,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(cons(hd(sk3),sk3),sk4))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_12660]) ).

tcf(c_15229,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15226,c_13784]) ).

tcf(c_15235,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(cons(hd(sk3),app(sk3,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk3,sk4))) ),
    inference(light_normalisation,[status(thm)],[c_15228,c_3365,c_10124]) ).

tcf(c_15236,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(cons(hd(sk3),app(sk3,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15235,c_4059]) ).

tcf(c_15241,plain,
    ( lt(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk3),app(sk3,sk3)))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_15227,c_10127]) ).

tcf(c_15242,plain,
    ( lt(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk3),app(sk3,sk3)))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15241,c_10117]) ).

tcf(c_15259,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(cons(hd(sk3),sk3))
      | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_12667]) ).

tcf(c_15260,plain,
    ( leq(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(cons(hd(sk3),sk3),sk3))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_12667]) ).

tcf(c_15261,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(cons(hd(sk3),sk3),sk4))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_12667]) ).

tcf(c_15262,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15259,c_13784]) ).

tcf(c_15268,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(cons(hd(sk3),app(sk3,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk3,sk4))) ),
    inference(light_normalisation,[status(thm)],[c_15261,c_3365,c_10124]) ).

tcf(c_15269,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(cons(hd(sk3),app(sk3,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15268,c_4059]) ).

tcf(c_15274,plain,
    ( leq(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk3),app(sk3,sk3)))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_15260,c_10127]) ).

tcf(c_15275,plain,
    ( leq(hd(sk3),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(cons(hd(sk3),app(sk3,sk3)))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15274,c_10117]) ).

tcf(c_15310,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk3))))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_11277]) ).

tcf(c_15311,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk3))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_11277]) ).

tcf(c_15312,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_11277]) ).

tcf(c_15320,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_15312,c_3365]) ).

tcf(c_15321,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15320,c_4059]) ).

tcf(c_15327,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk3))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15311,c_10117]) ).

tcf(c_15347,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk3))))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_11285]) ).

tcf(c_15348,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk3))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_11285]) ).

tcf(c_15349,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_11285]) ).

tcf(c_15357,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_15349,c_3365]) ).

tcf(c_15358,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15357,c_4059]) ).

tcf(c_15364,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),sk3))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15348,c_10117]) ).

tcf(c_15372,plain,
    app(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4),nil) = cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4),
    inference(global_subsumption_just,[status(thm)],[c_6395,c_5891,c_6395]) ).

tcf(c_15382,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))
      | ( app(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4),X0) != cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_15372,c_270]) ).

tcf(c_15383,plain,
    ! [X0: $i] :
      ( ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_15372,c_269]) ).

tcf(c_15384,plain,
    ! [X0: $i] :
      ( ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15383,c_259]) ).

tcf(c_15389,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))
      | ( app(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4),X0) != cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15382,c_259]) ).

tcf(c_15401,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_3952]) ).

tcf(c_15402,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_3952]) ).

tcf(c_15403,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_3952]) ).

tcf(c_15404,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(tl(X0),X1))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3952]) ).

tcf(c_15405,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(app(X1,X0),X2))) = hd(sk4) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3952]) ).

tcf(c_15406,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(cons(X2,X0),X1))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3952]) ).

tcf(c_15407,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),sk3),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3952]) ).

tcf(c_15408,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),sk3),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3952]) ).

tcf(c_15409,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),sk4),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3952]) ).

tcf(c_15410,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),sk4),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3952]) ).

tcf(c_15411,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),app(sk3,sk3)),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3952]) ).

tcf(c_15412,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk3,sk3)),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3952]) ).

tcf(c_15413,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk3,sk4)),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3952]) ).

tcf(c_15414,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk3,sk3)),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3952]) ).

tcf(c_15415,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),app(sk4,sk3)),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3952]) ).

tcf(c_15416,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk3,sk4)),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3952]) ).

tcf(c_15417,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk4,sk3)),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3952]) ).

tcf(c_15418,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk4,sk4)),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3952]) ).

tcf(c_15419,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk4,sk3)),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3952]) ).

tcf(c_15420,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk4,sk4)),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3952]) ).

tcf(c_15421,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),app(sk3,sk4)),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3952]) ).

tcf(c_15422,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),app(sk4,sk4)),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3952]) ).

tcf(c_15423,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3952]) ).

tcf(c_15424,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3952]) ).

tcf(c_15589,plain,
    hd(app(sk4,app(sk3,sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_15401]) ).

tcf(c_15590,plain,
    hd(app(sk4,app(sk3,sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_15401]) ).

tcf(c_15591,plain,
    hd(app(sk4,app(sk3,nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_15401]) ).

tcf(c_15592,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk3,tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15401]) ).

tcf(c_15593,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk3,app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15401]) ).

tcf(c_15594,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15401]) ).

tcf(c_15595,plain,
    hd(app(sk4,app(sk3,cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_15401]) ).

tcf(c_15596,plain,
    hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_15401]) ).

tcf(c_15597,plain,
    hd(app(sk4,app(sk3,cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_15401]) ).

tcf(c_15598,plain,
    hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_15401]) ).

tcf(c_15599,plain,
    hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_15401]) ).

tcf(c_15600,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15401]) ).

tcf(c_15601,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15401]) ).

tcf(c_15602,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15401]) ).

tcf(c_15603,plain,
    hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_15401]) ).

tcf(c_15604,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15401]) ).

tcf(c_15605,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15401]) ).

tcf(c_15606,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15401]) ).

tcf(c_15607,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15401]) ).

tcf(c_15608,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15401]) ).

tcf(c_15609,plain,
    hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_15401]) ).

tcf(c_15610,plain,
    hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_15401]) ).

tcf(c_15611,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15401]) ).

tcf(c_15612,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15401]) ).

tcf(c_15834,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,sk3))))
      | ( app(sk4,app(sk3,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,sk3)))
      | ~ ssList(app(sk4,app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_15589,c_280]) ).

tcf(c_15835,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,sk3))))
      | ( app(sk4,app(sk3,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,sk3)))
      | ~ ssList(app(sk4,app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_15589,c_279]) ).

tcf(c_15851,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,sk4))))
      | ( app(sk4,app(sk3,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,sk4)))
      | ~ ssList(app(sk4,app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_15590,c_280]) ).

tcf(c_15852,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,sk4))))
      | ( app(sk4,app(sk3,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,sk4)))
      | ~ ssList(app(sk4,app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_15590,c_279]) ).

tcf(c_15868,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
      | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_10218,c_280]) ).

tcf(c_15869,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
      | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_10218,c_279]) ).

tcf(c_15885,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),app(sk4,sk4)))))
      | ( app(sk3,cons(hd(sk4),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),app(sk4,sk4))))
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_10683,c_280]) ).

tcf(c_15886,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),app(sk4,sk4)))))
      | ( app(sk3,cons(hd(sk4),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),app(sk4,sk4))))
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_10683,c_279]) ).

tcf(c_15942,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),app(sk4,sk4)))))
      | ( app(sk4,cons(hd(sk4),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),app(sk4,sk4))))
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_10684,c_280]) ).

tcf(c_15943,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),app(sk4,sk4)))))
      | ( app(sk4,cons(hd(sk4),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),app(sk4,sk4))))
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_10684,c_279]) ).

tcf(c_15962,plain,
    hd(app(sk4,app(sk4,sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_15402]) ).

tcf(c_15963,plain,
    hd(app(sk4,app(sk4,sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_15402]) ).

tcf(c_15964,plain,
    hd(app(sk4,app(sk4,nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_15402]) ).

tcf(c_15965,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk4,tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15402]) ).

tcf(c_15966,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk4,app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15402]) ).

tcf(c_15967,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15402]) ).

tcf(c_15968,plain,
    hd(app(sk4,app(sk4,cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_15402]) ).

tcf(c_15969,plain,
    hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_15402]) ).

tcf(c_15970,plain,
    hd(app(sk4,app(sk4,cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_15402]) ).

tcf(c_15971,plain,
    hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_15402]) ).

tcf(c_15972,plain,
    hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_15402]) ).

tcf(c_15973,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15402]) ).

tcf(c_15974,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15402]) ).

tcf(c_15975,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15402]) ).

tcf(c_15976,plain,
    hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_15402]) ).

tcf(c_15977,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15402]) ).

tcf(c_15978,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15402]) ).

tcf(c_15979,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15402]) ).

tcf(c_15980,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15402]) ).

tcf(c_15981,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15402]) ).

tcf(c_15982,plain,
    hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_15402]) ).

tcf(c_15983,plain,
    hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_15402]) ).

tcf(c_15984,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15402]) ).

tcf(c_15985,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15402]) ).

tcf(c_16155,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,sk3))))
      | ( app(sk4,app(sk4,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,sk3)))
      | ~ ssList(app(sk4,app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_15962,c_280]) ).

tcf(c_16156,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,sk3))))
      | ( app(sk4,app(sk4,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,sk3)))
      | ~ ssList(app(sk4,app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_15962,c_279]) ).

tcf(c_16172,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,sk4))))
      | ( app(sk4,app(sk4,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,sk4)))
      | ~ ssList(app(sk4,app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_15963,c_280]) ).

tcf(c_16173,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,sk4))))
      | ( app(sk4,app(sk4,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,sk4)))
      | ~ ssList(app(sk4,app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_15963,c_279]) ).

tcf(c_16208,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk4))))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_12044]) ).

tcf(c_16209,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk3))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_12044]) ).

tcf(c_16210,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_12044]) ).

tcf(c_16218,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_16210,c_3365]) ).

tcf(c_16219,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16218,c_4059]) ).

tcf(c_16225,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk3))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16209,c_10117]) ).

tcf(c_16245,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk4))))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_12052]) ).

tcf(c_16246,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk3))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_12052]) ).

tcf(c_16247,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_12052]) ).

tcf(c_16255,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_16247,c_3365]) ).

tcf(c_16256,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16255,c_4059]) ).

tcf(c_16262,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),sk3))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16246,c_10117]) ).

tcf(c_16279,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk4,sk4))),nil) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk4,sk4))),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_11558,c_273]) ).

tcf(c_16280,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk4,sk4))),nil) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk4,sk4))),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(sk4),app(sk4,sk4))) != hd(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_16279,c_14397]) ).

tcf(c_16290,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk4))),nil) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk4))),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_11559,c_273]) ).

tcf(c_16291,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk4))),nil) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk4))),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(sk4),app(sk3,sk4))) != hd(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_16290,c_14398]) ).

tcf(c_16299,plain,
    app(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3),nil) = cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3),
    inference(global_subsumption_just,[status(thm)],[c_6396,c_5891,c_6396]) ).

tcf(c_16309,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))
      | ( app(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3),X0) != cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_16299,c_270]) ).

tcf(c_16310,plain,
    ! [X0: $i] :
      ( ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_16299,c_269]) ).

tcf(c_16311,plain,
    ! [X0: $i] :
      ( ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16310,c_259]) ).

tcf(c_16316,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))
      | ( app(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3),X0) != cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16309,c_259]) ).

tcf(c_16326,plain,
    hd(app(sk4,app(nil,sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_15403]) ).

tcf(c_16327,plain,
    hd(app(sk4,app(nil,sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_15403]) ).

tcf(c_16328,plain,
    hd(app(sk4,app(nil,nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_15403]) ).

tcf(c_16329,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(nil,tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15403]) ).

tcf(c_16330,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(nil,app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15403]) ).

tcf(c_16331,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(nil,cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15403]) ).

tcf(c_16332,plain,
    hd(app(sk4,app(nil,cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_15403]) ).

tcf(c_16333,plain,
    hd(app(sk4,app(nil,cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_15403]) ).

tcf(c_16334,plain,
    hd(app(sk4,app(nil,cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_15403]) ).

tcf(c_16335,plain,
    hd(app(sk4,app(nil,cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_15403]) ).

tcf(c_16336,plain,
    hd(app(sk4,app(nil,cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_15403]) ).

tcf(c_16337,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15403]) ).

tcf(c_16338,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15403]) ).

tcf(c_16339,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15403]) ).

tcf(c_16340,plain,
    hd(app(sk4,app(nil,cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_15403]) ).

tcf(c_16341,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15403]) ).

tcf(c_16342,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15403]) ).

tcf(c_16343,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15403]) ).

tcf(c_16344,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15403]) ).

tcf(c_16345,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15403]) ).

tcf(c_16346,plain,
    hd(app(sk4,app(nil,cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_15403]) ).

tcf(c_16347,plain,
    hd(app(sk4,app(nil,cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_15403]) ).

tcf(c_16348,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15403]) ).

tcf(c_16349,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15403]) ).

tcf(c_16547,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,sk3))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_3953]) ).

tcf(c_16548,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,sk4))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_3953]) ).

tcf(c_16549,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,nil))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_3953]) ).

tcf(c_16550,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,cons(X1,tl(X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3953]) ).

tcf(c_16551,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,cons(X2,app(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3953]) ).

tcf(c_16552,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,cons(X2,cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3953]) ).

tcf(c_16553,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk3),sk3)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3953]) ).

tcf(c_16554,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk4),sk3)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3953]) ).

tcf(c_16555,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk3),sk4)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3953]) ).

tcf(c_16556,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk4),sk4)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3953]) ).

tcf(c_16557,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk4),app(sk3,sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3953]) ).

tcf(c_16558,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk3,sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3953]) ).

tcf(c_16559,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk3,sk4))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3953]) ).

tcf(c_16560,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk3,sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3953]) ).

tcf(c_16561,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk4),app(sk4,sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3953]) ).

tcf(c_16562,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk3,sk4))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3953]) ).

tcf(c_16563,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk4,sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3953]) ).

tcf(c_16564,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk4,sk4))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3953]) ).

tcf(c_16565,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk4,sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3953]) ).

tcf(c_16566,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk4,sk4))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3953]) ).

tcf(c_16567,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk4),app(sk3,sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3953]) ).

tcf(c_16568,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk4),app(sk4,sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3953]) ).

tcf(c_16569,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3953]) ).

tcf(c_16570,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3953]) ).

tcf(c_16670,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,cons(hd(X0),sk3))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_16547]) ).

tcf(c_16680,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,cons(hd(X0),sk4))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_16548]) ).

tcf(c_16695,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk4,sk3))),nil) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk4,sk3))),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_11560,c_273]) ).

tcf(c_16696,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk4,sk3))),nil) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk4,sk3))),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(sk4),app(sk4,sk3))) != hd(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_16695,c_14399]) ).

tcf(c_16706,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),nil) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_11561,c_273]) ).

tcf(c_16707,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),nil) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(sk4),app(sk3,sk3))) != hd(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_16706,c_14400]) ).

tcf(c_16716,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),sk3)))))
      | ( app(sk4,app(sk3,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_15595,c_280]) ).

tcf(c_16717,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),sk3)))))
      | ( app(sk4,app(sk3,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_15595,c_279]) ).

tcf(c_16733,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_15596,c_280]) ).

tcf(c_16734,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_15596,c_279]) ).

tcf(c_16775,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),sk4)))))
      | ( app(sk4,app(sk3,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_15597,c_280]) ).

tcf(c_16776,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),sk4)))))
      | ( app(sk4,app(sk3,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_15597,c_279]) ).

tcf(c_16792,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_15598,c_280]) ).

tcf(c_16793,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_15598,c_279]) ).

tcf(c_16809,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),sk3)))))
      | ( app(sk4,app(sk4,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_15968,c_280]) ).

tcf(c_16810,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),sk3)))))
      | ( app(sk4,app(sk4,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_15968,c_279]) ).

tcf(c_16826,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_15969,c_280]) ).

tcf(c_16827,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_15969,c_279]) ).

tcf(c_16851,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),sk4)))))
      | ( app(sk4,app(sk4,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_15970,c_280]) ).

tcf(c_16852,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),sk4)))))
      | ( app(sk4,app(sk4,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_15970,c_279]) ).

tcf(c_16868,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_15971,c_280]) ).

tcf(c_16869,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_15971,c_279]) ).

tcf(c_16909,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_10123,c_254]) ).

tcf(c_16910,plain,
    ( ssList(cons(hd(sk3),app(sk4,sk4)))
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_10123,c_272]) ).

tcf(c_16911,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( app(cons(hd(sk3),sk4),X0) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10123,c_270]) ).

tcf(c_16912,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( cons(hd(sk3),app(sk4,sk4)) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_10123,c_269]) ).

tcf(c_16913,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk3),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10123,c_12749]) ).

tcf(c_16914,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_10123,c_14075]) ).

tcf(c_16915,plain,
    ( ( cons(hd(sk3),sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10123,c_9522]) ).

tcf(c_16916,plain,
    ( ( cons(hd(sk3),sk4) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10123,c_8547]) ).

tcf(c_16917,plain,
    ( ( cons(hd(sk3),sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10123,c_7763]) ).

tcf(c_16918,plain,
    ( ( cons(hd(sk3),sk4) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10123,c_6943]) ).

tcf(c_16919,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10123,c_10615]) ).

tcf(c_16920,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10123,c_10191]) ).

tcf(c_16921,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_10123,c_4679]) ).

tcf(c_16922,plain,
    ssList(cons(hd(sk3),app(sk4,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_16910,c_247,c_12796]) ).

tcf(c_16923,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( cons(hd(sk3),app(sk4,sk4)) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16921,c_12796]) ).

tcf(c_16926,plain,
    cons(hd(sk3),app(sk4,sk4)) != nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_16909,c_1243,c_247,c_12796]) ).

tcf(c_16927,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),nil) )
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16914,c_12796]) ).

tcf(c_16930,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk3) )
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16920,c_12796]) ).

tcf(c_16933,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk4) )
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16919,c_12796]) ).

tcf(c_16936,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk4,sk4)) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16912,c_247,c_12796]) ).

tcf(c_16940,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk3),sk4),X0) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16911,c_247,c_12796]) ).

tcf(c_16944,plain,
    ( ( cons(hd(sk3),sk4) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( cons(hd(sk3),app(sk4,sk4)) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16918,c_12796]) ).

tcf(c_16948,plain,
    ( ( cons(hd(sk3),sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( cons(hd(sk3),app(sk4,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16917,c_12796]) ).

tcf(c_16952,plain,
    ( ( cons(hd(sk3),sk4) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16916,c_12796]) ).

tcf(c_16956,plain,
    ( ( cons(hd(sk3),sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16915,c_12796]) ).

tcf(c_16960,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk3),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16913,c_12796]) ).

tcf(c_17001,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),app(sk4,sk4)),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3952]) ).

tcf(c_17002,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk3),app(sk4,sk4)),X0)) = app(cons(hd(sk3),app(sk4,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3050]) ).

tcf(c_17003,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk4,sk4)),X0),nil) = app(cons(hd(sk3),app(sk4,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3049]) ).

tcf(c_17004,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk4,sk4)),sk4),X0) = app(cons(hd(sk3),app(sk4,sk4)),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_4540]) ).

tcf(c_17005,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk4,sk4)),sk3),X0) = app(cons(hd(sk3),app(sk4,sk4)),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_4539]) ).

tcf(c_17006,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk3),app(sk4,sk4))),X0) = app(X1,app(cons(hd(sk3),app(sk4,sk4)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_271]) ).

tcf(c_17007,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk3),app(sk4,sk4)))) = app(cons(X1,X0),cons(hd(sk3),app(sk4,sk4))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_266]) ).

tcf(c_17008,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
      | ( app(tl(cons(hd(sk3),app(sk4,sk4))),X0) = tl(app(cons(hd(sk3),app(sk4,sk4)),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_274]) ).

tcf(c_17009,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
      | ( hd(app(cons(hd(sk3),app(sk4,sk4)),X0)) = hd(cons(hd(sk3),app(sk4,sk4))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_283]) ).

tcf(c_17010,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk3),app(sk4,sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3953]) ).

tcf(c_17011,plain,
    hd(app(sk4,app(nil,cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_15403]) ).

tcf(c_17012,plain,
    hd(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_15402]) ).

tcf(c_17013,plain,
    hd(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_15401]) ).

tcf(c_17014,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3951]) ).

tcf(c_17015,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),nil)) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3423]) ).

tcf(c_17016,plain,
    app(nil,app(nil,cons(hd(sk3),app(sk4,sk4)))) = app(nil,cons(hd(sk3),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_16922,c_13452]) ).

tcf(c_17017,plain,
    app(app(nil,cons(hd(sk3),app(sk4,sk4))),nil) = app(nil,cons(hd(sk3),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_16922,c_12354]) ).

tcf(c_17018,plain,
    app(app(sk4,cons(hd(sk3),app(sk4,sk4))),nil) = app(sk4,cons(hd(sk3),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_16922,c_12353]) ).

tcf(c_17019,plain,
    app(app(sk3,cons(hd(sk3),app(sk4,sk4))),nil) = app(sk3,cons(hd(sk3),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_16922,c_12352]) ).

tcf(c_17020,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk4))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_16922,c_3199]) ).

tcf(c_17021,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(nil,tl(cons(hd(sk3),app(sk4,sk4)))) = tl(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3066]) ).

tcf(c_17022,plain,
    app(nil,app(sk4,cons(hd(sk3),app(sk4,sk4)))) = app(sk4,cons(hd(sk3),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_16922,c_8061]) ).

tcf(c_17023,plain,
    app(app(sk4,sk4),cons(hd(sk3),app(sk4,sk4))) = app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_16922,c_8048]) ).

tcf(c_17024,plain,
    app(nil,app(sk3,cons(hd(sk3),app(sk4,sk4)))) = app(sk3,cons(hd(sk3),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_16922,c_5745]) ).

tcf(c_17025,plain,
    app(app(sk3,sk4),cons(hd(sk3),app(sk4,sk4))) = app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_16922,c_8047]) ).

tcf(c_17026,plain,
    app(app(sk4,sk3),cons(hd(sk3),app(sk4,sk4))) = app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_16922,c_5738]) ).

tcf(c_17027,plain,
    app(app(sk3,sk3),cons(hd(sk3),app(sk4,sk4))) = app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_16922,c_5737]) ).

tcf(c_17028,plain,
    app(tl(sk4),cons(hd(sk3),app(sk4,sk4))) = tl(app(sk4,cons(hd(sk3),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_16922,c_4136]) ).

tcf(c_17029,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk4,sk4)),sk4)) = app(cons(X0,cons(hd(sk3),app(sk4,sk4))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_4462]) ).

tcf(c_17030,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk4,sk4)),sk3)) = app(cons(X0,cons(hd(sk3),app(sk4,sk4))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_4461]) ).

tcf(c_17031,plain,
    app(tl(sk3),cons(hd(sk3),app(sk4,sk4))) = tl(app(sk3,cons(hd(sk3),app(sk4,sk4)))),
    inference(superposition,[status(thm)],[c_16922,c_4284]) ).

tcf(c_17032,plain,
    hd(app(sk3,cons(hd(sk3),app(sk4,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_4027]) ).

tcf(c_17033,plain,
    hd(app(sk4,cons(hd(sk3),app(sk4,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_3885]) ).

tcf(c_17034,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk3),app(sk4,sk4)))) = cons(X0,cons(hd(sk3),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3019]) ).

tcf(c_17035,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk4))),sk4),nil) = cons(hd(cons(hd(sk3),app(sk4,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3452]) ).

tcf(c_17036,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk4))),sk3),nil) = cons(hd(cons(hd(sk3),app(sk4,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3444]) ).

tcf(c_17037,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(tl(cons(hd(sk3),app(sk4,sk4))),nil) = tl(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3065]) ).

tcf(c_17038,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),sk4)) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3215]) ).

tcf(c_17039,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),sk3)) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3207]) ).

tcf(c_17040,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk3),app(sk4,sk4))) = cons(X0,cons(hd(sk3),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_253]) ).

tcf(c_17041,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( cons(hd(cons(hd(sk3),app(sk4,sk4))),tl(cons(hd(sk3),app(sk4,sk4)))) = cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_16922,c_275]) ).

tcf(c_17042,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk3),app(sk4,sk4))),nil) = cons(X0,cons(hd(sk3),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3018]) ).

tcf(c_17043,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk4))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_16922,c_3191]) ).

tcf(c_17044,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk4))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_16922,c_3183]) ).

tcf(c_17045,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk3),app(sk4,sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_284]) ).

tcf(c_17046,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk3),app(sk4,sk4)))) = cons(hd(sk3),app(sk4,sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_276]) ).

tcf(c_17047,plain,
    app(cons(hd(sk3),app(sk4,sk4)),nil) = cons(hd(sk3),app(sk4,sk4)),
    inference(superposition,[status(thm)],[c_16922,c_258]) ).

tcf(c_17048,plain,
    app(nil,cons(hd(sk3),app(sk4,sk4))) = cons(hd(sk3),app(sk4,sk4)),
    inference(superposition,[status(thm)],[c_16922,c_257]) ).

tcf(c_17260,plain,
    app(tl(cons(hd(sk4),app(sk3,sk3))),nil) = tl(cons(hd(sk4),app(sk3,sk3))),
    inference(global_subsumption_just,[status(thm)],[c_6397,c_5891,c_6397]) ).

tcf(c_17270,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ( app(tl(cons(hd(sk4),app(sk3,sk3))),X0) != tl(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_17260,c_270]) ).

tcf(c_17271,plain,
    ! [X0: $i] :
      ( ( tl(cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ( tl(cons(hd(sk4),app(sk3,sk3))) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_17260,c_269]) ).

tcf(c_17272,plain,
    ! [X0: $i] :
      ( ( tl(cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ( tl(cons(hd(sk4),app(sk3,sk3))) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17271,c_259]) ).

tcf(c_17277,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ( app(tl(cons(hd(sk4),app(sk3,sk3))),X0) != tl(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17270,c_259]) ).

tcf(c_17287,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,cons(hd(X0),nil))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_16549]) ).

tcf(c_17288,plain,
    hd(app(sk4,cons(hd(sk4),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_16549]) ).

tcf(c_17289,plain,
    hd(app(sk4,cons(hd(sk3),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10117,c_16549]) ).

tcf(c_17297,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk3),app(sk4,sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_17045]) ).

tcf(c_17298,plain,
    hd(cons(hd(sk4),cons(hd(sk3),app(sk4,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_17045]) ).

tcf(c_17299,plain,
    hd(cons(hd(sk3),cons(hd(sk3),app(sk4,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_17045]) ).

tcf(c_17348,plain,
    ( ( sk3 = nil )
    | ( hd(app(sk3,tl(sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_4036]) ).

tcf(c_17349,plain,
    ( ( sk4 = nil )
    | ( hd(app(sk3,tl(sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_247,c_4036]) ).

tcf(c_17351,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk3,tl(tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4036]) ).

tcf(c_17352,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk3,tl(app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4036]) ).

tcf(c_17353,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk3,tl(cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4036]) ).

tcf(c_17354,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk3),sk3)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_4036]) ).

tcf(c_17355,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk4),sk3)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_4036]) ).

tcf(c_17356,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk3),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_4036]) ).

tcf(c_17357,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_4036]) ).

tcf(c_17358,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_4036]) ).

tcf(c_17359,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4036]) ).

tcf(c_17360,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4036]) ).

tcf(c_17361,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4036]) ).

tcf(c_17362,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_4036]) ).

tcf(c_17363,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4036]) ).

tcf(c_17364,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4036]) ).

tcf(c_17365,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4036]) ).

tcf(c_17366,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4036]) ).

tcf(c_17367,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4036]) ).

tcf(c_17368,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_4036]) ).

tcf(c_17369,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_4036]) ).

tcf(c_17370,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4036]) ).

tcf(c_17371,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4036]) ).

tcf(c_17372,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_4036]) ).

tcf(c_17373,plain,
    hd(app(sk3,tl(sk4))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_17349,c_1243]) ).

tcf(c_17384,plain,
    hd(app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_17372,c_16926]) ).

tcf(c_17385,plain,
    hd(app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_17369,c_10611]) ).

tcf(c_17386,plain,
    hd(app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_17368,c_10190]) ).

tcf(c_17387,plain,
    hd(app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_17362,c_7545]) ).

tcf(c_17388,plain,
    hd(app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_17358,c_5891]) ).

tcf(c_17443,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,tl(sk4))))
      | ( app(sk3,tl(sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,tl(sk4)))
      | ~ ssList(app(sk3,tl(sk4))) ),
    inference(superposition,[status(thm)],[c_17373,c_280]) ).

tcf(c_17444,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,tl(sk4))))
      | ( app(sk3,tl(sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,tl(sk4)))
      | ~ ssList(app(sk3,tl(sk4))) ),
    inference(superposition,[status(thm)],[c_17373,c_279]) ).

tcf(c_17460,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),nil))))
      | ( app(sk4,cons(hd(sk4),nil)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),nil)))
      | ~ ssList(app(sk4,cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_17288,c_280]) ).

tcf(c_17461,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),nil))))
      | ( app(sk4,cons(hd(sk4),nil)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),nil)))
      | ~ ssList(app(sk4,cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_17288,c_279]) ).

tcf(c_17586,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),nil))))
      | ( app(sk4,cons(hd(sk3),nil)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),nil)))
      | ~ ssList(app(sk4,cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_17289,c_280]) ).

tcf(c_17587,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),nil))))
      | ( app(sk4,cons(hd(sk3),nil)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),nil)))
      | ~ ssList(app(sk4,cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_17289,c_279]) ).

tcf(c_17603,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),app(sk4,sk4)))))
      | ( app(sk3,cons(hd(sk3),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),app(sk4,sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17032,c_280]) ).

tcf(c_17604,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),app(sk4,sk4)))))
      | ( app(sk3,cons(hd(sk3),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),app(sk4,sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17032,c_279]) ).

tcf(c_17619,plain,
    hd(app(sk3,tl(sk3))) = hd(sk3),
    inference(global_subsumption_just,[status(thm)],[c_17348,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_17348]) ).

tcf(c_17622,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,tl(sk3))))
      | ( app(sk3,tl(sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,tl(sk3)))
      | ~ ssList(app(sk3,tl(sk3))) ),
    inference(superposition,[status(thm)],[c_17619,c_280]) ).

tcf(c_17623,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,tl(sk3))))
      | ( app(sk3,tl(sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,tl(sk3)))
      | ~ ssList(app(sk3,tl(sk3))) ),
    inference(superposition,[status(thm)],[c_17619,c_279]) ).

tcf(c_17644,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_16936]) ).

tcf(c_17645,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5702,c_16936]) ).

tcf(c_17646,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5719,c_16936]) ).

tcf(c_17660,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_3804,c_16940]) ).

tcf(c_17662,plain,
    cons(hd(sk3),app(sk4,sk4)) != cons(hd(sk3),sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_17660,c_1243,c_259]) ).

tcf(c_17664,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),app(sk4,sk4)))))
      | ( app(sk4,cons(hd(sk3),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),app(sk4,sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17033,c_280]) ).

tcf(c_17665,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),app(sk4,sk4)))))
      | ( app(sk4,cons(hd(sk3),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),app(sk4,sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17033,c_279]) ).

tcf(c_17683,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_10124,c_254]) ).

tcf(c_17684,plain,
    ( ssList(cons(hd(sk3),app(sk3,sk4)))
    | ~ ssList(sk4)
    | ~ ssList(cons(hd(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_10124,c_272]) ).

tcf(c_17685,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( app(cons(hd(sk3),sk3),X0) != cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10124,c_270]) ).

tcf(c_17686,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(sk4)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( cons(hd(sk3),app(sk3,sk4)) != app(X0,sk4) ) ),
    inference(superposition,[status(thm)],[c_10124,c_269]) ).

tcf(c_17687,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),sk4) )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10124,c_16936]) ).

tcf(c_17688,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_10124,c_12749]) ).

tcf(c_17689,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_10124,c_14075]) ).

tcf(c_17690,plain,
    ( ( cons(hd(sk3),sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10124,c_9522]) ).

tcf(c_17691,plain,
    ( ( cons(hd(sk3),sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10124,c_8547]) ).

tcf(c_17692,plain,
    ( ( cons(hd(sk3),sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10124,c_7763]) ).

tcf(c_17693,plain,
    ( ( cons(hd(sk3),sk3) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10124,c_6943]) ).

tcf(c_17694,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10124,c_10615]) ).

tcf(c_17695,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10124,c_10191]) ).

tcf(c_17696,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_10124,c_4679]) ).

tcf(c_17697,plain,
    ssList(cons(hd(sk3),app(sk3,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_17684,c_247,c_13784]) ).

tcf(c_17698,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( cons(hd(sk3),app(sk3,sk4)) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17696,c_13784]) ).

tcf(c_17701,plain,
    cons(hd(sk3),app(sk3,sk4)) != nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_17683,c_1243,c_247,c_13784]) ).

tcf(c_17702,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),nil) )
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17689,c_13784]) ).

tcf(c_17705,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk3) )
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17695,c_13784]) ).

tcf(c_17708,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk4) )
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17694,c_13784]) ).

tcf(c_17711,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),sk4) )
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17687,c_13784]) ).

tcf(c_17714,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk3,sk4)) != app(X0,sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17686,c_247,c_13784]) ).

tcf(c_17718,plain,
    ! [X0: $i] :
      ( ( X0 = sk4 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk3),sk3),X0) != cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17685,c_247,c_13784]) ).

tcf(c_17722,plain,
    ( ( cons(hd(sk3),sk3) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17693,c_13784]) ).

tcf(c_17726,plain,
    ( ( cons(hd(sk3),sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17692,c_13784]) ).

tcf(c_17730,plain,
    ( ( cons(hd(sk3),sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( cons(hd(sk3),app(sk3,sk4)) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17691,c_13784]) ).

tcf(c_17734,plain,
    ( ( cons(hd(sk3),sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( cons(hd(sk3),app(sk3,sk4)) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17690,c_13784]) ).

tcf(c_17738,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk3),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17688,c_13784]) ).

tcf(c_17758,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),app(sk3,sk4)),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3952]) ).

tcf(c_17759,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk3),app(sk3,sk4)),X0)) = app(cons(hd(sk3),app(sk3,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3050]) ).

tcf(c_17760,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk3,sk4)),X0),nil) = app(cons(hd(sk3),app(sk3,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3049]) ).

tcf(c_17761,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk3,sk4)),sk4),X0) = app(cons(hd(sk3),app(sk3,sk4)),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_4540]) ).

tcf(c_17762,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk3,sk4)),sk3),X0) = app(cons(hd(sk3),app(sk3,sk4)),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_4539]) ).

tcf(c_17763,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk3),app(sk3,sk4))),X0) = app(X1,app(cons(hd(sk3),app(sk3,sk4)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_271]) ).

tcf(c_17764,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk3),app(sk3,sk4)))) = app(cons(X1,X0),cons(hd(sk3),app(sk3,sk4))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_266]) ).

tcf(c_17765,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
      | ( app(tl(cons(hd(sk3),app(sk3,sk4))),X0) = tl(app(cons(hd(sk3),app(sk3,sk4)),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_274]) ).

tcf(c_17766,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
      | ( hd(app(cons(hd(sk3),app(sk3,sk4)),X0)) = hd(cons(hd(sk3),app(sk3,sk4))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_283]) ).

tcf(c_17767,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_4036]) ).

tcf(c_17768,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk3),app(sk3,sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3953]) ).

tcf(c_17769,plain,
    hd(app(sk4,app(nil,cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_15403]) ).

tcf(c_17770,plain,
    hd(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_15402]) ).

tcf(c_17771,plain,
    hd(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_15401]) ).

tcf(c_17772,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3951]) ).

tcf(c_17773,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),nil)) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3423]) ).

tcf(c_17774,plain,
    app(nil,app(nil,cons(hd(sk3),app(sk3,sk4)))) = app(nil,cons(hd(sk3),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_17697,c_13452]) ).

tcf(c_17775,plain,
    app(app(nil,cons(hd(sk3),app(sk3,sk4))),nil) = app(nil,cons(hd(sk3),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_17697,c_12354]) ).

tcf(c_17776,plain,
    app(app(sk4,cons(hd(sk3),app(sk3,sk4))),nil) = app(sk4,cons(hd(sk3),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_17697,c_12353]) ).

tcf(c_17777,plain,
    app(app(sk3,cons(hd(sk3),app(sk3,sk4))),nil) = app(sk3,cons(hd(sk3),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_17697,c_12352]) ).

tcf(c_17778,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk4))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_17697,c_3199]) ).

tcf(c_17779,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(nil,tl(cons(hd(sk3),app(sk3,sk4)))) = tl(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3066]) ).

tcf(c_17780,plain,
    app(nil,app(sk4,cons(hd(sk3),app(sk3,sk4)))) = app(sk4,cons(hd(sk3),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_17697,c_8061]) ).

tcf(c_17781,plain,
    app(app(sk4,sk4),cons(hd(sk3),app(sk3,sk4))) = app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_17697,c_8048]) ).

tcf(c_17782,plain,
    app(nil,app(sk3,cons(hd(sk3),app(sk3,sk4)))) = app(sk3,cons(hd(sk3),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_17697,c_5745]) ).

tcf(c_17783,plain,
    app(app(sk3,sk4),cons(hd(sk3),app(sk3,sk4))) = app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_17697,c_8047]) ).

tcf(c_17784,plain,
    app(app(sk4,sk3),cons(hd(sk3),app(sk3,sk4))) = app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_17697,c_5738]) ).

tcf(c_17785,plain,
    app(app(sk3,sk3),cons(hd(sk3),app(sk3,sk4))) = app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_17697,c_5737]) ).

tcf(c_17786,plain,
    app(tl(sk4),cons(hd(sk3),app(sk3,sk4))) = tl(app(sk4,cons(hd(sk3),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_17697,c_4136]) ).

tcf(c_17787,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk3,sk4)),sk4)) = app(cons(X0,cons(hd(sk3),app(sk3,sk4))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_4462]) ).

tcf(c_17788,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk3,sk4)),sk3)) = app(cons(X0,cons(hd(sk3),app(sk3,sk4))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_4461]) ).

tcf(c_17789,plain,
    app(tl(sk3),cons(hd(sk3),app(sk3,sk4))) = tl(app(sk3,cons(hd(sk3),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_17697,c_4284]) ).

tcf(c_17790,plain,
    hd(app(sk3,cons(hd(sk3),app(sk3,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_4027]) ).

tcf(c_17791,plain,
    hd(app(sk4,cons(hd(sk3),app(sk3,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_3885]) ).

tcf(c_17792,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk3),app(sk3,sk4)))) = cons(X0,cons(hd(sk3),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3019]) ).

tcf(c_17793,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk4))),sk4),nil) = cons(hd(cons(hd(sk3),app(sk3,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3452]) ).

tcf(c_17794,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk4))),sk3),nil) = cons(hd(cons(hd(sk3),app(sk3,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3444]) ).

tcf(c_17795,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(tl(cons(hd(sk3),app(sk3,sk4))),nil) = tl(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3065]) ).

tcf(c_17796,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),sk4)) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3215]) ).

tcf(c_17797,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),sk3)) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3207]) ).

tcf(c_17798,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk3),app(sk3,sk4))) = cons(X0,cons(hd(sk3),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_253]) ).

tcf(c_17799,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( cons(hd(cons(hd(sk3),app(sk3,sk4))),tl(cons(hd(sk3),app(sk3,sk4)))) = cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_17697,c_275]) ).

tcf(c_17800,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk3),app(sk3,sk4))),nil) = cons(X0,cons(hd(sk3),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3018]) ).

tcf(c_17801,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk4))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_17697,c_3191]) ).

tcf(c_17802,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk4))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_17697,c_3183]) ).

tcf(c_17803,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk3),app(sk3,sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_284]) ).

tcf(c_17804,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk3),app(sk3,sk4)))) = cons(hd(sk3),app(sk3,sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_276]) ).

tcf(c_17805,plain,
    app(cons(hd(sk3),app(sk3,sk4)),nil) = cons(hd(sk3),app(sk3,sk4)),
    inference(superposition,[status(thm)],[c_17697,c_258]) ).

tcf(c_17806,plain,
    app(nil,cons(hd(sk3),app(sk3,sk4))) = cons(hd(sk3),app(sk3,sk4)),
    inference(superposition,[status(thm)],[c_17697,c_257]) ).

tcf(c_17945,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)) = hd(cons(hd(sk4),app(sk3,sk3))),
    inference(global_subsumption_just,[status(thm)],[c_6398,c_5891,c_6398]) ).

tcf(c_17947,plain,
    ( ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) = nil )
    | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)) ),
    inference(superposition,[status(thm)],[c_17945,c_286]) ).

tcf(c_17948,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)))
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ totalorderedP(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)) ),
    inference(superposition,[status(thm)],[c_17945,c_280]) ).

tcf(c_17949,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)))
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ strictorderedP(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)) ),
    inference(superposition,[status(thm)],[c_17945,c_279]) ).

tcf(c_17979,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk3),app(sk3,sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_17803]) ).

tcf(c_17980,plain,
    hd(cons(hd(sk4),cons(hd(sk3),app(sk3,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_17803]) ).

tcf(c_17981,plain,
    hd(cons(hd(sk3),cons(hd(sk3),app(sk3,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_17803]) ).

tcf(c_17991,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_4037]) ).

tcf(c_17992,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_4037]) ).

tcf(c_17993,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_4037]) ).

tcf(c_17994,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(tl(X0),X1))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4037]) ).

tcf(c_17995,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(app(X1,X0),X2))) = hd(sk3) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4037]) ).

tcf(c_17996,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(cons(X2,X0),X1))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4037]) ).

tcf(c_17997,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),sk3),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_4037]) ).

tcf(c_17998,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),sk3),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_4037]) ).

tcf(c_17999,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),sk4),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_4037]) ).

tcf(c_18000,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),sk4),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_4037]) ).

tcf(c_18001,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),app(sk3,sk3)),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_4037]) ).

tcf(c_18002,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk3,sk3)),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4037]) ).

tcf(c_18003,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk3,sk4)),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4037]) ).

tcf(c_18004,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk3,sk3)),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4037]) ).

tcf(c_18005,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),app(sk4,sk3)),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_4037]) ).

tcf(c_18006,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk3,sk4)),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4037]) ).

tcf(c_18007,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk4,sk3)),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4037]) ).

tcf(c_18008,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk4,sk4)),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4037]) ).

tcf(c_18009,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk4,sk3)),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4037]) ).

tcf(c_18010,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk4,sk4)),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4037]) ).

tcf(c_18011,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),app(sk3,sk4)),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_4037]) ).

tcf(c_18012,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),app(sk4,sk4)),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_4037]) ).

tcf(c_18013,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4037]) ).

tcf(c_18014,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4037]) ).

tcf(c_18015,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),app(sk4,sk4)),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_4037]) ).

tcf(c_18016,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),app(sk3,sk4)),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_4037]) ).

tcf(c_18181,plain,
    hd(app(sk3,app(sk3,sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_17991]) ).

tcf(c_18182,plain,
    hd(app(sk3,app(sk3,sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_17991]) ).

tcf(c_18183,plain,
    hd(app(sk3,app(sk3,nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_17991]) ).

tcf(c_18184,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk3,tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_17991]) ).

tcf(c_18185,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk3,app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_17991]) ).

tcf(c_18186,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_17991]) ).

tcf(c_18187,plain,
    hd(app(sk3,app(sk3,cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_17991]) ).

tcf(c_18188,plain,
    hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_17991]) ).

tcf(c_18189,plain,
    hd(app(sk3,app(sk3,cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_17991]) ).

tcf(c_18190,plain,
    hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_17991]) ).

tcf(c_18191,plain,
    hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_17991]) ).

tcf(c_18192,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_17991]) ).

tcf(c_18193,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_17991]) ).

tcf(c_18194,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_17991]) ).

tcf(c_18195,plain,
    hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_17991]) ).

tcf(c_18196,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_17991]) ).

tcf(c_18197,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_17991]) ).

tcf(c_18198,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_17991]) ).

tcf(c_18199,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_17991]) ).

tcf(c_18200,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_17991]) ).

tcf(c_18201,plain,
    hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_17991]) ).

tcf(c_18202,plain,
    hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_17991]) ).

tcf(c_18203,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_17991]) ).

tcf(c_18204,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_17991]) ).

tcf(c_18205,plain,
    hd(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_17991]) ).

tcf(c_18206,plain,
    hd(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_17991]) ).

tcf(c_18422,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,sk3))))
      | ( app(sk3,app(sk3,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,sk3)))
      | ~ ssList(app(sk3,app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_18181,c_280]) ).

tcf(c_18423,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,sk3))))
      | ( app(sk3,app(sk3,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,sk3)))
      | ~ ssList(app(sk3,app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_18181,c_279]) ).

tcf(c_18439,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,sk4))))
      | ( app(sk3,app(sk3,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,sk4)))
      | ~ ssList(app(sk3,app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_18182,c_280]) ).

tcf(c_18440,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,sk4))))
      | ( app(sk3,app(sk3,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,sk4)))
      | ~ ssList(app(sk3,app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_18182,c_279]) ).

tcf(c_18456,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),app(sk3,sk4)))))
      | ( app(sk3,cons(hd(sk3),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),app(sk3,sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17790,c_280]) ).

tcf(c_18457,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),app(sk3,sk4)))))
      | ( app(sk3,cons(hd(sk3),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),app(sk3,sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17790,c_279]) ).

tcf(c_18473,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),app(sk3,sk4)))))
      | ( app(sk4,cons(hd(sk3),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),app(sk3,sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17791,c_280]) ).

tcf(c_18474,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),app(sk3,sk4)))))
      | ( app(sk4,cons(hd(sk3),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),app(sk3,sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17791,c_279]) ).

tcf(c_18493,plain,
    hd(app(sk3,app(sk4,sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_17992]) ).

tcf(c_18494,plain,
    hd(app(sk3,app(sk4,sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_17992]) ).

tcf(c_18495,plain,
    hd(app(sk3,app(sk4,nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_17992]) ).

tcf(c_18496,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk4,tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_17992]) ).

tcf(c_18497,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk4,app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_17992]) ).

tcf(c_18498,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_17992]) ).

tcf(c_18499,plain,
    hd(app(sk3,app(sk4,cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_17992]) ).

tcf(c_18500,plain,
    hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_17992]) ).

tcf(c_18501,plain,
    hd(app(sk3,app(sk4,cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_17992]) ).

tcf(c_18502,plain,
    hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_17992]) ).

tcf(c_18503,plain,
    hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_17992]) ).

tcf(c_18504,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_17992]) ).

tcf(c_18505,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_17992]) ).

tcf(c_18506,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_17992]) ).

tcf(c_18507,plain,
    hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_17992]) ).

tcf(c_18508,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_17992]) ).

tcf(c_18509,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_17992]) ).

tcf(c_18510,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_17992]) ).

tcf(c_18511,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_17992]) ).

tcf(c_18512,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_17992]) ).

tcf(c_18513,plain,
    hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_17992]) ).

tcf(c_18514,plain,
    hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_17992]) ).

tcf(c_18515,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_17992]) ).

tcf(c_18516,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_17992]) ).

tcf(c_18517,plain,
    hd(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_17992]) ).

tcf(c_18518,plain,
    hd(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_17992]) ).

tcf(c_18615,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,sk3))))
      | ( app(sk3,app(sk4,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,sk3)))
      | ~ ssList(app(sk3,app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_18493,c_280]) ).

tcf(c_18616,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,sk3))))
      | ( app(sk3,app(sk4,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,sk3)))
      | ~ ssList(app(sk3,app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_18493,c_279]) ).

tcf(c_18632,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,sk4))))
      | ( app(sk3,app(sk4,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,sk4)))
      | ~ ssList(app(sk3,app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_18494,c_280]) ).

tcf(c_18633,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,sk4))))
      | ( app(sk3,app(sk4,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,sk4)))
      | ~ ssList(app(sk3,app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_18494,c_279]) ).

tcf(c_18654,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_4070,c_17714]) ).

tcf(c_18655,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5702,c_17714]) ).

tcf(c_18656,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_5719,c_17714]) ).

tcf(c_18657,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),sk4) )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10123,c_17714]) ).

tcf(c_18672,plain,
    ( ( sk4 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_3768,c_17718]) ).

tcf(c_18674,plain,
    cons(hd(sk3),app(sk3,sk4)) != cons(hd(sk3),sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_18672,c_1243,c_259]) ).

tcf(c_18676,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),sk3)))))
      | ( app(sk3,app(sk3,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_18187,c_280]) ).

tcf(c_18677,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),sk3)))))
      | ( app(sk3,app(sk3,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_18187,c_279]) ).

tcf(c_18693,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_18188,c_280]) ).

tcf(c_18694,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_18188,c_279]) ).

tcf(c_18710,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),sk4)))))
      | ( app(sk3,app(sk3,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_18189,c_280]) ).

tcf(c_18711,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),sk4)))))
      | ( app(sk3,app(sk3,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_18189,c_279]) ).

tcf(c_18727,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_18190,c_280]) ).

tcf(c_18728,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))))
      | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_18190,c_279]) ).

tcf(c_18743,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)) = hd(cons(hd(sk4),app(sk3,sk3))),
    inference(global_subsumption_just,[status(thm)],[c_6399,c_5891,c_6399]) ).

tcf(c_18745,plain,
    ( ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) = nil )
    | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)) ),
    inference(superposition,[status(thm)],[c_18743,c_286]) ).

tcf(c_18746,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)))
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ totalorderedP(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)) ),
    inference(superposition,[status(thm)],[c_18743,c_280]) ).

tcf(c_18747,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)))
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ strictorderedP(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)) ),
    inference(superposition,[status(thm)],[c_18743,c_279]) ).

tcf(c_18769,plain,
    hd(app(sk3,app(nil,sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_17993]) ).

tcf(c_18770,plain,
    hd(app(sk3,app(nil,sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_17993]) ).

tcf(c_18771,plain,
    hd(app(sk3,app(nil,nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_17993]) ).

tcf(c_18772,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(nil,tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_17993]) ).

tcf(c_18773,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(nil,app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_17993]) ).

tcf(c_18774,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(nil,cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_17993]) ).

tcf(c_18775,plain,
    hd(app(sk3,app(nil,cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_17993]) ).

tcf(c_18776,plain,
    hd(app(sk3,app(nil,cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_17993]) ).

tcf(c_18777,plain,
    hd(app(sk3,app(nil,cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_17993]) ).

tcf(c_18778,plain,
    hd(app(sk3,app(nil,cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_17993]) ).

tcf(c_18779,plain,
    hd(app(sk3,app(nil,cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_17993]) ).

tcf(c_18780,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_17993]) ).

tcf(c_18781,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_17993]) ).

tcf(c_18782,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_17993]) ).

tcf(c_18783,plain,
    hd(app(sk3,app(nil,cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_17993]) ).

tcf(c_18784,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_17993]) ).

tcf(c_18785,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_17993]) ).

tcf(c_18786,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_17993]) ).

tcf(c_18787,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_17993]) ).

tcf(c_18788,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_17993]) ).

tcf(c_18789,plain,
    hd(app(sk3,app(nil,cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_17993]) ).

tcf(c_18790,plain,
    hd(app(sk3,app(nil,cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_17993]) ).

tcf(c_18791,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_17993]) ).

tcf(c_18792,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_17993]) ).

tcf(c_18793,plain,
    hd(app(sk3,app(nil,cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_17993]) ).

tcf(c_18794,plain,
    hd(app(sk3,app(nil,cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_17993]) ).

tcf(c_18845,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,sk3))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_4038]) ).

tcf(c_18846,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,sk4))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_4038]) ).

tcf(c_18847,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,nil))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_4038]) ).

tcf(c_18848,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,cons(X1,tl(X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4038]) ).

tcf(c_18849,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,cons(X2,app(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4038]) ).

tcf(c_18850,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,cons(X2,cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4038]) ).

tcf(c_18851,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk3),sk3)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_4038]) ).

tcf(c_18852,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk4),sk3)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_4038]) ).

tcf(c_18853,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk3),sk4)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_4038]) ).

tcf(c_18854,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk4),sk4)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_4038]) ).

tcf(c_18855,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk4),app(sk3,sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_4038]) ).

tcf(c_18856,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk3,sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4038]) ).

tcf(c_18857,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk3,sk4))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4038]) ).

tcf(c_18858,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk3,sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4038]) ).

tcf(c_18859,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk4),app(sk4,sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_4038]) ).

tcf(c_18860,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk3,sk4))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4038]) ).

tcf(c_18861,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk4,sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4038]) ).

tcf(c_18862,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk4,sk4))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4038]) ).

tcf(c_18863,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk4,sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4038]) ).

tcf(c_18864,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk4,sk4))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4038]) ).

tcf(c_18865,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk4),app(sk3,sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_4038]) ).

tcf(c_18866,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk4),app(sk4,sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_4038]) ).

tcf(c_18867,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4038]) ).

tcf(c_18868,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4038]) ).

tcf(c_18869,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk3),app(sk4,sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_4038]) ).

tcf(c_18870,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk3),app(sk3,sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_4038]) ).

tcf(c_19014,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,cons(hd(X0),sk3))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_18845]) ).

tcf(c_19024,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,cons(hd(X0),sk4))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_18846]) ).

tcf(c_19039,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),sk3)))))
      | ( app(sk3,app(sk4,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_18499,c_280]) ).

tcf(c_19040,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),sk3)))))
      | ( app(sk3,app(sk4,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_18499,c_279]) ).

tcf(c_19056,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_18500,c_280]) ).

tcf(c_19057,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_18500,c_279]) ).

tcf(c_19073,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),sk4)))))
      | ( app(sk3,app(sk4,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_18501,c_280]) ).

tcf(c_19074,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),sk4)))))
      | ( app(sk3,app(sk4,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_18501,c_279]) ).

tcf(c_19090,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_18502,c_280]) ).

tcf(c_19091,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_18502,c_279]) ).

tcf(c_19108,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_10126,c_255]) ).

tcf(c_19109,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_10126,c_254]) ).

tcf(c_19110,plain,
    ( ssList(cons(hd(sk3),app(sk4,sk3)))
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_10126,c_272]) ).

tcf(c_19111,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( app(cons(hd(sk3),sk4),X0) != cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10126,c_270]) ).

tcf(c_19112,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk4))
      | ( cons(hd(sk3),app(sk4,sk3)) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_10126,c_269]) ).

tcf(c_19113,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk3),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10126,c_13738]) ).

tcf(c_19114,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_10126,c_14022]) ).

tcf(c_19115,plain,
    ( ( cons(hd(sk3),sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10126,c_9243]) ).

tcf(c_19116,plain,
    ( ( cons(hd(sk3),sk4) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10126,c_8266]) ).

tcf(c_19117,plain,
    ( ( cons(hd(sk3),sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10126,c_7257]) ).

tcf(c_19118,plain,
    ( ( cons(hd(sk3),sk4) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10126,c_6600]) ).

tcf(c_19119,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10126,c_7546]) ).

tcf(c_19120,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10126,c_5892]) ).

tcf(c_19121,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_10126,c_4683]) ).

tcf(c_19122,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10126,c_16940]) ).

tcf(c_19123,plain,
    ssList(cons(hd(sk3),app(sk4,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_19110,c_246,c_12796]) ).

tcf(c_19124,plain,
    ( ( sk3 = sk4 )
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19122,c_246]) ).

tcf(c_19127,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( cons(hd(sk3),app(sk4,sk3)) != sk3 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19121,c_12796]) ).

tcf(c_19130,plain,
    ( ( sk3 = nil )
    | ( cons(hd(sk3),app(sk4,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19109,c_246,c_12796]) ).

tcf(c_19133,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( cons(hd(sk3),app(sk4,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19108,c_246,c_12796]) ).

tcf(c_19136,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),nil) )
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19114,c_12796]) ).

tcf(c_19139,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk3) )
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19120,c_12796]) ).

tcf(c_19142,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk4) )
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19119,c_12796]) ).

tcf(c_19145,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk4,sk3)) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19112,c_246,c_12796]) ).

tcf(c_19149,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk3),sk4),X0) != cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19111,c_246,c_12796]) ).

tcf(c_19153,plain,
    ( ( cons(hd(sk3),sk4) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( cons(hd(sk3),app(sk4,sk3)) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19118,c_12796]) ).

tcf(c_19157,plain,
    ( ( cons(hd(sk3),sk4) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( cons(hd(sk3),app(sk4,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19117,c_12796]) ).

tcf(c_19161,plain,
    ( ( cons(hd(sk3),sk4) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19116,c_12796]) ).

tcf(c_19165,plain,
    ( ( cons(hd(sk3),sk4) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19115,c_12796]) ).

tcf(c_19169,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk3),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19113,c_12796]) ).

tcf(c_19228,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),app(sk4,sk3)),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_4037]) ).

tcf(c_19229,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),app(sk4,sk3)),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3952]) ).

tcf(c_19230,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk3),app(sk4,sk3)),X0)) = app(cons(hd(sk3),app(sk4,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3050]) ).

tcf(c_19231,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk4,sk3)),X0),nil) = app(cons(hd(sk3),app(sk4,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3049]) ).

tcf(c_19232,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk4,sk3)),sk4),X0) = app(cons(hd(sk3),app(sk4,sk3)),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_4540]) ).

tcf(c_19233,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk4,sk3)),sk3),X0) = app(cons(hd(sk3),app(sk4,sk3)),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_4539]) ).

tcf(c_19234,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk3),app(sk4,sk3))),X0) = app(X1,app(cons(hd(sk3),app(sk4,sk3)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_271]) ).

tcf(c_19235,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk3),app(sk4,sk3)))) = app(cons(X1,X0),cons(hd(sk3),app(sk4,sk3))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_266]) ).

tcf(c_19236,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
      | ( app(tl(cons(hd(sk3),app(sk4,sk3))),X0) = tl(app(cons(hd(sk3),app(sk4,sk3)),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_274]) ).

tcf(c_19237,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
      | ( hd(app(cons(hd(sk3),app(sk4,sk3)),X0)) = hd(cons(hd(sk3),app(sk4,sk3))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_283]) ).

tcf(c_19238,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk3),app(sk4,sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_4038]) ).

tcf(c_19239,plain,
    hd(app(sk3,app(nil,cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_17993]) ).

tcf(c_19240,plain,
    hd(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_17992]) ).

tcf(c_19241,plain,
    hd(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_17991]) ).

tcf(c_19242,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_4036]) ).

tcf(c_19243,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk3),app(sk4,sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3953]) ).

tcf(c_19244,plain,
    hd(app(sk4,app(nil,cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_15403]) ).

tcf(c_19245,plain,
    hd(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_15402]) ).

tcf(c_19246,plain,
    hd(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_15401]) ).

tcf(c_19247,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3951]) ).

tcf(c_19248,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),nil)) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3423]) ).

tcf(c_19249,plain,
    app(nil,app(nil,cons(hd(sk3),app(sk4,sk3)))) = app(nil,cons(hd(sk3),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_19123,c_13452]) ).

tcf(c_19250,plain,
    app(app(nil,cons(hd(sk3),app(sk4,sk3))),nil) = app(nil,cons(hd(sk3),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_19123,c_12354]) ).

tcf(c_19251,plain,
    app(app(sk4,cons(hd(sk3),app(sk4,sk3))),nil) = app(sk4,cons(hd(sk3),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_19123,c_12353]) ).

tcf(c_19252,plain,
    app(app(sk3,cons(hd(sk3),app(sk4,sk3))),nil) = app(sk3,cons(hd(sk3),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_19123,c_12352]) ).

tcf(c_19253,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk3))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_19123,c_3199]) ).

tcf(c_19254,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(nil,tl(cons(hd(sk3),app(sk4,sk3)))) = tl(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3066]) ).

tcf(c_19255,plain,
    app(nil,app(sk4,cons(hd(sk3),app(sk4,sk3)))) = app(sk4,cons(hd(sk3),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_19123,c_8061]) ).

tcf(c_19256,plain,
    app(app(sk4,sk4),cons(hd(sk3),app(sk4,sk3))) = app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_19123,c_8048]) ).

tcf(c_19257,plain,
    app(nil,app(sk3,cons(hd(sk3),app(sk4,sk3)))) = app(sk3,cons(hd(sk3),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_19123,c_5745]) ).

tcf(c_19258,plain,
    app(app(sk3,sk4),cons(hd(sk3),app(sk4,sk3))) = app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_19123,c_8047]) ).

tcf(c_19259,plain,
    app(app(sk4,sk3),cons(hd(sk3),app(sk4,sk3))) = app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_19123,c_5738]) ).

tcf(c_19260,plain,
    app(app(sk3,sk3),cons(hd(sk3),app(sk4,sk3))) = app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_19123,c_5737]) ).

tcf(c_19261,plain,
    app(tl(sk4),cons(hd(sk3),app(sk4,sk3))) = tl(app(sk4,cons(hd(sk3),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_19123,c_4136]) ).

tcf(c_19262,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk4,sk3)),sk4)) = app(cons(X0,cons(hd(sk3),app(sk4,sk3))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_4462]) ).

tcf(c_19263,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk4,sk3)),sk3)) = app(cons(X0,cons(hd(sk3),app(sk4,sk3))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_4461]) ).

tcf(c_19264,plain,
    app(tl(sk3),cons(hd(sk3),app(sk4,sk3))) = tl(app(sk3,cons(hd(sk3),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_19123,c_4284]) ).

tcf(c_19265,plain,
    hd(app(sk3,cons(hd(sk3),app(sk4,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_4027]) ).

tcf(c_19266,plain,
    hd(app(sk4,cons(hd(sk3),app(sk4,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_3885]) ).

tcf(c_19267,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk3),app(sk4,sk3)))) = cons(X0,cons(hd(sk3),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3019]) ).

tcf(c_19268,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk3))),sk4),nil) = cons(hd(cons(hd(sk3),app(sk4,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3452]) ).

tcf(c_19269,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk3))),sk3),nil) = cons(hd(cons(hd(sk3),app(sk4,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3444]) ).

tcf(c_19270,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(tl(cons(hd(sk3),app(sk4,sk3))),nil) = tl(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3065]) ).

tcf(c_19271,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),sk4)) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3215]) ).

tcf(c_19272,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),sk3)) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3207]) ).

tcf(c_19273,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk3),app(sk4,sk3))) = cons(X0,cons(hd(sk3),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_253]) ).

tcf(c_19274,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( cons(hd(cons(hd(sk3),app(sk4,sk3))),tl(cons(hd(sk3),app(sk4,sk3)))) = cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_19123,c_275]) ).

tcf(c_19275,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk3),app(sk4,sk3))),nil) = cons(X0,cons(hd(sk3),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3018]) ).

tcf(c_19276,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk3))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_19123,c_3191]) ).

tcf(c_19277,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk3))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_19123,c_3183]) ).

tcf(c_19278,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk3),app(sk4,sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_284]) ).

tcf(c_19279,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk3),app(sk4,sk3)))) = cons(hd(sk3),app(sk4,sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_276]) ).

tcf(c_19280,plain,
    app(cons(hd(sk3),app(sk4,sk3)),nil) = cons(hd(sk3),app(sk4,sk3)),
    inference(superposition,[status(thm)],[c_19123,c_258]) ).

tcf(c_19281,plain,
    app(nil,cons(hd(sk3),app(sk4,sk3))) = cons(hd(sk3),app(sk4,sk3)),
    inference(superposition,[status(thm)],[c_19123,c_257]) ).

tcf(c_19513,plain,
    cons(hd(sk3),app(sk4,sk3)) != nil,
    inference(global_subsumption_just,[status(thm)],[c_19130,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_19130]) ).

tcf(c_19525,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_19145]) ).

tcf(c_19526,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4976,c_19145]) ).

tcf(c_19527,plain,
    ( ( cons(hd(sk3),sk4) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4999,c_19145]) ).

tcf(c_19541,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_3804,c_19149]) ).

tcf(c_19542,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10123,c_19149]) ).

tcf(c_19544,plain,
    ( ( sk3 = nil )
    | ( cons(hd(sk3),app(sk4,sk3)) != cons(hd(sk3),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19541,c_259]) ).

tcf(c_19548,plain,
    cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))) = cons(hd(sk4),app(sk3,sk3)),
    inference(global_subsumption_just,[status(thm)],[c_6401,c_5891,c_6401]) ).

tcf(c_19551,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_12052]) ).

tcf(c_19552,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_12044]) ).

tcf(c_19553,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_11285]) ).

tcf(c_19554,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_11277]) ).

tcf(c_19555,plain,
    ( leq(hd(sk3),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_12667]) ).

tcf(c_19556,plain,
    ( lt(hd(sk3),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_12660]) ).

tcf(c_19557,plain,
    ( leq(hd(sk3),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_12629]) ).

tcf(c_19558,plain,
    ( lt(hd(sk3),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_12622]) ).

tcf(c_19559,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_6332]) ).

tcf(c_19560,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_6325]) ).

tcf(c_19561,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_6196]) ).

tcf(c_19562,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_6189]) ).

tcf(c_19565,plain,
    ( lt(hd(cons(hd(sk4),app(sk3,sk3))),hd(tl(cons(hd(sk4),app(sk3,sk3)))))
    | ( tl(cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ strictorderedP(cons(hd(sk4),app(sk3,sk3)))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_19548,c_282]) ).

tcf(c_19566,plain,
    ( leq(hd(cons(hd(sk4),app(sk3,sk3))),hd(tl(cons(hd(sk4),app(sk3,sk3)))))
    | ( tl(cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk3)))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_19548,c_281]) ).

tcf(c_19567,plain,
    ( totalorderedP(tl(cons(hd(sk4),app(sk3,sk3))))
    | ( tl(cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk3)))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_19548,c_301]) ).

tcf(c_19568,plain,
    ( strictorderedP(tl(cons(hd(sk4),app(sk3,sk3))))
    | ( tl(cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ strictorderedP(cons(hd(sk4),app(sk3,sk3)))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_19548,c_288]) ).

tcf(c_19569,plain,
    ( ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ( tl(cons(hd(sk4),app(sk3,sk3))) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_19548,c_267]) ).

tcf(c_19571,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(cons(hd(sk4),app(sk3,sk3))),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk3))),cons(X1,X2)))
      | ~ totalorderedP(app(app(X0,cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3))))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_19548,c_300]) ).

tcf(c_19572,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(cons(hd(sk4),app(sk3,sk3))),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk3))),cons(X1,X2)))
      | ~ strictorderedP(app(app(X0,cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3))))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_19548,c_287]) ).

tcf(c_19573,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ( cons(hd(sk4),app(sk3,sk3)) != cons(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_19548,c_265]) ).

tcf(c_19574,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(cons(hd(sk4),app(sk3,sk3))) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ( cons(hd(sk4),app(sk3,sk3)) != cons(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_19548,c_264]) ).

tcf(c_19575,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk3))))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_300]) ).

tcf(c_19576,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk3))))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_287]) ).

tcf(c_19612,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19562,c_19548]) ).

tcf(c_19618,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19561,c_19548]) ).

tcf(c_19624,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19560,c_19548]) ).

tcf(c_19630,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19559,c_19548]) ).

tcf(c_19636,plain,
    ( lt(hd(sk3),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19558,c_19548]) ).

tcf(c_19642,plain,
    ( leq(hd(sk3),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19557,c_19548]) ).

tcf(c_19648,plain,
    ( lt(hd(sk3),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19556,c_19548]) ).

tcf(c_19654,plain,
    ( leq(hd(sk3),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19555,c_19548]) ).

tcf(c_19660,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19576,c_19548]) ).

tcf(c_19669,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19575,c_19548]) ).

tcf(c_19678,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(cons(hd(sk4),app(sk3,sk3))),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ~ strictorderedP(app(app(X0,cons(hd(sk4),app(sk3,sk3))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk3))),cons(X1,X2))) ),
    inference(light_normalisation,[status(thm)],[c_19572,c_19548]) ).

tcf(c_19687,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(cons(hd(sk4),app(sk3,sk3))),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
      | ~ totalorderedP(app(app(X0,cons(hd(sk4),app(sk3,sk3))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk3))),cons(X1,X2))) ),
    inference(light_normalisation,[status(thm)],[c_19571,c_19548]) ).

tcf(c_19696,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19554,c_19548]) ).

tcf(c_19703,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19553,c_19548]) ).

tcf(c_19710,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19552,c_19548]) ).

tcf(c_19717,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_19551,c_19548]) ).

tcf(c_19899,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,cons(hd(X0),nil))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_18847]) ).

tcf(c_19900,plain,
    hd(app(sk3,cons(hd(sk4),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4059,c_18847]) ).

tcf(c_19901,plain,
    hd(app(sk3,cons(hd(sk3),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_18847]) ).

tcf(c_19909,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk3),app(sk4,sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_19278]) ).

tcf(c_19910,plain,
    hd(cons(hd(sk4),cons(hd(sk3),app(sk4,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_19278]) ).

tcf(c_19911,plain,
    hd(cons(hd(sk3),cons(hd(sk3),app(sk4,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_19278]) ).

tcf(c_19919,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),cons(hd(sk4),sk4))) = cons(hd(sk4),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_4241]) ).

tcf(c_19920,plain,
    tl(cons(hd(sk4),cons(hd(sk4),sk4))) = cons(hd(sk4),sk4),
    inference(superposition,[status(thm)],[c_4059,c_4241]) ).

tcf(c_19921,plain,
    tl(cons(hd(sk3),cons(hd(sk4),sk4))) = cons(hd(sk4),sk4),
    inference(superposition,[status(thm)],[c_10117,c_4241]) ).

tcf(c_19931,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk3,app(app(tl(sk3),sk3),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4037]) ).

tcf(c_19932,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk4,app(app(tl(sk3),sk3),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3952]) ).

tcf(c_19933,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(nil,app(app(tl(sk3),sk3),X0)) = app(app(tl(sk3),sk3),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3050]) ).

tcf(c_19934,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(app(app(tl(sk3),sk3),X0),nil) = app(app(tl(sk3),sk3),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3049]) ).

tcf(c_19935,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(app(app(tl(sk3),sk3),sk4),X0) = app(app(tl(sk3),sk3),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4540]) ).

tcf(c_19936,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(app(app(tl(sk3),sk3),sk3),X0) = app(app(tl(sk3),sk3),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4539]) ).

tcf(c_19937,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(app(X1,app(tl(sk3),sk3)),X0) = app(X1,app(app(tl(sk3),sk3),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_271]) ).

tcf(c_19938,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( cons(X1,app(X0,app(tl(sk3),sk3))) = app(cons(X1,X0),app(tl(sk3),sk3)) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_266]) ).

tcf(c_19939,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(tl(sk3),sk3) = nil )
      | ( app(tl(app(tl(sk3),sk3)),X0) = tl(app(app(tl(sk3),sk3),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_274]) ).

tcf(c_19940,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(tl(sk3),sk3) = nil )
      | ( hd(app(app(tl(sk3),sk3),X0)) = hd(app(tl(sk3),sk3)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_283]) ).

tcf(c_19941,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk3,cons(X0,app(tl(sk3),sk3)))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4038]) ).

tcf(c_19942,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(nil,app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_17993]) ).

tcf(c_19943,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(sk4,app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_17992]) ).

tcf(c_19944,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(sk3,app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_17991]) ).

tcf(c_19945,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk3,tl(app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4036]) ).

tcf(c_19946,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk4,cons(X0,app(tl(sk3),sk3)))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3953]) ).

tcf(c_19947,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(nil,app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15403]) ).

tcf(c_19948,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(sk4,app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15402]) ).

tcf(c_19949,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(sk3,app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15401]) ).

tcf(c_19950,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk4,tl(app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3951]) ).

tcf(c_19951,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),nil)) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3423]) ).

tcf(c_19952,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(nil,app(nil,app(tl(sk3),sk3))) = app(nil,app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_13452]) ).

tcf(c_19953,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(app(nil,app(tl(sk3),sk3)),nil) = app(nil,app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_12354]) ).

tcf(c_19954,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(app(sk4,app(tl(sk3),sk3)),nil) = app(sk4,app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_12353]) ).

tcf(c_19955,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(app(sk3,app(tl(sk3),sk3)),nil) = app(sk3,app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_12352]) ).

tcf(c_19956,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk3)),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3199]) ).

tcf(c_19957,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(nil,tl(app(tl(sk3),sk3))) = tl(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3066]) ).

tcf(c_19958,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(nil,app(sk4,app(tl(sk3),sk3))) = app(sk4,app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_8061]) ).

tcf(c_19959,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(app(sk4,sk4),app(tl(sk3),sk3)) = app(sk4,app(sk4,app(tl(sk3),sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_8048]) ).

tcf(c_19960,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(nil,app(sk3,app(tl(sk3),sk3))) = app(sk3,app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_5745]) ).

tcf(c_19961,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(app(sk3,sk4),app(tl(sk3),sk3)) = app(sk3,app(sk4,app(tl(sk3),sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_8047]) ).

tcf(c_19962,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(app(sk4,sk3),app(tl(sk3),sk3)) = app(sk4,app(sk3,app(tl(sk3),sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_5738]) ).

tcf(c_19963,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(app(sk3,sk3),app(tl(sk3),sk3)) = app(sk3,app(sk3,app(tl(sk3),sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_5737]) ).

tcf(c_19964,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk4),app(tl(sk3),sk3)) = tl(app(sk4,app(tl(sk3),sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4136]) ).

tcf(c_19965,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( cons(X0,app(app(tl(sk3),sk3),sk4)) = app(cons(X0,app(tl(sk3),sk3)),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4462]) ).

tcf(c_19966,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( cons(X0,app(app(tl(sk3),sk3),sk3)) = app(cons(X0,app(tl(sk3),sk3)),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4461]) ).

tcf(c_19967,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),app(tl(sk3),sk3)) = tl(app(sk3,app(tl(sk3),sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4284]) ).

tcf(c_19968,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(tl(sk3),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4027]) ).

tcf(c_19969,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(tl(sk3),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3885]) ).

tcf(c_19970,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(nil,cons(X0,app(tl(sk3),sk3))) = cons(X0,app(tl(sk3),sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3019]) ).

tcf(c_19971,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(cons(hd(app(tl(sk3),sk3)),sk4),nil) = cons(hd(app(tl(sk3),sk3)),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3452]) ).

tcf(c_19972,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(cons(hd(app(tl(sk3),sk3)),sk3),nil) = cons(hd(app(tl(sk3),sk3)),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3444]) ).

tcf(c_19973,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(tl(app(tl(sk3),sk3)),nil) = tl(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3065]) ).

tcf(c_19974,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),sk4)) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3215]) ).

tcf(c_19975,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),sk3)) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3207]) ).

tcf(c_19976,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(cons(X0,nil),app(tl(sk3),sk3)) = cons(X0,app(tl(sk3),sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_253]) ).

tcf(c_19977,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( cons(hd(app(tl(sk3),sk3)),tl(app(tl(sk3),sk3))) = app(tl(sk3),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_275]) ).

tcf(c_19978,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(cons(X0,app(tl(sk3),sk3)),nil) = cons(X0,app(tl(sk3),sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3018]) ).

tcf(c_19979,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk3)),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3191]) ).

tcf(c_19980,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk3)),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3183]) ).

tcf(c_19981,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(cons(X0,app(tl(sk3),sk3))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_284]) ).

tcf(c_19982,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( tl(cons(X0,app(tl(sk3),sk3))) = app(tl(sk3),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_276]) ).

tcf(c_19983,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(app(tl(sk3),sk3),nil) = app(tl(sk3),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_258]) ).

tcf(c_19984,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(nil,app(tl(sk3),sk3)) = app(tl(sk3),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_257]) ).

tcf(c_20236,plain,
    ( ssList(app(sk4,sk4))
    | ~ ssList(sk4) ),
    inference(instantiation,[status(thm)],[c_6088]) ).

tcf(c_20372,plain,
    ! [X0: $i] :
      ( ssList(cons(hd(sk3),X0))
      | ~ ssList(X0)
      | ~ ssItem(hd(sk3)) ),
    inference(instantiation,[status(thm)],[c_268]) ).

tcf(c_20375,plain,
    ( ssList(cons(hd(sk3),nil))
    | ~ ssList(nil)
    | ~ ssItem(hd(sk3)) ),
    inference(instantiation,[status(thm)],[c_20372]) ).

tcf(c_20398,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),nil))))
      | ( app(sk3,cons(hd(sk4),nil)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),nil)))
      | ~ ssList(app(sk3,cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_19900,c_280]) ).

tcf(c_20399,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),nil))))
      | ( app(sk3,cons(hd(sk4),nil)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),nil)))
      | ~ ssList(app(sk3,cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_19900,c_279]) ).

tcf(c_20415,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),nil))))
      | ( app(sk3,cons(hd(sk3),nil)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),nil)))
      | ~ ssList(app(sk3,cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_19901,c_280]) ).

tcf(c_20416,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),nil))))
      | ( app(sk3,cons(hd(sk3),nil)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),nil)))
      | ~ ssList(app(sk3,cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_19901,c_279]) ).

tcf(c_20432,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),app(sk4,sk3)))))
      | ( app(sk3,cons(hd(sk3),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),app(sk4,sk3))))
      | ~ ssList(app(sk3,cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19265,c_280]) ).

tcf(c_20433,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),app(sk4,sk3)))))
      | ( app(sk3,cons(hd(sk3),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),app(sk4,sk3))))
      | ~ ssList(app(sk3,cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19265,c_279]) ).

tcf(c_20449,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),app(sk4,sk3)))))
      | ( app(sk4,cons(hd(sk3),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),app(sk4,sk3))))
      | ~ ssList(app(sk4,cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19266,c_280]) ).

tcf(c_20450,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),app(sk4,sk3)))))
      | ( app(sk4,cons(hd(sk3),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),app(sk4,sk3))))
      | ~ ssList(app(sk4,cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19266,c_279]) ).

tcf(c_20467,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_10127,c_255]) ).

tcf(c_20468,plain,
    ( ( sk3 = nil )
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != nil ) ),
    inference(superposition,[status(thm)],[c_10127,c_254]) ).

tcf(c_20469,plain,
    ( ssList(cons(hd(sk3),app(sk3,sk3)))
    | ~ ssList(sk3)
    | ~ ssList(cons(hd(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_10127,c_272]) ).

tcf(c_20470,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( app(cons(hd(sk3),sk3),X0) != cons(hd(sk3),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10127,c_270]) ).

tcf(c_20471,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(sk3)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),sk3))
      | ( cons(hd(sk3),app(sk3,sk3)) != app(X0,sk3) ) ),
    inference(superposition,[status(thm)],[c_10127,c_269]) ).

tcf(c_20472,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),sk4) )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10127,c_19145]) ).

tcf(c_20473,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_10127,c_13738]) ).

tcf(c_20474,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_10127,c_14022]) ).

tcf(c_20475,plain,
    ( ( cons(hd(sk3),sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10127,c_9243]) ).

tcf(c_20476,plain,
    ( ( cons(hd(sk3),sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10127,c_8266]) ).

tcf(c_20477,plain,
    ( ( cons(hd(sk3),sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10127,c_7257]) ).

tcf(c_20478,plain,
    ( ( cons(hd(sk3),sk3) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10127,c_6600]) ).

tcf(c_20479,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10127,c_7546]) ).

tcf(c_20480,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10127,c_5892]) ).

tcf(c_20481,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ~ ssList(cons(hd(sk3),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != sk3 ) ),
    inference(superposition,[status(thm)],[c_10127,c_4683]) ).

tcf(c_20482,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk3)
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10127,c_17718]) ).

tcf(c_20483,plain,
    ssList(cons(hd(sk3),app(sk3,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_20469,c_246,c_13784]) ).

tcf(c_20484,plain,
    ( ( sk3 = sk4 )
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20482,c_246]) ).

tcf(c_20487,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( cons(hd(sk3),app(sk3,sk3)) != sk3 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20481,c_13784]) ).

tcf(c_20490,plain,
    ( ( sk3 = nil )
    | ( cons(hd(sk3),app(sk3,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20468,c_246,c_13784]) ).

tcf(c_20493,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( cons(hd(sk3),app(sk3,sk3)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20467,c_246,c_13784]) ).

tcf(c_20496,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),nil) )
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20474,c_13784]) ).

tcf(c_20499,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk3) )
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20480,c_13784]) ).

tcf(c_20502,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk4) )
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20479,c_13784]) ).

tcf(c_20505,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),sk4) )
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20472,c_13784]) ).

tcf(c_20508,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk3,sk3)) != app(X0,sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20471,c_246,c_13784]) ).

tcf(c_20512,plain,
    ! [X0: $i] :
      ( ( X0 = sk3 )
      | ~ ssList(X0)
      | ( app(cons(hd(sk3),sk3),X0) != cons(hd(sk3),app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20470,c_246,c_13784]) ).

tcf(c_20516,plain,
    ( ( cons(hd(sk3),sk3) = app(sk3,sk3) )
    | ~ ssList(app(sk3,sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20478,c_13784]) ).

tcf(c_20520,plain,
    ( ( cons(hd(sk3),sk3) = app(sk4,sk3) )
    | ~ ssList(app(sk4,sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20477,c_13784]) ).

tcf(c_20524,plain,
    ( ( cons(hd(sk3),sk3) = app(sk3,sk4) )
    | ~ ssList(app(sk3,sk4))
    | ( cons(hd(sk3),app(sk3,sk3)) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20476,c_13784]) ).

tcf(c_20528,plain,
    ( ( cons(hd(sk3),sk3) = app(sk4,sk4) )
    | ~ ssList(app(sk4,sk4))
    | ( cons(hd(sk3),app(sk3,sk3)) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20475,c_13784]) ).

tcf(c_20532,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),nil) )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20473,c_13784]) ).

tcf(c_20538,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),app(sk3,sk3)),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_4037]) ).

tcf(c_20539,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),app(sk3,sk3)),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3952]) ).

tcf(c_20540,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk3),app(sk3,sk3)),X0)) = app(cons(hd(sk3),app(sk3,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3050]) ).

tcf(c_20541,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk3,sk3)),X0),nil) = app(cons(hd(sk3),app(sk3,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3049]) ).

tcf(c_20542,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk3,sk3)),sk4),X0) = app(cons(hd(sk3),app(sk3,sk3)),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_4540]) ).

tcf(c_20543,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk3,sk3)),sk3),X0) = app(cons(hd(sk3),app(sk3,sk3)),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_4539]) ).

tcf(c_20544,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk3),app(sk3,sk3))),X0) = app(X1,app(cons(hd(sk3),app(sk3,sk3)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_271]) ).

tcf(c_20545,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk3),app(sk3,sk3)))) = app(cons(X1,X0),cons(hd(sk3),app(sk3,sk3))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_266]) ).

tcf(c_20546,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
      | ( app(tl(cons(hd(sk3),app(sk3,sk3))),X0) = tl(app(cons(hd(sk3),app(sk3,sk3)),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_274]) ).

tcf(c_20547,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
      | ( hd(app(cons(hd(sk3),app(sk3,sk3)),X0)) = hd(cons(hd(sk3),app(sk3,sk3))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_283]) ).

tcf(c_20548,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk3),app(sk3,sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_4038]) ).

tcf(c_20549,plain,
    hd(app(sk3,app(nil,cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_17993]) ).

tcf(c_20550,plain,
    hd(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_17992]) ).

tcf(c_20551,plain,
    hd(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_17991]) ).

tcf(c_20552,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_4036]) ).

tcf(c_20553,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk3),app(sk3,sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3953]) ).

tcf(c_20554,plain,
    hd(app(sk4,app(nil,cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_15403]) ).

tcf(c_20555,plain,
    hd(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_15402]) ).

tcf(c_20556,plain,
    hd(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_15401]) ).

tcf(c_20557,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3951]) ).

tcf(c_20558,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),nil)) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3423]) ).

tcf(c_20559,plain,
    app(nil,app(nil,cons(hd(sk3),app(sk3,sk3)))) = app(nil,cons(hd(sk3),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_20483,c_13452]) ).

tcf(c_20560,plain,
    app(app(nil,cons(hd(sk3),app(sk3,sk3))),nil) = app(nil,cons(hd(sk3),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_20483,c_12354]) ).

tcf(c_20561,plain,
    app(app(sk4,cons(hd(sk3),app(sk3,sk3))),nil) = app(sk4,cons(hd(sk3),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_20483,c_12353]) ).

tcf(c_20562,plain,
    app(app(sk3,cons(hd(sk3),app(sk3,sk3))),nil) = app(sk3,cons(hd(sk3),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_20483,c_12352]) ).

tcf(c_20563,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk3))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_20483,c_3199]) ).

tcf(c_20564,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(nil,tl(cons(hd(sk3),app(sk3,sk3)))) = tl(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3066]) ).

tcf(c_20565,plain,
    app(nil,app(sk4,cons(hd(sk3),app(sk3,sk3)))) = app(sk4,cons(hd(sk3),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_20483,c_8061]) ).

tcf(c_20566,plain,
    app(app(sk4,sk4),cons(hd(sk3),app(sk3,sk3))) = app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_20483,c_8048]) ).

tcf(c_20567,plain,
    app(nil,app(sk3,cons(hd(sk3),app(sk3,sk3)))) = app(sk3,cons(hd(sk3),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_20483,c_5745]) ).

tcf(c_20568,plain,
    app(app(sk3,sk4),cons(hd(sk3),app(sk3,sk3))) = app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_20483,c_8047]) ).

tcf(c_20569,plain,
    app(app(sk4,sk3),cons(hd(sk3),app(sk3,sk3))) = app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_20483,c_5738]) ).

tcf(c_20570,plain,
    app(app(sk3,sk3),cons(hd(sk3),app(sk3,sk3))) = app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_20483,c_5737]) ).

tcf(c_20571,plain,
    app(tl(sk4),cons(hd(sk3),app(sk3,sk3))) = tl(app(sk4,cons(hd(sk3),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_20483,c_4136]) ).

tcf(c_20572,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk3,sk3)),sk4)) = app(cons(X0,cons(hd(sk3),app(sk3,sk3))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_4462]) ).

tcf(c_20573,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk3,sk3)),sk3)) = app(cons(X0,cons(hd(sk3),app(sk3,sk3))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_4461]) ).

tcf(c_20574,plain,
    app(tl(sk3),cons(hd(sk3),app(sk3,sk3))) = tl(app(sk3,cons(hd(sk3),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_20483,c_4284]) ).

tcf(c_20575,plain,
    hd(app(sk3,cons(hd(sk3),app(sk3,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_4027]) ).

tcf(c_20576,plain,
    hd(app(sk4,cons(hd(sk3),app(sk3,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_3885]) ).

tcf(c_20577,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk3),app(sk3,sk3)))) = cons(X0,cons(hd(sk3),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3019]) ).

tcf(c_20578,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk3))),sk4),nil) = cons(hd(cons(hd(sk3),app(sk3,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3452]) ).

tcf(c_20579,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk3))),sk3),nil) = cons(hd(cons(hd(sk3),app(sk3,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3444]) ).

tcf(c_20580,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(tl(cons(hd(sk3),app(sk3,sk3))),nil) = tl(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3065]) ).

tcf(c_20581,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),sk4)) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3215]) ).

tcf(c_20582,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),sk3)) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3207]) ).

tcf(c_20583,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk3),app(sk3,sk3))) = cons(X0,cons(hd(sk3),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_253]) ).

tcf(c_20584,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( cons(hd(cons(hd(sk3),app(sk3,sk3))),tl(cons(hd(sk3),app(sk3,sk3)))) = cons(hd(sk3),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_20483,c_275]) ).

tcf(c_20585,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk3),app(sk3,sk3))),nil) = cons(X0,cons(hd(sk3),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3018]) ).

tcf(c_20586,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk3))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_20483,c_3191]) ).

tcf(c_20587,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk3))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_20483,c_3183]) ).

tcf(c_20588,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk3),app(sk3,sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_284]) ).

tcf(c_20589,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk3),app(sk3,sk3)))) = cons(hd(sk3),app(sk3,sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_276]) ).

tcf(c_20590,plain,
    app(cons(hd(sk3),app(sk3,sk3)),nil) = cons(hd(sk3),app(sk3,sk3)),
    inference(superposition,[status(thm)],[c_20483,c_258]) ).

tcf(c_20591,plain,
    app(nil,cons(hd(sk3),app(sk3,sk3))) = cons(hd(sk3),app(sk3,sk3)),
    inference(superposition,[status(thm)],[c_20483,c_257]) ).

tcf(c_20706,plain,
    cons(hd(sk3),app(sk3,sk3)) != nil,
    inference(global_subsumption_just,[status(thm)],[c_20490,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_20490]) ).

tcf(c_20718,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),nil) )
    | ~ ssList(cons(hd(sk4),nil))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk4),sk3) ) ),
    inference(superposition,[status(thm)],[c_4071,c_20508]) ).

tcf(c_20719,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk3) )
    | ~ ssList(cons(hd(sk4),sk3))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4976,c_20508]) ).

tcf(c_20720,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk4),sk4) )
    | ~ ssList(cons(hd(sk4),sk4))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_4999,c_20508]) ).

tcf(c_20722,plain,
    ( ( cons(hd(sk3),sk3) = cons(hd(sk3),sk4) )
    | ~ ssList(cons(hd(sk3),sk4))
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10126,c_20508]) ).

tcf(c_20736,plain,
    ( ( sk3 = nil )
    | ~ ssList(nil)
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_3768,c_20512]) ).

tcf(c_20737,plain,
    ( ( sk3 = sk4 )
    | ~ ssList(sk4)
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10124,c_20512]) ).

tcf(c_20739,plain,
    ( ( sk3 = nil )
    | ( cons(hd(sk3),app(sk3,sk3)) != cons(hd(sk3),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20736,c_259]) ).

tcf(c_20744,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),app(sk3,sk3)))))
      | ( app(sk3,cons(hd(sk3),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),app(sk3,sk3))))
      | ~ ssList(app(sk3,cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20575,c_280]) ).

tcf(c_20745,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),app(sk3,sk3)))))
      | ( app(sk3,cons(hd(sk3),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),app(sk3,sk3))))
      | ~ ssList(app(sk3,cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20575,c_279]) ).

tcf(c_20760,plain,
    tl(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)) = sk4,
    inference(global_subsumption_just,[status(thm)],[c_6403,c_5891,c_6403]) ).

tcf(c_20764,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))
      | ( tl(X0) != sk4 )
      | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_20760,c_273]) ).

tcf(c_20765,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))
      | ( tl(X0) != sk4 )
      | ( hd(cons(hd(sk4),app(sk3,sk3))) != hd(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_20764,c_17945]) ).

tcf(c_20777,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk3),app(sk3,sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_20588]) ).

tcf(c_20778,plain,
    hd(cons(hd(sk4),cons(hd(sk3),app(sk3,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_20588]) ).

tcf(c_20779,plain,
    hd(cons(hd(sk3),cons(hd(sk3),app(sk3,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_20588]) ).

tcf(c_20901,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk3,app(app(tl(sk3),sk4),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4037]) ).

tcf(c_20902,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk4,app(app(tl(sk3),sk4),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3952]) ).

tcf(c_20903,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(nil,app(app(tl(sk3),sk4),X0)) = app(app(tl(sk3),sk4),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3050]) ).

tcf(c_20904,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(app(app(tl(sk3),sk4),X0),nil) = app(app(tl(sk3),sk4),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3049]) ).

tcf(c_20905,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(app(app(tl(sk3),sk4),sk4),X0) = app(app(tl(sk3),sk4),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4540]) ).

tcf(c_20906,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(app(app(tl(sk3),sk4),sk3),X0) = app(app(tl(sk3),sk4),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4539]) ).

tcf(c_20907,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(app(X1,app(tl(sk3),sk4)),X0) = app(X1,app(app(tl(sk3),sk4),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_271]) ).

tcf(c_20908,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( cons(X1,app(X0,app(tl(sk3),sk4))) = app(cons(X1,X0),app(tl(sk3),sk4)) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_266]) ).

tcf(c_20909,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(tl(sk3),sk4) = nil )
      | ( app(tl(app(tl(sk3),sk4)),X0) = tl(app(app(tl(sk3),sk4),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_274]) ).

tcf(c_20910,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(tl(sk3),sk4) = nil )
      | ( hd(app(app(tl(sk3),sk4),X0)) = hd(app(tl(sk3),sk4)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_283]) ).

tcf(c_20911,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk3,cons(X0,app(tl(sk3),sk4)))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4038]) ).

tcf(c_20912,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(nil,app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_17993]) ).

tcf(c_20913,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(sk4,app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_17992]) ).

tcf(c_20914,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(sk3,app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_17991]) ).

tcf(c_20915,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk3,tl(app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4036]) ).

tcf(c_20916,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk4,cons(X0,app(tl(sk3),sk4)))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3953]) ).

tcf(c_20917,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(nil,app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15403]) ).

tcf(c_20918,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(sk4,app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15402]) ).

tcf(c_20919,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(sk3,app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15401]) ).

tcf(c_20920,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk4,tl(app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3951]) ).

tcf(c_20921,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),nil)) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3423]) ).

tcf(c_20922,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(nil,app(nil,app(tl(sk3),sk4))) = app(nil,app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_13452]) ).

tcf(c_20923,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(app(nil,app(tl(sk3),sk4)),nil) = app(nil,app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_12354]) ).

tcf(c_20924,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(app(sk4,app(tl(sk3),sk4)),nil) = app(sk4,app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_12353]) ).

tcf(c_20925,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(app(sk3,app(tl(sk3),sk4)),nil) = app(sk3,app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_12352]) ).

tcf(c_20926,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk4)),nil)) = nil )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3199]) ).

tcf(c_20927,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(nil,tl(app(tl(sk3),sk4))) = tl(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3066]) ).

tcf(c_20928,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(nil,app(sk4,app(tl(sk3),sk4))) = app(sk4,app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_8061]) ).

tcf(c_20929,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(app(sk4,sk4),app(tl(sk3),sk4)) = app(sk4,app(sk4,app(tl(sk3),sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_8048]) ).

tcf(c_20930,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(nil,app(sk3,app(tl(sk3),sk4))) = app(sk3,app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_5745]) ).

tcf(c_20931,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(app(sk3,sk4),app(tl(sk3),sk4)) = app(sk3,app(sk4,app(tl(sk3),sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_8047]) ).

tcf(c_20932,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(app(sk4,sk3),app(tl(sk3),sk4)) = app(sk4,app(sk3,app(tl(sk3),sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_5738]) ).

tcf(c_20933,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(app(sk3,sk3),app(tl(sk3),sk4)) = app(sk3,app(sk3,app(tl(sk3),sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_5737]) ).

tcf(c_20934,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk4),app(tl(sk3),sk4)) = tl(app(sk4,app(tl(sk3),sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4136]) ).

tcf(c_20935,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( cons(X0,app(app(tl(sk3),sk4),sk4)) = app(cons(X0,app(tl(sk3),sk4)),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4462]) ).

tcf(c_20936,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( cons(X0,app(app(tl(sk3),sk4),sk3)) = app(cons(X0,app(tl(sk3),sk4)),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4461]) ).

tcf(c_20937,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),app(tl(sk3),sk4)) = tl(app(sk3,app(tl(sk3),sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4284]) ).

tcf(c_20938,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(tl(sk3),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4027]) ).

tcf(c_20939,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(tl(sk3),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3885]) ).

tcf(c_20940,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(nil,cons(X0,app(tl(sk3),sk4))) = cons(X0,app(tl(sk3),sk4)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3019]) ).

tcf(c_20941,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(cons(hd(app(tl(sk3),sk4)),sk4),nil) = cons(hd(app(tl(sk3),sk4)),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3452]) ).

tcf(c_20942,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(cons(hd(app(tl(sk3),sk4)),sk3),nil) = cons(hd(app(tl(sk3),sk4)),sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3444]) ).

tcf(c_20943,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(tl(app(tl(sk3),sk4)),nil) = tl(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3065]) ).

tcf(c_20944,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),sk4)) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3215]) ).

tcf(c_20945,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),sk3)) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3207]) ).

tcf(c_20946,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(cons(X0,nil),app(tl(sk3),sk4)) = cons(X0,app(tl(sk3),sk4)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_253]) ).

tcf(c_20947,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( cons(hd(app(tl(sk3),sk4)),tl(app(tl(sk3),sk4))) = app(tl(sk3),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_275]) ).

tcf(c_20948,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(cons(X0,app(tl(sk3),sk4)),nil) = cons(X0,app(tl(sk3),sk4)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3018]) ).

tcf(c_20949,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk4)),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3191]) ).

tcf(c_20950,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk4)),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3183]) ).

tcf(c_20951,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(cons(X0,app(tl(sk3),sk4))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_284]) ).

tcf(c_20952,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( tl(cons(X0,app(tl(sk3),sk4))) = app(tl(sk3),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_276]) ).

tcf(c_20953,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(app(tl(sk3),sk4),nil) = app(tl(sk3),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_258]) ).

tcf(c_20954,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(nil,app(tl(sk3),sk4)) = app(tl(sk3),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_257]) ).

tcf(c_21301,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),cons(hd(sk4),sk3))) = cons(hd(sk4),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_4377]) ).

tcf(c_21302,plain,
    tl(cons(hd(sk4),cons(hd(sk4),sk3))) = cons(hd(sk4),sk3),
    inference(superposition,[status(thm)],[c_4059,c_4377]) ).

tcf(c_21303,plain,
    tl(cons(hd(sk3),cons(hd(sk4),sk3))) = cons(hd(sk4),sk3),
    inference(superposition,[status(thm)],[c_10117,c_4377]) ).

tcf(c_21313,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk3,app(app(tl(sk4),sk3),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4037]) ).

tcf(c_21314,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk4,app(app(tl(sk4),sk3),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3952]) ).

tcf(c_21315,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(nil,app(app(tl(sk4),sk3),X0)) = app(app(tl(sk4),sk3),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3050]) ).

tcf(c_21316,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(app(app(tl(sk4),sk3),X0),nil) = app(app(tl(sk4),sk3),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3049]) ).

tcf(c_21317,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(app(app(tl(sk4),sk3),sk4),X0) = app(app(tl(sk4),sk3),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4540]) ).

tcf(c_21318,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(app(app(tl(sk4),sk3),sk3),X0) = app(app(tl(sk4),sk3),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4539]) ).

tcf(c_21319,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(app(X1,app(tl(sk4),sk3)),X0) = app(X1,app(app(tl(sk4),sk3),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_271]) ).

tcf(c_21320,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( cons(X1,app(X0,app(tl(sk4),sk3))) = app(cons(X1,X0),app(tl(sk4),sk3)) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_266]) ).

tcf(c_21321,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(tl(sk4),sk3) = nil )
      | ( app(tl(app(tl(sk4),sk3)),X0) = tl(app(app(tl(sk4),sk3),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_274]) ).

tcf(c_21322,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(tl(sk4),sk3) = nil )
      | ( hd(app(app(tl(sk4),sk3),X0)) = hd(app(tl(sk4),sk3)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_283]) ).

tcf(c_21323,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk3,cons(X0,app(tl(sk4),sk3)))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4038]) ).

tcf(c_21324,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(nil,app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_17993]) ).

tcf(c_21325,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(sk4,app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_17992]) ).

tcf(c_21326,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(sk3,app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_17991]) ).

tcf(c_21327,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk3,tl(app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4036]) ).

tcf(c_21328,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk4,cons(X0,app(tl(sk4),sk3)))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3953]) ).

tcf(c_21329,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(nil,app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15403]) ).

tcf(c_21330,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(sk4,app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15402]) ).

tcf(c_21331,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(sk3,app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15401]) ).

tcf(c_21332,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk4,tl(app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3951]) ).

tcf(c_21333,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),nil)) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3423]) ).

tcf(c_21334,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(nil,app(nil,app(tl(sk4),sk3))) = app(nil,app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_13452]) ).

tcf(c_21335,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(app(nil,app(tl(sk4),sk3)),nil) = app(nil,app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_12354]) ).

tcf(c_21336,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(app(sk4,app(tl(sk4),sk3)),nil) = app(sk4,app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_12353]) ).

tcf(c_21337,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(app(sk3,app(tl(sk4),sk3)),nil) = app(sk3,app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_12352]) ).

tcf(c_21338,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk3)),nil)) = nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3199]) ).

tcf(c_21339,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(nil,tl(app(tl(sk4),sk3))) = tl(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3066]) ).

tcf(c_21340,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(nil,app(sk4,app(tl(sk4),sk3))) = app(sk4,app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_8061]) ).

tcf(c_21341,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(app(sk4,sk4),app(tl(sk4),sk3)) = app(sk4,app(sk4,app(tl(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_8048]) ).

tcf(c_21342,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(nil,app(sk3,app(tl(sk4),sk3))) = app(sk3,app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_5745]) ).

tcf(c_21343,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(app(sk3,sk4),app(tl(sk4),sk3)) = app(sk3,app(sk4,app(tl(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_8047]) ).

tcf(c_21344,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(app(sk4,sk3),app(tl(sk4),sk3)) = app(sk4,app(sk3,app(tl(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_5738]) ).

tcf(c_21345,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(app(sk3,sk3),app(tl(sk4),sk3)) = app(sk3,app(sk3,app(tl(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_5737]) ).

tcf(c_21346,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),app(tl(sk4),sk3)) = tl(app(sk4,app(tl(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4136]) ).

tcf(c_21347,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( cons(X0,app(app(tl(sk4),sk3),sk4)) = app(cons(X0,app(tl(sk4),sk3)),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4462]) ).

tcf(c_21348,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( cons(X0,app(app(tl(sk4),sk3),sk3)) = app(cons(X0,app(tl(sk4),sk3)),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4461]) ).

tcf(c_21349,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk3),app(tl(sk4),sk3)) = tl(app(sk3,app(tl(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4284]) ).

tcf(c_21350,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(tl(sk4),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4027]) ).

tcf(c_21351,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(tl(sk4),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3885]) ).

tcf(c_21352,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(nil,cons(X0,app(tl(sk4),sk3))) = cons(X0,app(tl(sk4),sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3019]) ).

tcf(c_21353,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(cons(hd(app(tl(sk4),sk3)),sk4),nil) = cons(hd(app(tl(sk4),sk3)),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3452]) ).

tcf(c_21354,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(cons(hd(app(tl(sk4),sk3)),sk3),nil) = cons(hd(app(tl(sk4),sk3)),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3444]) ).

tcf(c_21355,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(tl(app(tl(sk4),sk3)),nil) = tl(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3065]) ).

tcf(c_21356,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),sk4)) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3215]) ).

tcf(c_21357,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),sk3)) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3207]) ).

tcf(c_21358,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(cons(X0,nil),app(tl(sk4),sk3)) = cons(X0,app(tl(sk4),sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_253]) ).

tcf(c_21359,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( cons(hd(app(tl(sk4),sk3)),tl(app(tl(sk4),sk3))) = app(tl(sk4),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_275]) ).

tcf(c_21360,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(cons(X0,app(tl(sk4),sk3)),nil) = cons(X0,app(tl(sk4),sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3018]) ).

tcf(c_21361,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk3)),sk4)) = sk4 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3191]) ).

tcf(c_21362,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk3)),sk3)) = sk3 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3183]) ).

tcf(c_21363,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(cons(X0,app(tl(sk4),sk3))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_284]) ).

tcf(c_21364,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( tl(cons(X0,app(tl(sk4),sk3))) = app(tl(sk4),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_276]) ).

tcf(c_21365,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(app(tl(sk4),sk3),nil) = app(tl(sk4),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_258]) ).

tcf(c_21366,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(nil,app(tl(sk4),sk3)) = app(tl(sk4),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_257]) ).

tcf(c_21743,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),app(sk3,sk3)))))
      | ( app(sk4,cons(hd(sk3),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),app(sk3,sk3))))
      | ~ ssList(app(sk4,cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20576,c_280]) ).

tcf(c_21744,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),app(sk3,sk3)))))
      | ( app(sk4,cons(hd(sk3),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),app(sk3,sk3))))
      | ~ ssList(app(sk4,cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20576,c_279]) ).

tcf(c_21764,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),app(sk3,sk3)))))
      | ( cons(hd(sk4),cons(hd(sk4),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_11626,c_280]) ).

tcf(c_21765,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),app(sk3,sk3)))))
      | ( cons(hd(sk4),cons(hd(sk4),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_11626,c_279]) ).

tcf(c_21840,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),app(sk3,sk3)))))
      | ( cons(hd(sk3),cons(hd(sk4),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_11627,c_280]) ).

tcf(c_21841,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),app(sk3,sk3)))))
      | ( cons(hd(sk3),cons(hd(sk4),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk4),app(sk3,sk3))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_11627,c_279]) ).

tcf(c_21857,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),app(sk4,sk3)))))
      | ( cons(hd(sk4),cons(hd(sk4),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_11636,c_280]) ).

tcf(c_21858,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),app(sk4,sk3)))))
      | ( cons(hd(sk4),cons(hd(sk4),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_11636,c_279]) ).

tcf(c_21874,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_14819,c_280]) ).

tcf(c_21875,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_14819,c_279]) ).

tcf(c_21891,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_14820,c_280]) ).

tcf(c_21892,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_14820,c_279]) ).

tcf(c_21961,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_14821,c_280]) ).

tcf(c_21962,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_14821,c_279]) ).

tcf(c_21978,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_14822,c_280]) ).

tcf(c_21979,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_14822,c_279]) ).

tcf(c_21999,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17384,c_280]) ).

tcf(c_22000,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17384,c_279]) ).

tcf(c_22020,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17385,c_280]) ).

tcf(c_22021,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17385,c_279]) ).

tcf(c_22037,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_17386,c_280]) ).

tcf(c_22038,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_17386,c_279]) ).

tcf(c_22058,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_17387,c_280]) ).

tcf(c_22059,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_17387,c_279]) ).

tcf(c_22078,plain,
    tl(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)) = sk3,
    inference(global_subsumption_just,[status(thm)],[c_6404,c_5891,c_6404]) ).

tcf(c_22082,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))
      | ( tl(X0) != sk3 )
      | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_22078,c_273]) ).

tcf(c_22083,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) = nil )
      | ( cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))
      | ( tl(X0) != sk3 )
      | ( hd(cons(hd(sk4),app(sk3,sk3))) != hd(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_22082,c_18743]) ).

tcf(c_22091,plain,
    ( ssList(app(tl(sk4),sk4))
    | ( app(sk4,sk4) = nil ) ),
    inference(global_subsumption_just,[status(thm)],[c_5638,c_247,c_5638,c_20236]) ).

tcf(c_22097,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk3,app(app(tl(sk4),sk4),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_4037]) ).

tcf(c_22098,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk4,app(app(tl(sk4),sk4),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3952]) ).

tcf(c_22099,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(nil,app(app(tl(sk4),sk4),X0)) = app(app(tl(sk4),sk4),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3050]) ).

tcf(c_22100,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(app(app(tl(sk4),sk4),X0),nil) = app(app(tl(sk4),sk4),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3049]) ).

tcf(c_22101,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(app(app(tl(sk4),sk4),sk4),X0) = app(app(tl(sk4),sk4),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_4540]) ).

tcf(c_22102,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(app(app(tl(sk4),sk4),sk3),X0) = app(app(tl(sk4),sk4),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_4539]) ).

tcf(c_22103,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(app(X1,app(tl(sk4),sk4)),X0) = app(X1,app(app(tl(sk4),sk4),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_271]) ).

tcf(c_22104,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( cons(X1,app(X0,app(tl(sk4),sk4))) = app(cons(X1,X0),app(tl(sk4),sk4)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_266]) ).

tcf(c_22105,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(tl(sk4),sk4) = nil )
      | ( app(tl(app(tl(sk4),sk4)),X0) = tl(app(app(tl(sk4),sk4),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_274]) ).

tcf(c_22106,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(tl(sk4),sk4) = nil )
      | ( hd(app(app(tl(sk4),sk4),X0)) = hd(app(tl(sk4),sk4)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_283]) ).

tcf(c_22107,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk3,cons(X0,app(tl(sk4),sk4)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_4038]) ).

tcf(c_22108,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(nil,app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_17993]) ).

tcf(c_22109,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(sk4,app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_17992]) ).

tcf(c_22110,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(sk3,app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_17991]) ).

tcf(c_22111,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk3,tl(app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_4036]) ).

tcf(c_22112,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk4,cons(X0,app(tl(sk4),sk4)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3953]) ).

tcf(c_22113,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(nil,app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_15403]) ).

tcf(c_22114,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(sk4,app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_15402]) ).

tcf(c_22115,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(sk3,app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_15401]) ).

tcf(c_22116,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk4,tl(app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3951]) ).

tcf(c_22117,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),nil)) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3423]) ).

tcf(c_22118,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(nil,app(nil,app(tl(sk4),sk4))) = app(nil,app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_13452]) ).

tcf(c_22119,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(app(nil,app(tl(sk4),sk4)),nil) = app(nil,app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_12354]) ).

tcf(c_22120,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(app(sk4,app(tl(sk4),sk4)),nil) = app(sk4,app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_12353]) ).

tcf(c_22121,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(app(sk3,app(tl(sk4),sk4)),nil) = app(sk3,app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_12352]) ).

tcf(c_22122,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk4)),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_22091,c_3199]) ).

tcf(c_22123,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(nil,tl(app(tl(sk4),sk4))) = tl(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3066]) ).

tcf(c_22124,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(nil,app(sk4,app(tl(sk4),sk4))) = app(sk4,app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_8061]) ).

tcf(c_22125,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(app(sk4,sk4),app(tl(sk4),sk4)) = app(sk4,app(sk4,app(tl(sk4),sk4))) ) ),
    inference(superposition,[status(thm)],[c_22091,c_8048]) ).

tcf(c_22126,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(nil,app(sk3,app(tl(sk4),sk4))) = app(sk3,app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_5745]) ).

tcf(c_22127,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(app(sk3,sk4),app(tl(sk4),sk4)) = app(sk3,app(sk4,app(tl(sk4),sk4))) ) ),
    inference(superposition,[status(thm)],[c_22091,c_8047]) ).

tcf(c_22128,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(app(sk4,sk3),app(tl(sk4),sk4)) = app(sk4,app(sk3,app(tl(sk4),sk4))) ) ),
    inference(superposition,[status(thm)],[c_22091,c_5738]) ).

tcf(c_22129,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(app(sk3,sk3),app(tl(sk4),sk4)) = app(sk3,app(sk3,app(tl(sk4),sk4))) ) ),
    inference(superposition,[status(thm)],[c_22091,c_5737]) ).

tcf(c_22130,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),app(tl(sk4),sk4)) = tl(app(sk4,app(tl(sk4),sk4))) ) ),
    inference(superposition,[status(thm)],[c_22091,c_4136]) ).

tcf(c_22131,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( cons(X0,app(app(tl(sk4),sk4),sk4)) = app(cons(X0,app(tl(sk4),sk4)),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_4462]) ).

tcf(c_22132,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( cons(X0,app(app(tl(sk4),sk4),sk3)) = app(cons(X0,app(tl(sk4),sk4)),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_4461]) ).

tcf(c_22133,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk3),app(tl(sk4),sk4)) = tl(app(sk3,app(tl(sk4),sk4))) ) ),
    inference(superposition,[status(thm)],[c_22091,c_4284]) ).

tcf(c_22134,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(tl(sk4),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_4027]) ).

tcf(c_22135,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(tl(sk4),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3885]) ).

tcf(c_22136,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(nil,cons(X0,app(tl(sk4),sk4))) = cons(X0,app(tl(sk4),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3019]) ).

tcf(c_22137,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(cons(hd(app(tl(sk4),sk4)),sk4),nil) = cons(hd(app(tl(sk4),sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3452]) ).

tcf(c_22138,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(cons(hd(app(tl(sk4),sk4)),sk3),nil) = cons(hd(app(tl(sk4),sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3444]) ).

tcf(c_22139,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(tl(app(tl(sk4),sk4)),nil) = tl(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3065]) ).

tcf(c_22140,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),sk4)) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3215]) ).

tcf(c_22141,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),sk3)) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3207]) ).

tcf(c_22142,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(cons(X0,nil),app(tl(sk4),sk4)) = cons(X0,app(tl(sk4),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_253]) ).

tcf(c_22143,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( cons(hd(app(tl(sk4),sk4)),tl(app(tl(sk4),sk4))) = app(tl(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_275]) ).

tcf(c_22144,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(cons(X0,app(tl(sk4),sk4)),nil) = cons(X0,app(tl(sk4),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3018]) ).

tcf(c_22145,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk4)),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_22091,c_3191]) ).

tcf(c_22146,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk4)),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_22091,c_3183]) ).

tcf(c_22147,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(cons(X0,app(tl(sk4),sk4))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_284]) ).

tcf(c_22148,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( tl(cons(X0,app(tl(sk4),sk4))) = app(tl(sk4),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_276]) ).

tcf(c_22149,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(app(tl(sk4),sk4),nil) = app(tl(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_258]) ).

tcf(c_22150,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(nil,app(tl(sk4),sk4)) = app(tl(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_257]) ).

tcf(c_22527,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(cons(hd(sk4),app(sk3,sk3)),X0) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_6407,c_270]) ).

tcf(c_22528,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( cons(hd(sk4),app(sk3,sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_6407,c_269]) ).

tcf(c_22529,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk3,sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22528,c_259,c_5886]) ).

tcf(c_22533,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),app(sk3,sk3)),X0) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22527,c_259,c_5886]) ).

tcf(c_22546,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( cons(hd(sk4),app(sk3,sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_6408,c_270]) ).

tcf(c_22547,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(X0,cons(hd(sk4),app(sk3,sk3))) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_6408,c_269]) ).

tcf(c_22548,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk4),app(sk3,sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_6408,c_300]) ).

tcf(c_22549,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk4),app(sk3,sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_6408,c_287]) ).

tcf(c_22550,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk4),app(sk3,sk3))) != cons(hd(sk4),app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22547,c_259,c_5886]) ).

tcf(c_22554,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk3,sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22546,c_259,c_5886]) ).

tcf(c_22558,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_22549,c_6408]) ).

tcf(c_22559,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22558,c_259,c_4059]) ).

tcf(c_22566,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_22548,c_6408]) ).

tcf(c_22567,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk3)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22566,c_259,c_4059]) ).

tcf(c_22606,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(cons(hd(sk4),app(sk4,sk3)),X0) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7605,c_270]) ).

tcf(c_22607,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( cons(hd(sk4),app(sk4,sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_7605,c_269]) ).

tcf(c_22608,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk4,sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22607,c_259,c_7540]) ).

tcf(c_22612,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),app(sk4,sk3)),X0) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22606,c_259,c_7540]) ).

tcf(c_22618,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),app(sk4,sk3)))))
      | ( cons(hd(sk3),cons(hd(sk4),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_11637,c_280]) ).

tcf(c_22619,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),app(sk4,sk3)))))
      | ( cons(hd(sk3),cons(hd(sk4),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_11637,c_279]) ).

tcf(c_22635,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),app(sk3,sk4)))))
      | ( cons(hd(sk4),cons(hd(sk4),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_12331,c_280]) ).

tcf(c_22636,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),app(sk3,sk4)))))
      | ( cons(hd(sk4),cons(hd(sk4),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_12331,c_279]) ).

tcf(c_22652,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),app(sk3,sk4)))))
      | ( cons(hd(sk3),cons(hd(sk4),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_12332,c_280]) ).

tcf(c_22653,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),app(sk3,sk4)))))
      | ( cons(hd(sk3),cons(hd(sk4),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_12332,c_279]) ).

tcf(c_22691,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),app(sk4,sk4)))))
      | ( cons(hd(sk4),cons(hd(sk4),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_12341,c_280]) ).

tcf(c_22692,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),app(sk4,sk4)))))
      | ( cons(hd(sk4),cons(hd(sk4),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_12341,c_279]) ).

tcf(c_22708,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_17388,c_280]) ).

tcf(c_22709,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_17388,c_279]) ).

tcf(c_22725,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_15599,c_280]) ).

tcf(c_22726,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_15599,c_279]) ).

tcf(c_22742,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_15603,c_280]) ).

tcf(c_22743,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_15603,c_279]) ).

tcf(c_22790,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_15609,c_280]) ).

tcf(c_22791,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_15609,c_279]) ).

tcf(c_22807,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_15610,c_280]) ).

tcf(c_22808,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_15610,c_279]) ).

tcf(c_22856,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_15972,c_280]) ).

tcf(c_22857,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_15972,c_279]) ).

tcf(c_22882,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_15976,c_280]) ).

tcf(c_22883,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_15976,c_279]) ).

tcf(c_22940,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_15982,c_280]) ).

tcf(c_22941,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_15982,c_279]) ).

tcf(c_22958,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_7188,c_255]) ).

tcf(c_22959,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_7188,c_254]) ).

tcf(c_22960,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_7188,c_272]) ).

tcf(c_22961,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != app(app(sk4,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_7188,c_270]) ).

tcf(c_22962,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != app(X0,cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_7188,c_269]) ).

tcf(c_22963,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(app(sk4,sk3),cons(hd(sk4),sk3)),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7188,c_300]) ).

tcf(c_22964,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(app(sk4,sk3),cons(hd(sk4),sk3)),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7188,c_287]) ).

tcf(c_22965,plain,
    ( ( cons(hd(sk4),sk3) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_7188,c_7768]) ).

tcf(c_22966,plain,
    ( ( cons(hd(sk4),sk3) = sk3 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7188,c_7262]) ).

tcf(c_22967,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22960,c_4358]) ).

tcf(c_22974,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22959,c_4430,c_4358]) ).

tcf(c_22977,plain,
    ( ( cons(hd(sk4),sk3) = sk3 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22966,c_4358]) ).

tcf(c_22981,plain,
    ( ( cons(hd(sk4),sk3) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22965,c_4358]) ).

tcf(c_22985,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != app(X0,cons(hd(sk4),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22962,c_4358]) ).

tcf(c_22990,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) != app(app(sk4,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22961,c_4358]) ).

tcf(c_22995,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_22964,c_7188]) ).

tcf(c_22996,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22995,c_246,c_4059]) ).

tcf(c_23003,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_22963,c_7188]) ).

tcf(c_23004,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23003,c_246,c_4059]) ).

tcf(c_23019,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4037]) ).

tcf(c_23020,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3952]) ).

tcf(c_23021,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)) = app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3050]) ).

tcf(c_23022,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0),nil) = app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3049]) ).

tcf(c_23023,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4),X0) = app(app(sk4,app(sk3,cons(hd(sk4),sk3))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4540]) ).

tcf(c_23024,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk3),X0) = app(app(sk4,app(sk3,cons(hd(sk4),sk3))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4539]) ).

tcf(c_23025,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk3,cons(hd(sk4),sk3)))),X0) = app(X1,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_271]) ).

tcf(c_23026,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(cons(X1,X0),app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_266]) ).

tcf(c_23027,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))),X0) = tl(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_274]) ).

tcf(c_23028,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_283]) ).

tcf(c_23029,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4038]) ).

tcf(c_23030,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_17993]) ).

tcf(c_23031,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_17992]) ).

tcf(c_23032,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_17991]) ).

tcf(c_23033,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4036]) ).

tcf(c_23034,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3953]) ).

tcf(c_23035,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15403]) ).

tcf(c_23036,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15402]) ).

tcf(c_23037,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15401]) ).

tcf(c_23038,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3951]) ).

tcf(c_23039,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil)) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3423]) ).

tcf(c_23040,plain,
    ( ( app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_13452]) ).

tcf(c_23041,plain,
    ( ( app(app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil) = app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_12354]) ).

tcf(c_23042,plain,
    ( ( app(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_12353]) ).

tcf(c_23043,plain,
    ( ( app(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_12352]) ).

tcf(c_23044,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil)) = nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3199]) ).

tcf(c_23045,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))) = tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3066]) ).

tcf(c_23046,plain,
    ( ( app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_8061]) ).

tcf(c_23047,plain,
    ( ( app(app(sk4,sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))) = app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_8048]) ).

tcf(c_23048,plain,
    ( ( app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_5745]) ).

tcf(c_23049,plain,
    ( ( app(app(sk3,sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))) = app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_8047]) ).

tcf(c_23050,plain,
    ( ( app(app(sk4,sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))) = app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_5738]) ).

tcf(c_23051,plain,
    ( ( app(app(sk3,sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))) = app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_5737]) ).

tcf(c_23052,plain,
    ( ( app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))) = tl(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4136]) ).

tcf(c_23053,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4462]) ).

tcf(c_23054,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk3)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4461]) ).

tcf(c_23055,plain,
    ( ( app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))) = tl(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4284]) ).

tcf(c_23056,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4027]) ).

tcf(c_23057,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3885]) ).

tcf(c_23058,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3019]) ).

tcf(c_23059,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3452]) ).

tcf(c_23060,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3444]) ).

tcf(c_23061,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil) = tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3065]) ).

tcf(c_23062,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4)) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3215]) ).

tcf(c_23063,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3)) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3207]) ).

tcf(c_23064,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk3,cons(hd(sk4),sk3)))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_253]) ).

tcf(c_23065,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(sk4,app(sk3,cons(hd(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_275]) ).

tcf(c_23066,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3018]) ).

tcf(c_23067,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4)) = sk4 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3191]) ).

tcf(c_23068,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3)) = sk3 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3183]) ).

tcf(c_23069,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_284]) ).

tcf(c_23070,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(sk4,app(sk3,cons(hd(sk4),sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_276]) ).

tcf(c_23071,plain,
    ( ( app(app(sk4,app(sk3,cons(hd(sk4),sk3))),nil) = app(sk4,app(sk3,cons(hd(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_258]) ).

tcf(c_23072,plain,
    ( ( app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3)))) = app(sk4,app(sk3,cons(hd(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_257]) ).

tcf(c_23188,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_23028,c_15596]) ).

tcf(c_23199,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(sk4,app(sk3,cons(hd(sk4),sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_23065,c_15596]) ).

tcf(c_23428,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( cons(hd(sk4),app(sk4,sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_7606,c_270]) ).

tcf(c_23429,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(X0,cons(hd(sk4),app(sk4,sk3))) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7606,c_269]) ).

tcf(c_23430,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk4),app(sk4,sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7606,c_300]) ).

tcf(c_23431,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk4),app(sk4,sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7606,c_287]) ).

tcf(c_23432,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk4),app(sk4,sk3))) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23429,c_259,c_7540]) ).

tcf(c_23436,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk4,sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23428,c_259,c_7540]) ).

tcf(c_23440,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_23431,c_7606]) ).

tcf(c_23441,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23440,c_259,c_4059]) ).

tcf(c_23448,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_23430,c_7606]) ).

tcf(c_23449,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk3)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23448,c_259,c_4059]) ).

tcf(c_23487,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(cons(hd(sk4),app(sk3,sk4)),X0) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10232,c_270]) ).

tcf(c_23488,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( cons(hd(sk4),app(sk3,sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_10232,c_269]) ).

tcf(c_23489,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk3,sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23488,c_259,c_10188]) ).

tcf(c_23493,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),app(sk3,sk4)),X0) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23487,c_259,c_10188]) ).

tcf(c_23506,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( cons(hd(sk4),app(sk3,sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_10233,c_270]) ).

tcf(c_23507,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(X0,cons(hd(sk4),app(sk3,sk4))) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10233,c_269]) ).

tcf(c_23508,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk4),app(sk3,sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10233,c_300]) ).

tcf(c_23509,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk4),app(sk3,sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10233,c_287]) ).

tcf(c_23510,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk4),app(sk3,sk4))) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23507,c_259,c_10188]) ).

tcf(c_23514,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk3,sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23506,c_259,c_10188]) ).

tcf(c_23518,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_23509,c_10233]) ).

tcf(c_23519,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23518,c_259,c_4059]) ).

tcf(c_23526,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_23508,c_10233]) ).

tcf(c_23527,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk3,sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23526,c_259,c_4059]) ).

tcf(c_23537,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),app(sk4,sk4)))))
      | ( cons(hd(sk3),cons(hd(sk4),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),app(sk4,sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_12342,c_280]) ).

tcf(c_23538,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),app(sk4,sk4)))))
      | ( cons(hd(sk3),cons(hd(sk4),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk4),app(sk4,sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_12342,c_279]) ).

tcf(c_23554,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),app(sk4,sk4)))))
      | ( cons(hd(sk4),cons(hd(sk3),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),app(sk4,sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17298,c_280]) ).

tcf(c_23555,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),app(sk4,sk4)))))
      | ( cons(hd(sk4),cons(hd(sk3),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk3),app(sk4,sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17298,c_279]) ).

tcf(c_23571,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),app(sk4,sk4)))))
      | ( cons(hd(sk3),cons(hd(sk3),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17299,c_280]) ).

tcf(c_23572,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),app(sk4,sk4)))))
      | ( cons(hd(sk3),cons(hd(sk3),app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17299,c_279]) ).

tcf(c_23633,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),app(sk3,sk4)))))
      | ( cons(hd(sk4),cons(hd(sk3),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),app(sk3,sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17980,c_280]) ).

tcf(c_23634,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),app(sk3,sk4)))))
      | ( cons(hd(sk4),cons(hd(sk3),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk3),app(sk3,sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17980,c_279]) ).

tcf(c_23661,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk3))))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_22996]) ).

tcf(c_23662,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk3))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_22996]) ).

tcf(c_23663,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_22996]) ).

tcf(c_23664,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_22996]) ).

tcf(c_23672,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_23663,c_3365]) ).

tcf(c_23673,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23672,c_4059]) ).

tcf(c_23679,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk3))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23662,c_10117]) ).

tcf(c_23686,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_23664,c_19548]) ).

tcf(c_23706,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk3))))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_23004]) ).

tcf(c_23707,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk3))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_23004]) ).

tcf(c_23708,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_23004]) ).

tcf(c_23709,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_23004]) ).

tcf(c_23717,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_23708,c_3365]) ).

tcf(c_23718,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23717,c_4059]) ).

tcf(c_23724,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),sk3))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23707,c_10117]) ).

tcf(c_23731,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_23709,c_19548]) ).

tcf(c_23740,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_15983,c_280]) ).

tcf(c_23741,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_15983,c_279]) ).

tcf(c_23758,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17012,c_280]) ).

tcf(c_23759,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17012,c_279]) ).

tcf(c_23775,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17013,c_280]) ).

tcf(c_23776,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17013,c_279]) ).

tcf(c_23793,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_17770,c_280]) ).

tcf(c_23794,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_17770,c_279]) ).

tcf(c_23811,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_7189,c_255]) ).

tcf(c_23812,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_7189,c_254]) ).

tcf(c_23813,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_7189,c_272]) ).

tcf(c_23814,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != app(app(sk4,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_7189,c_270]) ).

tcf(c_23815,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != app(X0,cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_7189,c_269]) ).

tcf(c_23816,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(app(sk4,sk3),cons(hd(sk4),sk4)),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7189,c_300]) ).

tcf(c_23817,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(app(sk4,sk3),cons(hd(sk4),sk4)),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7189,c_287]) ).

tcf(c_23818,plain,
    ( ( cons(hd(sk4),sk4) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_7189,c_7768]) ).

tcf(c_23819,plain,
    ( ( cons(hd(sk4),sk4) = sk3 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7189,c_7262]) ).

tcf(c_23820,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23813,c_4223]) ).

tcf(c_23827,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23812,c_4281,c_4223]) ).

tcf(c_23830,plain,
    ( ( cons(hd(sk4),sk4) = sk3 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23819,c_4223]) ).

tcf(c_23834,plain,
    ( ( cons(hd(sk4),sk4) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23818,c_4223]) ).

tcf(c_23838,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != app(X0,cons(hd(sk4),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23815,c_4223]) ).

tcf(c_23843,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) != app(app(sk4,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23814,c_4223]) ).

tcf(c_23848,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_23817,c_7189]) ).

tcf(c_23849,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23848,c_247,c_4059]) ).

tcf(c_23856,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_23816,c_7189]) ).

tcf(c_23857,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23856,c_247,c_4059]) ).

tcf(c_23872,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4037]) ).

tcf(c_23873,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3952]) ).

tcf(c_23874,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)) = app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3050]) ).

tcf(c_23875,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0),nil) = app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3049]) ).

tcf(c_23876,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4),X0) = app(app(sk4,app(sk3,cons(hd(sk4),sk4))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4540]) ).

tcf(c_23877,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk3),X0) = app(app(sk4,app(sk3,cons(hd(sk4),sk4))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4539]) ).

tcf(c_23878,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk3,cons(hd(sk4),sk4)))),X0) = app(X1,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_271]) ).

tcf(c_23879,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(cons(X1,X0),app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_266]) ).

tcf(c_23880,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))),X0) = tl(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_274]) ).

tcf(c_23881,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_283]) ).

tcf(c_23882,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4038]) ).

tcf(c_23883,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_17993]) ).

tcf(c_23884,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_17992]) ).

tcf(c_23885,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_17991]) ).

tcf(c_23886,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4036]) ).

tcf(c_23887,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3953]) ).

tcf(c_23888,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15403]) ).

tcf(c_23889,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15402]) ).

tcf(c_23890,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15401]) ).

tcf(c_23891,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3951]) ).

tcf(c_23892,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil)) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3423]) ).

tcf(c_23893,plain,
    ( ( app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_13452]) ).

tcf(c_23894,plain,
    ( ( app(app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil) = app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_12354]) ).

tcf(c_23895,plain,
    ( ( app(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_12353]) ).

tcf(c_23896,plain,
    ( ( app(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_12352]) ).

tcf(c_23897,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil)) = nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3199]) ).

tcf(c_23898,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))) = tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3066]) ).

tcf(c_23899,plain,
    ( ( app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_8061]) ).

tcf(c_23900,plain,
    ( ( app(app(sk4,sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))) = app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_8048]) ).

tcf(c_23901,plain,
    ( ( app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_5745]) ).

tcf(c_23902,plain,
    ( ( app(app(sk3,sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))) = app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_8047]) ).

tcf(c_23903,plain,
    ( ( app(app(sk4,sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))) = app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_5738]) ).

tcf(c_23904,plain,
    ( ( app(app(sk3,sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))) = app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_5737]) ).

tcf(c_23905,plain,
    ( ( app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))) = tl(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4136]) ).

tcf(c_23906,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4462]) ).

tcf(c_23907,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk3)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4461]) ).

tcf(c_23908,plain,
    ( ( app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))) = tl(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4284]) ).

tcf(c_23909,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4027]) ).

tcf(c_23910,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3885]) ).

tcf(c_23911,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3019]) ).

tcf(c_23912,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3452]) ).

tcf(c_23913,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3444]) ).

tcf(c_23914,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil) = tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3065]) ).

tcf(c_23915,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4)) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3215]) ).

tcf(c_23916,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3)) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3207]) ).

tcf(c_23917,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk3,cons(hd(sk4),sk4)))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_253]) ).

tcf(c_23918,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(sk4,app(sk3,cons(hd(sk4),sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_275]) ).

tcf(c_23919,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3018]) ).

tcf(c_23920,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4)) = sk4 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3191]) ).

tcf(c_23921,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3)) = sk3 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3183]) ).

tcf(c_23922,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_284]) ).

tcf(c_23923,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(sk4,app(sk3,cons(hd(sk4),sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_276]) ).

tcf(c_23924,plain,
    ( ( app(app(sk4,app(sk3,cons(hd(sk4),sk4))),nil) = app(sk4,app(sk3,cons(hd(sk4),sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_258]) ).

tcf(c_23925,plain,
    ( ( app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4)))) = app(sk4,app(sk3,cons(hd(sk4),sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_257]) ).

tcf(c_24041,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_23881,c_15598]) ).

tcf(c_24052,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(sk4,app(sk3,cons(hd(sk4),sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_23918,c_15598]) ).

tcf(c_24518,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( tl(cons(X1,tl(X0))) = tl(X0) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_276]) ).

tcf(c_24548,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X1,tl(X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_284]) ).

tcf(c_24549,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(cons(X2,app(X1,X0))) = X2 )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_284]) ).

tcf(c_24597,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ( hd(cons(X0,tl(sk3))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_24548]) ).

tcf(c_24606,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(sk3))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_24597,c_7100]) ).

tcf(c_24635,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(sk3,X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_24549]) ).

tcf(c_24756,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ( tl(cons(X0,tl(sk3))) = tl(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_24518]) ).

tcf(c_24765,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(sk3))) = tl(sk3) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_24756,c_7100]) ).

tcf(c_24793,plain,
    ( ( sk4 = nil )
    | ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_247,c_275]) ).

tcf(c_24796,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( cons(hd(app(X1,X0)),tl(app(X1,X0))) = app(X1,X0) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_275]) ).

tcf(c_24798,plain,
    cons(hd(sk4),tl(sk4)) = sk4,
    inference(forward_subsumption_resolution,[status(thm)],[c_24793,c_1243]) ).

tcf(c_25166,plain,
    ! [X0: $i] :
      ( ( app(sk3,X0) = nil )
      | ( cons(hd(app(sk3,X0)),tl(app(sk3,X0))) = app(sk3,X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_24796]) ).

tcf(c_25241,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ( hd(app(sk3,X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_283]) ).

tcf(c_25250,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_25241,c_7100]) ).

tcf(c_26586,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(hd(X0),X0))
      | ( X0 = nil )
      | ~ totalorderedP(X0)
      | ~ ssList(X0)
      | ~ ssItem(hd(X0)) ),
    inference(superposition,[status(thm)],[c_307,c_280]) ).

tcf(c_26618,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(hd(X0),X0))
      | ( X0 = nil )
      | ~ totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_26586,c_286,c_5405]) ).

tcf(c_27808,plain,
    ( totalorderedP(tl(sk4))
    | ( tl(sk4) = nil )
    | ~ totalorderedP(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(superposition,[status(thm)],[c_24798,c_301]) ).

tcf(c_27809,plain,
    ( strictorderedP(tl(sk4))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(superposition,[status(thm)],[c_24798,c_288]) ).

tcf(c_28286,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk4,sk4)))
      | ( app(cons(hd(sk4),app(sk4,sk4)),X0) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10698,c_270]) ).

tcf(c_28287,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk4,sk4)))
      | ( cons(hd(sk4),app(sk4,sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_10698,c_269]) ).

tcf(c_28288,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk4,sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28287,c_259,c_10606]) ).

tcf(c_28292,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk4),app(sk4,sk4)),X0) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28286,c_259,c_10606]) ).

tcf(c_28305,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk4,sk4)))
      | ( cons(hd(sk4),app(sk4,sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_10699,c_270]) ).

tcf(c_28306,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),app(sk4,sk4)))
      | ( app(X0,cons(hd(sk4),app(sk4,sk4))) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10699,c_269]) ).

tcf(c_28307,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk4),app(sk4,sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10699,c_300]) ).

tcf(c_28308,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk4),app(sk4,sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10699,c_287]) ).

tcf(c_28309,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk4),app(sk4,sk4))) != cons(hd(sk4),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28306,c_259,c_10606]) ).

tcf(c_28313,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk4),app(sk4,sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28305,c_259,c_10606]) ).

tcf(c_28317,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_28308,c_10699]) ).

tcf(c_28318,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28317,c_259,c_4059]) ).

tcf(c_28325,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_28307,c_10699]) ).

tcf(c_28326,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk4),app(sk4,sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28325,c_259,c_4059]) ).

tcf(c_28344,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4037]) ).

tcf(c_28345,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3952]) ).

tcf(c_28346,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3050]) ).

tcf(c_28347,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0),nil) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3049]) ).

tcf(c_28348,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),sk4),X0) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4540]) ).

tcf(c_28349,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),sk3),X0) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4539]) ).

tcf(c_28350,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),X0) = app(X1,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_271]) ).

tcf(c_28351,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(cons(X1,X0),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_266]) ).

tcf(c_28352,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),X0) = tl(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_274]) ).

tcf(c_28353,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_283]) ).

tcf(c_28354,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4038]) ).

tcf(c_28355,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_17993]) ).

tcf(c_28356,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_17992]) ).

tcf(c_28357,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_17991]) ).

tcf(c_28358,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4036]) ).

tcf(c_28359,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3953]) ).

tcf(c_28360,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15403]) ).

tcf(c_28361,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15402]) ).

tcf(c_28362,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15401]) ).

tcf(c_28363,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3951]) ).

tcf(c_28364,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3423]) ).

tcf(c_28365,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_13452]) ).

tcf(c_28366,plain,
    ( ( app(app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_12354]) ).

tcf(c_28367,plain,
    ( ( app(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_12353]) ).

tcf(c_28368,plain,
    ( ( app(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_12352]) ).

tcf(c_28369,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3199]) ).

tcf(c_28370,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3066]) ).

tcf(c_28371,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_8061]) ).

tcf(c_28372,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_8048]) ).

tcf(c_28373,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_5745]) ).

tcf(c_28374,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_8047]) ).

tcf(c_28375,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_5738]) ).

tcf(c_28376,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_5737]) ).

tcf(c_28377,plain,
    ( ( app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = tl(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4136]) ).

tcf(c_28378,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),sk4)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4462]) ).

tcf(c_28379,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),sk3)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4461]) ).

tcf(c_28380,plain,
    ( ( app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = tl(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4284]) ).

tcf(c_28381,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4027]) ).

tcf(c_28382,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3885]) ).

tcf(c_28383,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3019]) ).

tcf(c_28384,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3452]) ).

tcf(c_28385,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3444]) ).

tcf(c_28386,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3065]) ).

tcf(c_28387,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3215]) ).

tcf(c_28388,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3207]) ).

tcf(c_28389,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_253]) ).

tcf(c_28390,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_275]) ).

tcf(c_28391,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3018]) ).

tcf(c_28392,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3191]) ).

tcf(c_28393,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3183]) ).

tcf(c_28394,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_284]) ).

tcf(c_28395,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_276]) ).

tcf(c_28396,plain,
    ( ( app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),nil) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_258]) ).

tcf(c_28397,plain,
    ( ( app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_257]) ).

tcf(c_28513,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_28353,c_18191]) ).

tcf(c_28524,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_28390,c_18191]) ).

tcf(c_28619,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),app(sk3,sk4)))))
      | ( cons(hd(sk3),cons(hd(sk3),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17981,c_280]) ).

tcf(c_28620,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),app(sk3,sk4)))))
      | ( cons(hd(sk3),cons(hd(sk3),app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17981,c_279]) ).

tcf(c_28636,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),app(sk4,sk3)))))
      | ( cons(hd(sk4),cons(hd(sk3),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),app(sk4,sk3))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19910,c_280]) ).

tcf(c_28637,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),app(sk4,sk3)))))
      | ( cons(hd(sk4),cons(hd(sk3),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk3),app(sk4,sk3))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19910,c_279]) ).

tcf(c_28653,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),app(sk4,sk3)))))
      | ( cons(hd(sk3),cons(hd(sk3),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk3))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19911,c_280]) ).

tcf(c_28654,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),app(sk4,sk3)))))
      | ( cons(hd(sk3),cons(hd(sk3),app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk3))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19911,c_279]) ).

tcf(c_28691,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),cons(hd(sk4),sk4)) = nil )
      | ( cons(hd(sk4),cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk4)))
      | ( cons(hd(sk4),sk4) != tl(X0) )
      | ( hd(cons(hd(sk4),cons(hd(sk4),sk4))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_19920,c_273]) ).

tcf(c_28692,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),cons(hd(sk4),sk4)) = nil )
      | ( cons(hd(sk4),cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk4)))
      | ( hd(X0) != hd(sk4) )
      | ( cons(hd(sk4),sk4) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_28691,c_5647]) ).

tcf(c_28712,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk4))))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_23849]) ).

tcf(c_28713,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk3))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_23849]) ).

tcf(c_28714,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_23849]) ).

tcf(c_28715,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_23849]) ).

tcf(c_28723,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_28714,c_3365]) ).

tcf(c_28724,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28723,c_4059]) ).

tcf(c_28730,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk3))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28713,c_10117]) ).

tcf(c_28737,plain,
    ( lt(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_28715,c_19548]) ).

tcf(c_28757,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk4))))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_23857]) ).

tcf(c_28758,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk3))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_23857]) ).

tcf(c_28759,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_23857]) ).

tcf(c_28760,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_19548,c_23857]) ).

tcf(c_28768,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_28759,c_3365]) ).

tcf(c_28769,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28768,c_4059]) ).

tcf(c_28775,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),sk3))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28758,c_10117]) ).

tcf(c_28782,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssItem(hd(cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_28760,c_19548]) ).

tcf(c_28791,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_17771,c_280]) ).

tcf(c_28792,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_17771,c_279]) ).

tcf(c_28808,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_18191,c_280]) ).

tcf(c_28809,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_18191,c_279]) ).

tcf(c_28825,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_18195,c_280]) ).

tcf(c_28826,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_18195,c_279]) ).

tcf(c_28862,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18201,c_280]) ).

tcf(c_28863,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18201,c_279]) ).

tcf(c_28879,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18202,c_280]) ).

tcf(c_28880,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18202,c_279]) ).

tcf(c_28896,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18205,c_280]) ).

tcf(c_28897,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18205,c_279]) ).

tcf(c_28914,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_7190,c_255]) ).

tcf(c_28915,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_7190,c_254]) ).

tcf(c_28916,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_7190,c_272]) ).

tcf(c_28917,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(app(sk4,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_7190,c_270]) ).

tcf(c_28918,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(X0,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7190,c_269]) ).

tcf(c_28919,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(app(sk4,sk3),cons(hd(sk4),app(sk3,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7190,c_300]) ).

tcf(c_28920,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(app(sk4,sk3),cons(hd(sk4),app(sk3,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7190,c_287]) ).

tcf(c_28921,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_7190,c_7768]) ).

tcf(c_28922,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk3 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7190,c_7262]) ).

tcf(c_28923,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk4,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28916,c_5886]) ).

tcf(c_28930,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28915,c_5891,c_5886]) ).

tcf(c_28933,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28922,c_5887,c_5886]) ).

tcf(c_28936,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28921,c_5886]) ).

tcf(c_28940,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(X0,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28918,c_5886]) ).

tcf(c_28945,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(app(sk4,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28917,c_5886]) ).

tcf(c_28950,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_28920,c_7190]) ).

tcf(c_28951,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28950,c_4059]) ).

tcf(c_28959,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_28919,c_7190]) ).

tcf(c_28960,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28959,c_4059]) ).

tcf(c_28976,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),cons(hd(sk3),sk4))) = cons(hd(sk3),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_13195]) ).

tcf(c_28977,plain,
    tl(cons(hd(sk4),cons(hd(sk3),sk4))) = cons(hd(sk3),sk4),
    inference(superposition,[status(thm)],[c_4059,c_13195]) ).

tcf(c_28978,plain,
    tl(cons(hd(sk3),cons(hd(sk3),sk4))) = cons(hd(sk3),sk4),
    inference(superposition,[status(thm)],[c_10117,c_13195]) ).

tcf(c_28996,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),cons(hd(sk3),sk3))) = cons(hd(sk3),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_13823]) ).

tcf(c_28997,plain,
    tl(cons(hd(sk4),cons(hd(sk3),sk3))) = cons(hd(sk3),sk3),
    inference(superposition,[status(thm)],[c_4059,c_13823]) ).

tcf(c_28998,plain,
    tl(cons(hd(sk3),cons(hd(sk3),sk3))) = cons(hd(sk3),sk3),
    inference(superposition,[status(thm)],[c_10117,c_13823]) ).

tcf(c_29010,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk4,sk4)))
      | ( app(cons(hd(sk3),app(sk4,sk4)),X0) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_17047,c_270]) ).

tcf(c_29011,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk4,sk4)))
      | ( cons(hd(sk3),app(sk4,sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_17047,c_269]) ).

tcf(c_29012,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk4,sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29011,c_259,c_16922]) ).

tcf(c_29016,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk3),app(sk4,sk4)),X0) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29010,c_259,c_16922]) ).

tcf(c_29029,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk4,sk4)))
      | ( cons(hd(sk3),app(sk4,sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_17048,c_270]) ).

tcf(c_29030,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk4,sk4)))
      | ( app(X0,cons(hd(sk3),app(sk4,sk4))) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_17048,c_269]) ).

tcf(c_29031,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk3),app(sk4,sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_17048,c_300]) ).

tcf(c_29032,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk3),app(sk4,sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_17048,c_287]) ).

tcf(c_29033,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk3),app(sk4,sk4))) != cons(hd(sk3),app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29030,c_259,c_16922]) ).

tcf(c_29037,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk4,sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29029,c_259,c_16922]) ).

tcf(c_29041,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29032,c_17048]) ).

tcf(c_29042,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29041,c_259,c_10117]) ).

tcf(c_29049,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29031,c_17048]) ).

tcf(c_29050,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29049,c_259,c_10117]) ).

tcf(c_29071,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),cons(hd(sk4),sk4)) = nil )
      | ( cons(hd(sk3),cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk4)))
      | ( cons(hd(sk4),sk4) != tl(X0) )
      | ( hd(cons(hd(sk3),cons(hd(sk4),sk4))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_19921,c_273]) ).

tcf(c_29072,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),cons(hd(sk4),sk4)) = nil )
      | ( cons(hd(sk3),cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk4)))
      | ( hd(X0) != hd(sk3) )
      | ( cons(hd(sk4),sk4) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_29071,c_10125]) ).

tcf(c_29081,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),app(sk3,sk3)))))
      | ( cons(hd(sk4),cons(hd(sk3),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),app(sk3,sk3))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20778,c_280]) ).

tcf(c_29082,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),app(sk3,sk3)))))
      | ( cons(hd(sk4),cons(hd(sk3),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk3),app(sk3,sk3))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20778,c_279]) ).

tcf(c_29098,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),app(sk3,sk3)))))
      | ( cons(hd(sk3),cons(hd(sk3),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk3))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20779,c_280]) ).

tcf(c_29099,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),app(sk3,sk3)))))
      | ( cons(hd(sk3),cons(hd(sk3),app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk3))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20779,c_279]) ).

tcf(c_29126,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),cons(hd(sk4),sk3)) = nil )
      | ( cons(hd(sk4),cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk3)))
      | ( cons(hd(sk4),sk3) != tl(X0) )
      | ( hd(cons(hd(sk4),cons(hd(sk4),sk3))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_21302,c_273]) ).

tcf(c_29127,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),cons(hd(sk4),sk3)) = nil )
      | ( cons(hd(sk4),cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk3)))
      | ( hd(X0) != hd(sk4) )
      | ( cons(hd(sk4),sk3) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_29126,c_8020]) ).

tcf(c_29136,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18206,c_280]) ).

tcf(c_29137,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18206,c_279]) ).

tcf(c_29153,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_18503,c_280]) ).

tcf(c_29154,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_18503,c_279]) ).

tcf(c_29170,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_18507,c_280]) ).

tcf(c_29171,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_18507,c_279]) ).

tcf(c_29197,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18513,c_280]) ).

tcf(c_29198,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18513,c_279]) ).

tcf(c_29214,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18514,c_280]) ).

tcf(c_29215,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18514,c_279]) ).

tcf(c_29231,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18517,c_280]) ).

tcf(c_29232,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18517,c_279]) ).

tcf(c_29248,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18518,c_280]) ).

tcf(c_29249,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18518,c_279]) ).

tcf(c_29279,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_7584,c_255]) ).

tcf(c_29280,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_7584,c_254]) ).

tcf(c_29281,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_7584,c_272]) ).

tcf(c_29282,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(app(sk4,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_7584,c_270]) ).

tcf(c_29283,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(X0,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7584,c_269]) ).

tcf(c_29284,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(app(sk4,sk3),cons(hd(sk4),app(sk4,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7584,c_300]) ).

tcf(c_29285,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(app(sk4,sk3),cons(hd(sk4),app(sk4,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7584,c_287]) ).

tcf(c_29286,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_7584,c_7768]) ).

tcf(c_29287,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk3 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7584,c_7262]) ).

tcf(c_29288,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk4,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29281,c_7540]) ).

tcf(c_29295,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29280,c_7545,c_7540]) ).

tcf(c_29298,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29287,c_7541,c_7540]) ).

tcf(c_29301,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29286,c_7540]) ).

tcf(c_29305,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(X0,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29283,c_7540]) ).

tcf(c_29310,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(app(sk4,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29282,c_7540]) ).

tcf(c_29315,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29285,c_7584]) ).

tcf(c_29316,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29315,c_4059]) ).

tcf(c_29323,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29284,c_7584]) ).

tcf(c_29324,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29323,c_4059]) ).

tcf(c_29347,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk3,sk4)))
      | ( app(cons(hd(sk3),app(sk3,sk4)),X0) != cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_17805,c_270]) ).

tcf(c_29348,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk3,sk4)))
      | ( cons(hd(sk3),app(sk3,sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_17805,c_269]) ).

tcf(c_29349,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk3,sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29348,c_259,c_17697]) ).

tcf(c_29353,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk3),app(sk3,sk4)),X0) != cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29347,c_259,c_17697]) ).

tcf(c_29402,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk3,sk4)))
      | ( cons(hd(sk3),app(sk3,sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_17806,c_270]) ).

tcf(c_29403,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk3,sk4)))
      | ( app(X0,cons(hd(sk3),app(sk3,sk4))) != cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_17806,c_269]) ).

tcf(c_29404,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk3),app(sk3,sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_17806,c_300]) ).

tcf(c_29405,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk3),app(sk3,sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_17806,c_287]) ).

tcf(c_29406,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk3),app(sk3,sk4))) != cons(hd(sk3),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29403,c_259,c_17697]) ).

tcf(c_29410,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk3,sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29402,c_259,c_17697]) ).

tcf(c_29414,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29405,c_17806]) ).

tcf(c_29415,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29414,c_259,c_10117]) ).

tcf(c_29422,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29404,c_17806]) ).

tcf(c_29423,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29422,c_259,c_10117]) ).

tcf(c_29460,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk4,sk3)))
      | ( app(cons(hd(sk3),app(sk4,sk3)),X0) != cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_19280,c_270]) ).

tcf(c_29461,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk4,sk3)))
      | ( cons(hd(sk3),app(sk4,sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_19280,c_269]) ).

tcf(c_29462,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk4,sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29461,c_259,c_19123]) ).

tcf(c_29466,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk3),app(sk4,sk3)),X0) != cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29460,c_259,c_19123]) ).

tcf(c_29479,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk4,sk3)))
      | ( cons(hd(sk3),app(sk4,sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_19281,c_270]) ).

tcf(c_29480,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk4,sk3)))
      | ( app(X0,cons(hd(sk3),app(sk4,sk3))) != cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_19281,c_269]) ).

tcf(c_29481,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk3),app(sk4,sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_19281,c_300]) ).

tcf(c_29482,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk3),app(sk4,sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_19281,c_287]) ).

tcf(c_29483,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk3),app(sk4,sk3))) != cons(hd(sk3),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29480,c_259,c_19123]) ).

tcf(c_29487,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk4,sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29479,c_259,c_19123]) ).

tcf(c_29491,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29482,c_19281]) ).

tcf(c_29492,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29491,c_259,c_10117]) ).

tcf(c_29499,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29481,c_19281]) ).

tcf(c_29500,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk4,sk3)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29499,c_259,c_10117]) ).

tcf(c_29511,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),cons(hd(sk4),sk3)) = nil )
      | ( cons(hd(sk3),cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk3)))
      | ( cons(hd(sk4),sk3) != tl(X0) )
      | ( hd(cons(hd(sk3),cons(hd(sk4),sk3))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_21303,c_273]) ).

tcf(c_29512,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),cons(hd(sk4),sk3)) = nil )
      | ( cons(hd(sk3),cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk3)))
      | ( hd(X0) != hd(sk3) )
      | ( cons(hd(sk4),sk3) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_29511,c_10122]) ).

tcf(c_29522,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),cons(hd(sk3),sk4)) = nil )
      | ( cons(hd(sk4),cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk4)))
      | ( cons(hd(sk3),sk4) != tl(X0) )
      | ( hd(cons(hd(sk4),cons(hd(sk3),sk4))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_28977,c_273]) ).

tcf(c_29523,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),cons(hd(sk3),sk4)) = nil )
      | ( cons(hd(sk4),cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk4)))
      | ( hd(X0) != hd(sk4) )
      | ( cons(hd(sk3),sk4) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_29522,c_13439]) ).

tcf(c_29533,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),cons(hd(sk3),sk4)) = nil )
      | ( cons(hd(sk3),cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk4)))
      | ( cons(hd(sk3),sk4) != tl(X0) )
      | ( hd(cons(hd(sk3),cons(hd(sk3),sk4))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_28978,c_273]) ).

tcf(c_29534,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),cons(hd(sk3),sk4)) = nil )
      | ( cons(hd(sk3),cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk4)))
      | ( hd(X0) != hd(sk3) )
      | ( cons(hd(sk3),sk4) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_29533,c_13440]) ).

tcf(c_29547,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),cons(hd(sk3),sk3)) = nil )
      | ( cons(hd(sk4),cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk3)))
      | ( cons(hd(sk3),sk3) != tl(X0) )
      | ( hd(cons(hd(sk4),cons(hd(sk3),sk3))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_28997,c_273]) ).

tcf(c_29548,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),cons(hd(sk3),sk3)) = nil )
      | ( cons(hd(sk4),cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk3)))
      | ( hd(X0) != hd(sk4) )
      | ( cons(hd(sk3),sk3) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_29547,c_14346]) ).

tcf(c_29557,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19240,c_280]) ).

tcf(c_29558,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19240,c_279]) ).

tcf(c_29580,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19241,c_280]) ).

tcf(c_29581,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19241,c_279]) ).

tcf(c_29598,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19245,c_280]) ).

tcf(c_29599,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19245,c_279]) ).

tcf(c_29615,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19246,c_280]) ).

tcf(c_29616,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19246,c_279]) ).

tcf(c_29671,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20550,c_280]) ).

tcf(c_29672,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20550,c_279]) ).

tcf(c_29688,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20551,c_280]) ).

tcf(c_29689,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20551,c_279]) ).

tcf(c_29706,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_7585,c_255]) ).

tcf(c_29707,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_7585,c_254]) ).

tcf(c_29708,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_7585,c_272]) ).

tcf(c_29709,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(app(sk3,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_7585,c_270]) ).

tcf(c_29710,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(X0,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7585,c_269]) ).

tcf(c_29711,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(app(sk3,sk3),cons(hd(sk4),app(sk4,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7585,c_300]) ).

tcf(c_29712,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(app(sk3,sk3),cons(hd(sk4),app(sk4,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_7585,c_287]) ).

tcf(c_29713,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_7585,c_6948]) ).

tcf(c_29714,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_7585,c_6605]) ).

tcf(c_29715,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk3,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29708,c_7540]) ).

tcf(c_29722,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29707,c_7545,c_7540]) ).

tcf(c_29725,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29714,c_7541,c_7540]) ).

tcf(c_29728,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29713,c_7540]) ).

tcf(c_29732,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(X0,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29710,c_7540]) ).

tcf(c_29737,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(app(sk3,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29709,c_7540]) ).

tcf(c_29742,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29712,c_7585]) ).

tcf(c_29743,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29742,c_4059]) ).

tcf(c_29751,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29711,c_7585]) ).

tcf(c_29752,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29751,c_4059]) ).

tcf(c_29772,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk3,sk3)))
      | ( app(cons(hd(sk3),app(sk3,sk3)),X0) != cons(hd(sk3),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_20590,c_270]) ).

tcf(c_29773,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk3,sk3)))
      | ( cons(hd(sk3),app(sk3,sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_20590,c_269]) ).

tcf(c_29774,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk3,sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29773,c_259,c_20483]) ).

tcf(c_29778,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk3),app(sk3,sk3)),X0) != cons(hd(sk3),app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29772,c_259,c_20483]) ).

tcf(c_29791,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk3,sk3)))
      | ( cons(hd(sk3),app(sk3,sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_20591,c_270]) ).

tcf(c_29792,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),app(sk3,sk3)))
      | ( app(X0,cons(hd(sk3),app(sk3,sk3))) != cons(hd(sk3),app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_20591,c_269]) ).

tcf(c_29793,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk3),app(sk3,sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_20591,c_300]) ).

tcf(c_29794,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk3),app(sk3,sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_20591,c_287]) ).

tcf(c_29795,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk3),app(sk3,sk3))) != cons(hd(sk3),app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29792,c_259,c_20483]) ).

tcf(c_29799,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),app(sk3,sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29791,c_259,c_20483]) ).

tcf(c_29803,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29794,c_20591]) ).

tcf(c_29804,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29803,c_259,c_10117]) ).

tcf(c_29811,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_29793,c_20591]) ).

tcf(c_29812,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),app(sk3,sk3)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29811,c_259,c_10117]) ).

tcf(c_29852,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4037]) ).

tcf(c_29853,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3952]) ).

tcf(c_29854,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3050]) ).

tcf(c_29855,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0),nil) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3049]) ).

tcf(c_29856,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),sk4),X0) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4540]) ).

tcf(c_29857,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),sk3),X0) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4539]) ).

tcf(c_29858,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),X0) = app(X1,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_271]) ).

tcf(c_29859,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(cons(X1,X0),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_266]) ).

tcf(c_29860,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),X0) = tl(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_274]) ).

tcf(c_29861,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_283]) ).

tcf(c_29862,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4038]) ).

tcf(c_29863,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_17993]) ).

tcf(c_29864,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_17992]) ).

tcf(c_29865,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_17991]) ).

tcf(c_29866,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4036]) ).

tcf(c_29867,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3953]) ).

tcf(c_29868,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15403]) ).

tcf(c_29869,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15402]) ).

tcf(c_29870,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15401]) ).

tcf(c_29871,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3951]) ).

tcf(c_29872,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3423]) ).

tcf(c_29873,plain,
    ( ( app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_13452]) ).

tcf(c_29874,plain,
    ( ( app(app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_12354]) ).

tcf(c_29875,plain,
    ( ( app(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_12353]) ).

tcf(c_29876,plain,
    ( ( app(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_12352]) ).

tcf(c_29877,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil)) = nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3199]) ).

tcf(c_29878,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3066]) ).

tcf(c_29879,plain,
    ( ( app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_8061]) ).

tcf(c_29880,plain,
    ( ( app(app(sk4,sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_8048]) ).

tcf(c_29881,plain,
    ( ( app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_5745]) ).

tcf(c_29882,plain,
    ( ( app(app(sk3,sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_8047]) ).

tcf(c_29883,plain,
    ( ( app(app(sk4,sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_5738]) ).

tcf(c_29884,plain,
    ( ( app(app(sk3,sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_5737]) ).

tcf(c_29885,plain,
    ( ( app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = tl(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4136]) ).

tcf(c_29886,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),sk4)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4462]) ).

tcf(c_29887,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),sk3)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4461]) ).

tcf(c_29888,plain,
    ( ( app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = tl(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4284]) ).

tcf(c_29889,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4027]) ).

tcf(c_29890,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3885]) ).

tcf(c_29891,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3019]) ).

tcf(c_29892,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3452]) ).

tcf(c_29893,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3444]) ).

tcf(c_29894,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3065]) ).

tcf(c_29895,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3215]) ).

tcf(c_29896,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3207]) ).

tcf(c_29897,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_253]) ).

tcf(c_29898,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_275]) ).

tcf(c_29899,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3018]) ).

tcf(c_29900,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4)) = sk4 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3191]) ).

tcf(c_29901,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3)) = sk3 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3183]) ).

tcf(c_29902,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_284]) ).

tcf(c_29903,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_276]) ).

tcf(c_29904,plain,
    ( ( app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),nil) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_258]) ).

tcf(c_29905,plain,
    ( ( app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_257]) ).

tcf(c_30021,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_29861,c_15599]) ).

tcf(c_30032,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_29898,c_15599]) ).

tcf(c_30451,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4037]) ).

tcf(c_30452,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3952]) ).

tcf(c_30453,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3050]) ).

tcf(c_30454,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0),nil) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3049]) ).

tcf(c_30455,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),sk4),X0) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4540]) ).

tcf(c_30456,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),sk3),X0) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4539]) ).

tcf(c_30457,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),X0) = app(X1,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_271]) ).

tcf(c_30458,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(cons(X1,X0),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_266]) ).

tcf(c_30459,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),X0) = tl(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_274]) ).

tcf(c_30460,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_283]) ).

tcf(c_30461,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4038]) ).

tcf(c_30462,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_17993]) ).

tcf(c_30463,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_17992]) ).

tcf(c_30464,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_17991]) ).

tcf(c_30465,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4036]) ).

tcf(c_30466,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3953]) ).

tcf(c_30467,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15403]) ).

tcf(c_30468,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15402]) ).

tcf(c_30469,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15401]) ).

tcf(c_30470,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3951]) ).

tcf(c_30471,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3423]) ).

tcf(c_30472,plain,
    ( ( app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_13452]) ).

tcf(c_30473,plain,
    ( ( app(app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_12354]) ).

tcf(c_30474,plain,
    ( ( app(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_12353]) ).

tcf(c_30475,plain,
    ( ( app(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_12352]) ).

tcf(c_30476,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil)) = nil )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3199]) ).

tcf(c_30477,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3066]) ).

tcf(c_30478,plain,
    ( ( app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_8061]) ).

tcf(c_30479,plain,
    ( ( app(app(sk4,sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_8048]) ).

tcf(c_30480,plain,
    ( ( app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_5745]) ).

tcf(c_30481,plain,
    ( ( app(app(sk3,sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_8047]) ).

tcf(c_30482,plain,
    ( ( app(app(sk4,sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_5738]) ).

tcf(c_30483,plain,
    ( ( app(app(sk3,sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_5737]) ).

tcf(c_30484,plain,
    ( ( app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = tl(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4136]) ).

tcf(c_30485,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),sk4)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4462]) ).

tcf(c_30486,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),sk3)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4461]) ).

tcf(c_30487,plain,
    ( ( app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = tl(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4284]) ).

tcf(c_30488,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4027]) ).

tcf(c_30489,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3885]) ).

tcf(c_30490,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3019]) ).

tcf(c_30491,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3452]) ).

tcf(c_30492,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3444]) ).

tcf(c_30493,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3065]) ).

tcf(c_30494,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3215]) ).

tcf(c_30495,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3207]) ).

tcf(c_30496,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_253]) ).

tcf(c_30497,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_275]) ).

tcf(c_30498,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3018]) ).

tcf(c_30499,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4)) = sk4 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3191]) ).

tcf(c_30500,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3)) = sk3 )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3183]) ).

tcf(c_30501,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_284]) ).

tcf(c_30502,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_276]) ).

tcf(c_30503,plain,
    ( ( app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),nil) = app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_258]) ).

tcf(c_30504,plain,
    ( ( app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_257]) ).

tcf(c_30620,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_30460,c_15603]) ).

tcf(c_30631,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_30497,c_15603]) ).

tcf(c_30892,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),cons(hd(sk3),sk3)) = nil )
      | ( cons(hd(sk3),cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk3)))
      | ( cons(hd(sk3),sk3) != tl(X0) )
      | ( hd(cons(hd(sk3),cons(hd(sk3),sk3))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_28998,c_273]) ).

tcf(c_30893,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),cons(hd(sk3),sk3)) = nil )
      | ( cons(hd(sk3),cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk3)))
      | ( hd(X0) != hd(sk3) )
      | ( cons(hd(sk3),sk3) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_30892,c_14347]) ).

tcf(c_30901,plain,
    cons(hd(sk4),sk3) != cons(hd(sk4),nil),
    inference(global_subsumption_just,[status(thm)],[c_14158,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_14158]) ).

tcf(c_30905,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20555,c_280]) ).

tcf(c_30906,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20555,c_279]) ).

tcf(c_30922,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20556,c_280]) ).

tcf(c_30923,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20556,c_279]) ).

tcf(c_30946,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( app(sk3,cons(hd(sk4),sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_8852,c_270]) ).

tcf(c_30947,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( app(X0,app(sk3,cons(hd(sk4),sk3))) != app(sk3,cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_8852,c_269]) ).

tcf(c_30948,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( app(X0,app(sk3,cons(hd(sk4),sk3))) != app(sk3,cons(hd(sk4),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_30947,c_259]) ).

tcf(c_30953,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( app(sk3,cons(hd(sk4),sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_30946,c_259]) ).

tcf(c_30967,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( app(sk3,cons(hd(sk4),sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_8853,c_270]) ).

tcf(c_30968,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( app(X0,app(sk3,cons(hd(sk4),sk4))) != app(sk3,cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_8853,c_269]) ).

tcf(c_30969,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( app(X0,app(sk3,cons(hd(sk4),sk4))) != app(sk3,cons(hd(sk4),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_30968,c_259]) ).

tcf(c_30974,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( app(sk3,cons(hd(sk4),sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_30967,c_259]) ).

tcf(c_30988,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( app(sk4,cons(hd(sk4),sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_9876,c_270]) ).

tcf(c_30989,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( app(X0,app(sk4,cons(hd(sk4),sk3))) != app(sk4,cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_9876,c_269]) ).

tcf(c_30990,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( app(X0,app(sk4,cons(hd(sk4),sk3))) != app(sk4,cons(hd(sk4),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_30989,c_259]) ).

tcf(c_30995,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( app(sk4,cons(hd(sk4),sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_30988,c_259]) ).

tcf(c_31009,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( app(sk4,cons(hd(sk4),sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_9877,c_270]) ).

tcf(c_31010,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( app(X0,app(sk4,cons(hd(sk4),sk4))) != app(sk4,cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_9877,c_269]) ).

tcf(c_31011,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( app(X0,app(sk4,cons(hd(sk4),sk4))) != app(sk4,cons(hd(sk4),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31010,c_259]) ).

tcf(c_31016,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( app(sk4,cons(hd(sk4),sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31009,c_259]) ).

tcf(c_31038,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( app(app(sk3,cons(hd(sk4),sk3)),X0) != app(sk3,cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_12807,c_270]) ).

tcf(c_31039,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( app(sk3,cons(hd(sk4),sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_12807,c_269]) ).

tcf(c_31040,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( app(sk3,cons(hd(sk4),sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31039,c_259]) ).

tcf(c_31045,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk3)))
      | ( app(app(sk3,cons(hd(sk4),sk3)),X0) != app(sk3,cons(hd(sk4),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31038,c_259]) ).

tcf(c_31051,plain,
    ( ssList(app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))
    | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_7586,c_278]) ).

tcf(c_31052,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = nil )
      | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3))))
      | ( hd(app(sk4,cons(hd(sk4),app(sk4,sk3)))) != hd(X0) )
      | ( app(tl(sk4),cons(hd(sk4),app(sk4,sk3))) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_7586,c_273]) ).

tcf(c_31056,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = nil )
      | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3))))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),cons(hd(sk4),app(sk4,sk3))) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_31052,c_7591]) ).

tcf(c_31085,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4037]) ).

tcf(c_31086,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3952]) ).

tcf(c_31087,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3050]) ).

tcf(c_31088,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0),nil) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3049]) ).

tcf(c_31089,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),sk4),X0) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4540]) ).

tcf(c_31090,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),sk3),X0) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4539]) ).

tcf(c_31091,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),X0) = app(X1,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_271]) ).

tcf(c_31092,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(cons(X1,X0),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_266]) ).

tcf(c_31093,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),X0) = tl(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_274]) ).

tcf(c_31094,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_283]) ).

tcf(c_31095,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4038]) ).

tcf(c_31096,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_17993]) ).

tcf(c_31097,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_17992]) ).

tcf(c_31098,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_17991]) ).

tcf(c_31099,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4036]) ).

tcf(c_31100,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3953]) ).

tcf(c_31101,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15403]) ).

tcf(c_31102,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15402]) ).

tcf(c_31103,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15401]) ).

tcf(c_31104,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3951]) ).

tcf(c_31105,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3423]) ).

tcf(c_31106,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_13452]) ).

tcf(c_31107,plain,
    ( ( app(app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_12354]) ).

tcf(c_31108,plain,
    ( ( app(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_12353]) ).

tcf(c_31109,plain,
    ( ( app(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_12352]) ).

tcf(c_31110,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3199]) ).

tcf(c_31111,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3066]) ).

tcf(c_31112,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_8061]) ).

tcf(c_31113,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_8048]) ).

tcf(c_31114,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_5745]) ).

tcf(c_31115,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_8047]) ).

tcf(c_31116,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_5738]) ).

tcf(c_31117,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_5737]) ).

tcf(c_31118,plain,
    ( ( app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = tl(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4136]) ).

tcf(c_31119,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),sk4)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4462]) ).

tcf(c_31120,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),sk3)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4461]) ).

tcf(c_31121,plain,
    ( ( app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = tl(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4284]) ).

tcf(c_31122,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4027]) ).

tcf(c_31123,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3885]) ).

tcf(c_31124,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3019]) ).

tcf(c_31125,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3452]) ).

tcf(c_31126,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3444]) ).

tcf(c_31127,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3065]) ).

tcf(c_31128,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3215]) ).

tcf(c_31129,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3207]) ).

tcf(c_31130,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_253]) ).

tcf(c_31131,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_275]) ).

tcf(c_31132,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3018]) ).

tcf(c_31133,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3191]) ).

tcf(c_31134,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3183]) ).

tcf(c_31135,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_284]) ).

tcf(c_31136,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_276]) ).

tcf(c_31137,plain,
    ( ( app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),nil) = app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_258]) ).

tcf(c_31138,plain,
    ( ( app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_257]) ).

tcf(c_31254,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_31094,c_18195]) ).

tcf(c_31265,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_31131,c_18195]) ).

tcf(c_31513,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( app(app(sk3,cons(hd(sk4),sk4)),X0) != app(sk3,cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12808,c_270]) ).

tcf(c_31514,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( app(sk3,cons(hd(sk4),sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_12808,c_269]) ).

tcf(c_31515,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( app(sk3,cons(hd(sk4),sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31514,c_259]) ).

tcf(c_31520,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),sk4)))
      | ( app(app(sk3,cons(hd(sk4),sk4)),X0) != app(sk3,cons(hd(sk4),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31513,c_259]) ).

tcf(c_31533,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( app(app(sk4,cons(hd(sk4),sk3)),X0) != app(sk4,cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_12883,c_270]) ).

tcf(c_31534,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( app(sk4,cons(hd(sk4),sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_12883,c_269]) ).

tcf(c_31535,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( app(sk4,cons(hd(sk4),sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31534,c_259]) ).

tcf(c_31540,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk3)))
      | ( app(app(sk4,cons(hd(sk4),sk3)),X0) != app(sk4,cons(hd(sk4),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31533,c_259]) ).

tcf(c_31553,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( app(app(sk4,cons(hd(sk4),sk4)),X0) != app(sk4,cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12884,c_270]) ).

tcf(c_31554,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( app(sk4,cons(hd(sk4),sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_12884,c_269]) ).

tcf(c_31555,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( app(sk4,cons(hd(sk4),sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31554,c_259]) ).

tcf(c_31560,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),sk4)))
      | ( app(app(sk4,cons(hd(sk4),sk4)),X0) != app(sk4,cons(hd(sk4),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31553,c_259]) ).

tcf(c_31577,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( app(app(sk4,cons(hd(sk3),sk4)),X0) != app(sk4,cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_13167,c_270]) ).

tcf(c_31578,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( app(sk4,cons(hd(sk3),sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_13167,c_269]) ).

tcf(c_31579,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( app(sk4,cons(hd(sk3),sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31578,c_259]) ).

tcf(c_31584,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( app(app(sk4,cons(hd(sk3),sk4)),X0) != app(sk4,cons(hd(sk3),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31577,c_259]) ).

tcf(c_31598,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( app(app(sk3,cons(hd(sk3),sk4)),X0) != app(sk3,cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_13168,c_270]) ).

tcf(c_31599,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( app(sk3,cons(hd(sk3),sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_13168,c_269]) ).

tcf(c_31600,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( app(sk3,cons(hd(sk3),sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31599,c_259]) ).

tcf(c_31605,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( app(app(sk3,cons(hd(sk3),sk4)),X0) != app(sk3,cons(hd(sk3),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31598,c_259]) ).

tcf(c_31612,plain,
    ( ssList(app(tl(sk3),cons(hd(sk3),sk4)))
    | ( app(sk3,cons(hd(sk3),sk4)) = nil )
    | ~ ssList(app(sk3,cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13180,c_278]) ).

tcf(c_31613,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk3),sk4)) = nil )
      | ( app(sk3,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( hd(app(sk3,cons(hd(sk3),sk4))) != hd(X0) )
      | ( app(tl(sk3),cons(hd(sk3),sk4)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_13180,c_273]) ).

tcf(c_31617,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk3),sk4)) = nil )
      | ( app(sk3,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),cons(hd(sk3),sk4)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_31613,c_13181]) ).

tcf(c_31633,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( app(app(sk4,cons(hd(sk3),sk3)),X0) != app(sk4,cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13795,c_270]) ).

tcf(c_31634,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( app(sk4,cons(hd(sk3),sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_13795,c_269]) ).

tcf(c_31635,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( app(sk4,cons(hd(sk3),sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31634,c_259]) ).

tcf(c_31640,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( app(app(sk4,cons(hd(sk3),sk3)),X0) != app(sk4,cons(hd(sk3),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31633,c_259]) ).

tcf(c_31654,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( app(app(sk3,cons(hd(sk3),sk3)),X0) != app(sk3,cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13796,c_270]) ).

tcf(c_31655,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( app(sk3,cons(hd(sk3),sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_13796,c_269]) ).

tcf(c_31656,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( app(sk3,cons(hd(sk3),sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31655,c_259]) ).

tcf(c_31661,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( app(app(sk3,cons(hd(sk3),sk3)),X0) != app(sk3,cons(hd(sk3),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31654,c_259]) ).

tcf(c_31675,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( app(sk4,cons(hd(sk3),sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_13799,c_270]) ).

tcf(c_31676,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( app(X0,app(sk4,cons(hd(sk3),sk3))) != app(sk4,cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13799,c_269]) ).

tcf(c_31677,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( app(X0,app(sk4,cons(hd(sk3),sk3))) != app(sk4,cons(hd(sk3),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31676,c_259]) ).

tcf(c_31682,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( app(sk4,cons(hd(sk3),sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31675,c_259]) ).

tcf(c_31695,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( app(sk3,cons(hd(sk3),sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_13801,c_270]) ).

tcf(c_31696,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( app(X0,app(sk3,cons(hd(sk3),sk3))) != app(sk3,cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13801,c_269]) ).

tcf(c_31697,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( app(X0,app(sk3,cons(hd(sk3),sk3))) != app(sk3,cons(hd(sk3),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31696,c_259]) ).

tcf(c_31702,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( app(sk3,cons(hd(sk3),sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31695,c_259]) ).

tcf(c_31708,plain,
    ( ssList(app(tl(sk4),cons(hd(sk3),sk3)))
    | ( app(sk4,cons(hd(sk3),sk3)) = nil )
    | ~ ssList(app(sk4,cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_13805,c_278]) ).

tcf(c_31709,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk3),sk3)) = nil )
      | ( app(sk4,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( hd(app(sk4,cons(hd(sk3),sk3))) != hd(X0) )
      | ( app(tl(sk4),cons(hd(sk3),sk3)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_13805,c_273]) ).

tcf(c_31713,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk3),sk3)) = nil )
      | ( app(sk4,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk3)))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),cons(hd(sk3),sk3)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_31709,c_13810]) ).

tcf(c_31722,plain,
    ( ssList(app(tl(sk3),cons(hd(sk4),app(sk4,sk3))))
    | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_7589,c_278]) ).

tcf(c_31723,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = nil )
      | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3))))
      | ( hd(app(sk3,cons(hd(sk4),app(sk4,sk3)))) != hd(X0) )
      | ( app(tl(sk3),cons(hd(sk4),app(sk4,sk3))) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_7589,c_273]) ).

tcf(c_31727,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = nil )
      | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3))))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),cons(hd(sk4),app(sk4,sk3))) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_31723,c_7590]) ).

tcf(c_31780,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ( hd(cons(X0,tl(sk3))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_3153]) ).

tcf(c_31781,plain,
    ! [X0: $i] :
      ( ( sk4 = nil )
      | ( hd(cons(X0,tl(sk4))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_3153]) ).

tcf(c_31783,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(X1,tl(tl(X0)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3153]) ).

tcf(c_31784,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(X2,tl(app(X1,X0)))) = X2 )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3153]) ).

tcf(c_31785,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(X2,tl(cons(X1,X0)))) = X2 )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3153]) ).

tcf(c_31786,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk3),sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3153]) ).

tcf(c_31787,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk4),sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3153]) ).

tcf(c_31788,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk3),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3153]) ).

tcf(c_31789,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk4),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3153]) ).

tcf(c_31790,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(tl(sk3),sk3) = nil )
      | ( hd(cons(X0,tl(app(tl(sk3),sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3153]) ).

tcf(c_31791,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(tl(sk3),sk4) = nil )
      | ( hd(cons(X0,tl(app(tl(sk3),sk4)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3153]) ).

tcf(c_31792,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(tl(sk4),sk3) = nil )
      | ( hd(cons(X0,tl(app(tl(sk4),sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3153]) ).

tcf(c_31793,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(tl(sk4),sk4) = nil )
      | ( hd(cons(X0,tl(app(tl(sk4),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3153]) ).

tcf(c_31794,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk4),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3153]) ).

tcf(c_31795,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,sk3)) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3153]) ).

tcf(c_31796,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,sk4)) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3153]) ).

tcf(c_31797,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,sk3)) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3153]) ).

tcf(c_31798,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk4),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3153]) ).

tcf(c_31799,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,sk4)) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3153]) ).

tcf(c_31800,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,sk3)) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3153]) ).

tcf(c_31801,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,sk4)) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3153]) ).

tcf(c_31802,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,sk3)) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3153]) ).

tcf(c_31803,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,sk4)) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3153]) ).

tcf(c_31804,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk4),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3153]) ).

tcf(c_31805,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk4),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3153]) ).

tcf(c_31806,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3153]) ).

tcf(c_31807,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3153]) ).

tcf(c_31808,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3153]) ).

tcf(c_31809,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk3),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3153]) ).

tcf(c_31810,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk3),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3153]) ).

tcf(c_31811,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk3),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3153]) ).

tcf(c_31812,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk3),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3153]) ).

tcf(c_31813,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3153]) ).

tcf(c_31814,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3153]) ).

tcf(c_31815,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3153]) ).

tcf(c_31816,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3153]) ).

tcf(c_31817,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3153]) ).

tcf(c_31818,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(sk4))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31781,c_1243]) ).

tcf(c_31824,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = nil )
      | ( hd(cons(X0,sk4)) = X0 )
      | ~ ssItem(X0) ),
    inference(light_normalisation,[status(thm)],[c_31789,c_3280]) ).

tcf(c_31827,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = nil )
      | ( hd(cons(X0,sk3)) = X0 )
      | ~ ssItem(X0) ),
    inference(light_normalisation,[status(thm)],[c_31787,c_3246]) ).

tcf(c_31835,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(cons(hd(sk3),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31812,c_20706]) ).

tcf(c_31838,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(cons(hd(sk3),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31811,c_17701]) ).

tcf(c_31841,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(cons(hd(sk3),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31810,c_19513]) ).

tcf(c_31844,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(cons(hd(sk3),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31809,c_16926]) ).

tcf(c_31847,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(cons(hd(sk4),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31805,c_10611]) ).

tcf(c_31850,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(cons(hd(sk4),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31804,c_10190]) ).

tcf(c_31853,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(cons(hd(sk4),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31798,c_7545]) ).

tcf(c_31856,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(cons(hd(sk4),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31794,c_5891]) ).

tcf(c_32098,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(sk4))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_31818]) ).

tcf(c_32099,plain,
    hd(cons(hd(sk4),tl(sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_31818]) ).

tcf(c_32100,plain,
    hd(cons(hd(sk3),tl(sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_31818]) ).

tcf(c_32105,plain,
    ! [X0: $i] :
      ( ~ ssItem(X0)
      | ( hd(cons(X0,tl(sk3))) = X0 ) ),
    inference(global_subsumption_just,[status(thm)],[c_31780,c_24606]) ).

tcf(c_32106,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,tl(sk3))) = X0 )
      | ~ ssItem(X0) ),
    inference(renaming,[status(thm)],[c_32105]) ).

tcf(c_32111,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(sk3))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_32106]) ).

tcf(c_32112,plain,
    hd(cons(hd(sk4),tl(sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_32106]) ).

tcf(c_32113,plain,
    hd(cons(hd(sk3),tl(sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_32106]) ).

tcf(c_32175,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(sk4))))
      | ( cons(hd(sk3),tl(sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(sk4)))
      | ~ ssList(cons(hd(sk3),tl(sk4))) ),
    inference(superposition,[status(thm)],[c_32100,c_280]) ).

tcf(c_32176,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(sk4))))
      | ( cons(hd(sk3),tl(sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(sk4)))
      | ~ ssList(cons(hd(sk3),tl(sk4))) ),
    inference(superposition,[status(thm)],[c_32100,c_279]) ).

tcf(c_32192,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),tl(sk3))))
      | ( cons(hd(sk4),tl(sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),tl(sk3)))
      | ~ ssList(cons(hd(sk4),tl(sk3))) ),
    inference(superposition,[status(thm)],[c_32112,c_280]) ).

tcf(c_32193,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),tl(sk3))))
      | ( cons(hd(sk4),tl(sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),tl(sk3)))
      | ~ ssList(cons(hd(sk4),tl(sk3))) ),
    inference(superposition,[status(thm)],[c_32112,c_279]) ).

tcf(c_32209,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(sk3))))
      | ( cons(hd(sk3),tl(sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(sk3)))
      | ~ ssList(cons(hd(sk3),tl(sk3))) ),
    inference(superposition,[status(thm)],[c_32113,c_280]) ).

tcf(c_32210,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(sk3))))
      | ( cons(hd(sk3),tl(sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(sk3)))
      | ~ ssList(cons(hd(sk3),tl(sk3))) ),
    inference(superposition,[status(thm)],[c_32113,c_279]) ).

tcf(c_32233,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( app(sk4,cons(hd(sk3),sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_13171,c_270]) ).

tcf(c_32234,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( app(X0,app(sk4,cons(hd(sk3),sk4))) != app(sk4,cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_13171,c_269]) ).

tcf(c_32235,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( app(X0,app(sk4,cons(hd(sk3),sk4))) != app(sk4,cons(hd(sk3),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_32234,c_259]) ).

tcf(c_32240,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( app(sk4,cons(hd(sk3),sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_32233,c_259]) ).

tcf(c_32288,plain,
    ( ssList(app(tl(sk3),cons(hd(sk3),sk3)))
    | ( app(sk3,cons(hd(sk3),sk3)) = nil )
    | ~ ssList(app(sk3,cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_13808,c_278]) ).

tcf(c_32289,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk3),sk3)) = nil )
      | ( app(sk3,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( hd(app(sk3,cons(hd(sk3),sk3))) != hd(X0) )
      | ( app(tl(sk3),cons(hd(sk3),sk3)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_13808,c_273]) ).

tcf(c_32293,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk3),sk3)) = nil )
      | ( app(sk3,cons(hd(sk3),sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk3)))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),cons(hd(sk3),sk3)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_32289,c_13809]) ).

tcf(c_32301,plain,
    app(sk4,app(sk4,sk4)) != app(sk4,sk4),
    inference(global_subsumption_just,[status(thm)],[c_14001,c_247,c_14001,c_20236]) ).

tcf(c_32307,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_15407]) ).

tcf(c_32308,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_15407]) ).

tcf(c_32309,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_15407]) ).

tcf(c_32310,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(cons(hd(sk3),sk3),tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15407]) ).

tcf(c_32311,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15407]) ).

tcf(c_32312,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),sk3),cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15407]) ).

tcf(c_32313,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_15407]) ).

tcf(c_32314,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_15407]) ).

tcf(c_32315,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_15407]) ).

tcf(c_32316,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_15407]) ).

tcf(c_32317,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(cons(hd(sk3),sk3),app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15407]) ).

tcf(c_32318,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(cons(hd(sk3),sk3),app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15407]) ).

tcf(c_32319,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(cons(hd(sk3),sk3),app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15407]) ).

tcf(c_32320,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(cons(hd(sk3),sk3),app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_15407]) ).

tcf(c_32321,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_15407]) ).

tcf(c_32322,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15407]) ).

tcf(c_32323,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15407]) ).

tcf(c_32324,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15407]) ).

tcf(c_32325,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_15407]) ).

tcf(c_32326,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15407]) ).

tcf(c_32327,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15407]) ).

tcf(c_32328,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15407]) ).

tcf(c_32329,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15407]) ).

tcf(c_32330,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15407]) ).

tcf(c_32331,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_15407]) ).

tcf(c_32332,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_15407]) ).

tcf(c_32333,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15407]) ).

tcf(c_32334,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15407]) ).

tcf(c_32335,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15407]) ).

tcf(c_32336,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_15407]) ).

tcf(c_32337,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_15407]) ).

tcf(c_32338,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_15407]) ).

tcf(c_32339,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_15407]) ).

tcf(c_32340,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15407]) ).

tcf(c_32341,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15407]) ).

tcf(c_32342,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15407]) ).

tcf(c_32343,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15407]) ).

tcf(c_32344,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15407]) ).

tcf(c_32555,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_15408]) ).

tcf(c_32556,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_15408]) ).

tcf(c_32557,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_15408]) ).

tcf(c_32558,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(cons(hd(sk4),sk3),tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15408]) ).

tcf(c_32559,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15408]) ).

tcf(c_32560,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),sk3),cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15408]) ).

tcf(c_32561,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_15408]) ).

tcf(c_32562,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_15408]) ).

tcf(c_32563,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_15408]) ).

tcf(c_32564,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_15408]) ).

tcf(c_32565,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(cons(hd(sk4),sk3),app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15408]) ).

tcf(c_32566,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(cons(hd(sk4),sk3),app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15408]) ).

tcf(c_32567,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(cons(hd(sk4),sk3),app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15408]) ).

tcf(c_32568,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(cons(hd(sk4),sk3),app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_15408]) ).

tcf(c_32569,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_15408]) ).

tcf(c_32570,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15408]) ).

tcf(c_32571,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15408]) ).

tcf(c_32572,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15408]) ).

tcf(c_32573,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_15408]) ).

tcf(c_32574,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15408]) ).

tcf(c_32575,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15408]) ).

tcf(c_32576,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15408]) ).

tcf(c_32577,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15408]) ).

tcf(c_32578,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15408]) ).

tcf(c_32579,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_15408]) ).

tcf(c_32580,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_15408]) ).

tcf(c_32581,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15408]) ).

tcf(c_32582,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15408]) ).

tcf(c_32583,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15408]) ).

tcf(c_32584,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_15408]) ).

tcf(c_32585,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_15408]) ).

tcf(c_32586,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_15408]) ).

tcf(c_32587,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_15408]) ).

tcf(c_32588,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15408]) ).

tcf(c_32589,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15408]) ).

tcf(c_32590,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15408]) ).

tcf(c_32591,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15408]) ).

tcf(c_32592,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15408]) ).

tcf(c_32964,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_15410]) ).

tcf(c_32965,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_15410]) ).

tcf(c_32966,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_15410]) ).

tcf(c_32967,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(cons(hd(sk4),sk4),tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15410]) ).

tcf(c_32968,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15410]) ).

tcf(c_32969,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk4),sk4),cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15410]) ).

tcf(c_32970,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_15410]) ).

tcf(c_32971,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_15410]) ).

tcf(c_32972,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_15410]) ).

tcf(c_32973,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_15410]) ).

tcf(c_32974,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(cons(hd(sk4),sk4),app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15410]) ).

tcf(c_32975,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(cons(hd(sk4),sk4),app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15410]) ).

tcf(c_32976,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(cons(hd(sk4),sk4),app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15410]) ).

tcf(c_32977,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(cons(hd(sk4),sk4),app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_15410]) ).

tcf(c_32978,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_15410]) ).

tcf(c_32979,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15410]) ).

tcf(c_32980,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15410]) ).

tcf(c_32981,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15410]) ).

tcf(c_32982,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_15410]) ).

tcf(c_32983,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15410]) ).

tcf(c_32984,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15410]) ).

tcf(c_32985,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15410]) ).

tcf(c_32986,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15410]) ).

tcf(c_32987,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15410]) ).

tcf(c_32988,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_15410]) ).

tcf(c_32989,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_15410]) ).

tcf(c_32990,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15410]) ).

tcf(c_32991,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15410]) ).

tcf(c_32992,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15410]) ).

tcf(c_32993,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_15410]) ).

tcf(c_32994,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_15410]) ).

tcf(c_32995,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_15410]) ).

tcf(c_32996,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_15410]) ).

tcf(c_32997,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15410]) ).

tcf(c_32998,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15410]) ).

tcf(c_32999,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15410]) ).

tcf(c_33000,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15410]) ).

tcf(c_33001,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15410]) ).

tcf(c_33088,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,cons(hd(X0),cons(hd(sk3),sk3)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_16553]) ).

tcf(c_33089,plain,
    hd(app(sk4,cons(hd(sk4),cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_16553]) ).

tcf(c_33090,plain,
    hd(app(sk4,cons(hd(sk3),cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10117,c_16553]) ).

tcf(c_33112,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,cons(hd(X0),cons(hd(sk4),sk3)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_16554]) ).

tcf(c_33113,plain,
    hd(app(sk4,cons(hd(sk4),cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_16554]) ).

tcf(c_33114,plain,
    hd(app(sk4,cons(hd(sk3),cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10117,c_16554]) ).

tcf(c_33122,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,cons(hd(X0),cons(hd(sk4),sk4)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_16556]) ).

tcf(c_33123,plain,
    hd(app(sk4,cons(hd(sk4),cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_16556]) ).

tcf(c_33124,plain,
    hd(app(sk4,cons(hd(sk3),cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10117,c_16556]) ).

tcf(c_33128,plain,
    app(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4),nil) = cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4),
    inference(global_subsumption_just,[status(thm)],[c_7593,c_7545,c_7593]) ).

tcf(c_33138,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4))
      | ( app(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4),X0) != cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_33128,c_270]) ).

tcf(c_33139,plain,
    ! [X0: $i] :
      ( ( cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4))
      | ( cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_33128,c_269]) ).

tcf(c_33140,plain,
    ! [X0: $i] :
      ( ( cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4))
      | ( cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_33139,c_259]) ).

tcf(c_33145,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4))
      | ( app(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4),X0) != cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_33138,c_259]) ).

tcf(c_33158,plain,
    ( ( sk4 = nil )
    | ( hd(cons(hd(sk4),tl(sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_32098]) ).

tcf(c_33160,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),tl(sk4))) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_32098]) ).

tcf(c_33161,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),tl(sk4))) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_32098]) ).

tcf(c_33162,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),tl(sk4))) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_32098]) ).

tcf(c_33163,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),tl(sk4))) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_32098]) ).

tcf(c_33164,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),tl(sk4))) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_32098]) ).

tcf(c_33165,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),tl(sk4))) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_32098]) ).

tcf(c_33166,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),tl(sk4))) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_32098]) ).

tcf(c_33167,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),tl(sk4))) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_32098]) ).

tcf(c_33168,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),tl(sk4))) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_32098]) ).

tcf(c_33169,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),tl(sk4))) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_32098]) ).

tcf(c_33170,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),tl(sk4))) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_32098]) ).

tcf(c_33171,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(sk4))) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_32098]) ).

tcf(c_33172,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),tl(sk4))) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_32098]) ).

tcf(c_33173,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),tl(sk4))) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_32098]) ).

tcf(c_33174,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),tl(sk4))) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_32098]) ).

tcf(c_33175,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),tl(sk4))) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_32098]) ).

tcf(c_33176,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),tl(sk4))) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_32098]) ).

tcf(c_33177,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),tl(sk4))) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_32098]) ).

tcf(c_33178,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),tl(sk4))) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_32098]) ).

tcf(c_33179,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),tl(sk4))) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_32098]) ).

tcf(c_33180,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),tl(sk4))) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_32098]) ).

tcf(c_33181,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),tl(sk4))) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_32098]) ).

tcf(c_33182,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),tl(sk4))) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_32098]) ).

tcf(c_33183,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),tl(sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_32098]) ).

tcf(c_33184,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),tl(sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_32098]) ).

tcf(c_33185,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_32098]) ).

tcf(c_33186,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),tl(sk4))) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_32098]) ).

tcf(c_33187,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),tl(sk4))) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_32098]) ).

tcf(c_33188,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),tl(sk4))) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_32098]) ).

tcf(c_33189,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),tl(sk4))) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_32098]) ).

tcf(c_33190,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),tl(sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_32098]) ).

tcf(c_33191,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),tl(sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_32098]) ).

tcf(c_33192,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_32098]) ).

tcf(c_33193,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_32098]) ).

tcf(c_33194,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_32098]) ).

tcf(c_33212,plain,
    hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),tl(sk4))) = hd(cons(hd(sk3),app(sk3,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33189,c_20706]) ).

tcf(c_33213,plain,
    hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),tl(sk4))) = hd(cons(hd(sk3),app(sk3,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33188,c_17701]) ).

tcf(c_33214,plain,
    hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),tl(sk4))) = hd(cons(hd(sk3),app(sk4,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33187,c_19513]) ).

tcf(c_33215,plain,
    hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),tl(sk4))) = hd(cons(hd(sk3),app(sk4,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33186,c_16926]) ).

tcf(c_33216,plain,
    hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),tl(sk4))) = hd(cons(hd(sk4),app(sk4,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33182,c_10611]) ).

tcf(c_33217,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),tl(sk4))) = hd(cons(hd(sk4),app(sk3,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33181,c_10190]) ).

tcf(c_33218,plain,
    hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),tl(sk4))) = hd(cons(hd(sk4),app(sk4,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33175,c_7545]) ).

tcf(c_33219,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(sk4))) = hd(cons(hd(sk4),app(sk3,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33171,c_5891]) ).

tcf(c_33282,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),tl(sk3))) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_32111]) ).

tcf(c_33283,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),tl(sk3))) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_32111]) ).

tcf(c_33284,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),tl(sk3))) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_32111]) ).

tcf(c_33285,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),tl(sk3))) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_32111]) ).

tcf(c_33286,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),tl(sk3))) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_32111]) ).

tcf(c_33287,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),tl(sk3))) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_32111]) ).

tcf(c_33288,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),tl(sk3))) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_32111]) ).

tcf(c_33289,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),tl(sk3))) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_32111]) ).

tcf(c_33290,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),tl(sk3))) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_32111]) ).

tcf(c_33291,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),tl(sk3))) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_32111]) ).

tcf(c_33292,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),tl(sk3))) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_32111]) ).

tcf(c_33293,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(sk3))) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_32111]) ).

tcf(c_33294,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),tl(sk3))) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_32111]) ).

tcf(c_33295,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),tl(sk3))) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_32111]) ).

tcf(c_33296,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),tl(sk3))) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_32111]) ).

tcf(c_33297,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),tl(sk3))) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_32111]) ).

tcf(c_33298,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),tl(sk3))) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_32111]) ).

tcf(c_33299,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),tl(sk3))) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_32111]) ).

tcf(c_33300,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),tl(sk3))) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_32111]) ).

tcf(c_33301,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),tl(sk3))) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_32111]) ).

tcf(c_33302,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),tl(sk3))) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_32111]) ).

tcf(c_33303,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),tl(sk3))) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_32111]) ).

tcf(c_33304,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),tl(sk3))) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_32111]) ).

tcf(c_33305,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),tl(sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_32111]) ).

tcf(c_33306,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),tl(sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_32111]) ).

tcf(c_33307,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_32111]) ).

tcf(c_33308,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),tl(sk3))) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_32111]) ).

tcf(c_33309,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),tl(sk3))) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_32111]) ).

tcf(c_33310,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),tl(sk3))) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_32111]) ).

tcf(c_33311,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),tl(sk3))) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_32111]) ).

tcf(c_33312,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),tl(sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_32111]) ).

tcf(c_33313,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),tl(sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_32111]) ).

tcf(c_33314,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_32111]) ).

tcf(c_33315,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_32111]) ).

tcf(c_33316,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_32111]) ).

tcf(c_33333,plain,
    hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),tl(sk3))) = hd(cons(hd(sk3),app(sk3,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33311,c_20706]) ).

tcf(c_33334,plain,
    hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),tl(sk3))) = hd(cons(hd(sk3),app(sk3,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33310,c_17701]) ).

tcf(c_33335,plain,
    hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),tl(sk3))) = hd(cons(hd(sk3),app(sk4,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33309,c_19513]) ).

tcf(c_33336,plain,
    hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),tl(sk3))) = hd(cons(hd(sk3),app(sk4,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33308,c_16926]) ).

tcf(c_33337,plain,
    hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),tl(sk3))) = hd(cons(hd(sk4),app(sk4,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33304,c_10611]) ).

tcf(c_33338,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),tl(sk3))) = hd(cons(hd(sk4),app(sk3,sk4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33303,c_10190]) ).

tcf(c_33339,plain,
    hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),tl(sk3))) = hd(cons(hd(sk4),app(sk4,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33297,c_7545]) ).

tcf(c_33340,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(sk3))) = hd(cons(hd(sk4),app(sk3,sk3))),
    inference(forward_subsumption_resolution,[status(thm)],[c_33293,c_5891]) ).

tcf(c_33401,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(sk3,X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_3154]) ).

tcf(c_33402,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(sk4,X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_3154]) ).

tcf(c_33403,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(nil,X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_3154]) ).

tcf(c_33404,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X2,app(tl(X0),X1))) = X2 )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3154]) ).

tcf(c_33405,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hd(cons(X3,app(app(X1,X0),X2))) = X3 )
      | ~ ssItem(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3154]) ).

tcf(c_33406,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hd(cons(X3,app(cons(X2,X0),X1))) = X3 )
      | ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3154]) ).

tcf(c_33407,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk3),sk3),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3154]) ).

tcf(c_33408,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk4),sk3),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3154]) ).

tcf(c_33409,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk3),sk4),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3154]) ).

tcf(c_33410,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk4),sk4),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3154]) ).

tcf(c_33411,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(cons(X1,app(app(tl(sk3),sk3),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3154]) ).

tcf(c_33412,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(cons(X1,app(app(tl(sk3),sk4),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3154]) ).

tcf(c_33413,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(cons(X1,app(app(tl(sk4),sk3),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3154]) ).

tcf(c_33414,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(cons(X1,app(app(tl(sk4),sk4),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3154]) ).

tcf(c_33415,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk4),app(sk3,sk3)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3154]) ).

tcf(c_33416,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk3,sk3)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3154]) ).

tcf(c_33417,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk3,sk4)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3154]) ).

tcf(c_33418,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk3,sk3)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3154]) ).

tcf(c_33419,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk4),app(sk4,sk3)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3154]) ).

tcf(c_33420,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk3,sk4)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3154]) ).

tcf(c_33421,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk4,sk3)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3154]) ).

tcf(c_33422,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk4,sk4)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3154]) ).

tcf(c_33423,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk4,sk3)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3154]) ).

tcf(c_33424,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk4,sk4)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3154]) ).

tcf(c_33425,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk4),app(sk3,sk4)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3154]) ).

tcf(c_33426,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk4),app(sk4,sk4)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3154]) ).

tcf(c_33427,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3154]) ).

tcf(c_33428,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3154]) ).

tcf(c_33429,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3154]) ).

tcf(c_33430,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk3),app(sk4,sk4)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3154]) ).

tcf(c_33431,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk3),app(sk4,sk3)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3154]) ).

tcf(c_33432,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk3),app(sk3,sk4)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3154]) ).

tcf(c_33433,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk3),app(sk3,sk3)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3154]) ).

tcf(c_33434,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3154]) ).

tcf(c_33435,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3154]) ).

tcf(c_33436,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3154]) ).

tcf(c_33437,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3154]) ).

tcf(c_33438,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3154]) ).

tcf(c_33739,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,sk3))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_33401]) ).

tcf(c_33740,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,sk4))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_33401]) ).

tcf(c_33741,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,nil))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_33401]) ).

tcf(c_33742,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X1,app(sk3,tl(X0)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_33401]) ).

tcf(c_33743,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(cons(X2,app(sk3,app(X1,X0)))) = X2 )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_33401]) ).

tcf(c_33744,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(cons(X2,app(sk3,cons(X1,X0)))) = X2 )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_33401]) ).

tcf(c_33745,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk3),sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_33401]) ).

tcf(c_33746,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk4),sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_33401]) ).

tcf(c_33747,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk3),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_33401]) ).

tcf(c_33748,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk4),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_33401]) ).

tcf(c_33749,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(cons(X0,app(sk3,app(tl(sk3),sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_33401]) ).

tcf(c_33750,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(cons(X0,app(sk3,app(tl(sk3),sk4)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_33401]) ).

tcf(c_33751,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(cons(X0,app(sk3,app(tl(sk4),sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_33401]) ).

tcf(c_33752,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(cons(X0,app(sk3,app(tl(sk4),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_33401]) ).

tcf(c_33753,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_33401]) ).

tcf(c_33754,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_33401]) ).

tcf(c_33755,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_33401]) ).

tcf(c_33756,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_33401]) ).

tcf(c_33757,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_33401]) ).

tcf(c_33758,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_33401]) ).

tcf(c_33759,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_33401]) ).

tcf(c_33760,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_33401]) ).

tcf(c_33761,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_33401]) ).

tcf(c_33762,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_33401]) ).

tcf(c_33763,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_33401]) ).

tcf(c_33764,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk4),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_33401]) ).

tcf(c_33765,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_33401]) ).

tcf(c_33766,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_33401]) ).

tcf(c_33767,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_33401]) ).

tcf(c_33768,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk3),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_33401]) ).

tcf(c_33769,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk3),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_33401]) ).

tcf(c_33770,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk3),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_33401]) ).

tcf(c_33771,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk3),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_33401]) ).

tcf(c_33772,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_33401]) ).

tcf(c_33773,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_33401]) ).

tcf(c_33774,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_33401]) ).

tcf(c_33775,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_33401]) ).

tcf(c_33776,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_33401]) ).

tcf(c_34101,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,sk3))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33739]) ).

tcf(c_34102,plain,
    hd(cons(hd(sk4),app(sk3,sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33739]) ).

tcf(c_34103,plain,
    hd(cons(hd(sk3),app(sk3,sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33739]) ).

tcf(c_34109,plain,
    cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk3)))) = cons(hd(sk4),app(sk3,sk3)),
    inference(demodulation,[status(thm)],[c_19548,c_34102]) ).

tcf(c_34116,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,sk3))))
      | ( cons(hd(sk4),app(sk3,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,sk3)))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_34102,c_280]) ).

tcf(c_34117,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,sk3))))
      | ( cons(hd(sk4),app(sk3,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,sk3)))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_34102,c_279]) ).

tcf(c_34118,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,sk3))))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34117,c_5891,c_5886]) ).

tcf(c_34123,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,sk3))))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34116,c_5891,c_5886]) ).

tcf(c_34131,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,sk3))))
      | ( cons(hd(sk3),app(sk3,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,sk3)))
      | ~ ssList(cons(hd(sk3),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_34103,c_280]) ).

tcf(c_34132,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,sk3))))
      | ( cons(hd(sk3),app(sk3,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,sk3)))
      | ~ ssList(cons(hd(sk3),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_34103,c_279]) ).

tcf(c_34133,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,sk3))))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34132,c_20706,c_20483]) ).

tcf(c_34138,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,sk3))))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34131,c_20706,c_20483]) ).

tcf(c_34149,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,sk4))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33740]) ).

tcf(c_34150,plain,
    hd(cons(hd(sk4),app(sk3,sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33740]) ).

tcf(c_34151,plain,
    hd(cons(hd(sk3),app(sk3,sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33740]) ).

tcf(c_34162,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,sk3))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_33402]) ).

tcf(c_34163,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,sk4))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_33402]) ).

tcf(c_34164,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,nil))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_33402]) ).

tcf(c_34165,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X1,app(sk4,tl(X0)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_33402]) ).

tcf(c_34166,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(cons(X2,app(sk4,app(X1,X0)))) = X2 )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_33402]) ).

tcf(c_34167,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(cons(X2,app(sk4,cons(X1,X0)))) = X2 )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_33402]) ).

tcf(c_34168,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk3),sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_33402]) ).

tcf(c_34169,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk4),sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_33402]) ).

tcf(c_34170,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk3),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_33402]) ).

tcf(c_34171,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk4),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_33402]) ).

tcf(c_34172,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(cons(X0,app(sk4,app(tl(sk3),sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_33402]) ).

tcf(c_34173,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(cons(X0,app(sk4,app(tl(sk3),sk4)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_33402]) ).

tcf(c_34174,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(cons(X0,app(sk4,app(tl(sk4),sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_33402]) ).

tcf(c_34175,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(cons(X0,app(sk4,app(tl(sk4),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_33402]) ).

tcf(c_34176,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_33402]) ).

tcf(c_34177,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_33402]) ).

tcf(c_34178,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_33402]) ).

tcf(c_34179,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_33402]) ).

tcf(c_34180,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_33402]) ).

tcf(c_34181,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_33402]) ).

tcf(c_34182,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_33402]) ).

tcf(c_34183,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_33402]) ).

tcf(c_34184,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_33402]) ).

tcf(c_34185,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_33402]) ).

tcf(c_34186,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_33402]) ).

tcf(c_34187,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk4),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_33402]) ).

tcf(c_34188,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_33402]) ).

tcf(c_34189,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_33402]) ).

tcf(c_34190,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_33402]) ).

tcf(c_34191,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk3),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_33402]) ).

tcf(c_34192,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk3),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_33402]) ).

tcf(c_34193,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk3),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_33402]) ).

tcf(c_34194,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk3),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_33402]) ).

tcf(c_34195,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_33402]) ).

tcf(c_34196,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_33402]) ).

tcf(c_34197,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_33402]) ).

tcf(c_34198,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_33402]) ).

tcf(c_34199,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_33402]) ).

tcf(c_34490,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,sk3))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34162]) ).

tcf(c_34491,plain,
    hd(cons(hd(sk4),app(sk4,sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34162]) ).

tcf(c_34492,plain,
    hd(cons(hd(sk3),app(sk4,sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34162]) ).

tcf(c_34548,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,sk4))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34163]) ).

tcf(c_34549,plain,
    hd(cons(hd(sk4),app(sk4,sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34163]) ).

tcf(c_34550,plain,
    hd(cons(hd(sk3),app(sk4,sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34163]) ).

tcf(c_34556,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,sk4))))
      | ( cons(hd(sk4),app(sk3,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4)))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_34150,c_280]) ).

tcf(c_34557,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,sk4))))
      | ( cons(hd(sk4),app(sk3,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,sk4)))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_34150,c_279]) ).

tcf(c_34558,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,sk4))))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34557,c_10190,c_10188]) ).

tcf(c_34563,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,sk4))))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34556,c_10190,c_10188]) ).

tcf(c_34571,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,sk4))))
      | ( cons(hd(sk3),app(sk3,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,sk4)))
      | ~ ssList(cons(hd(sk3),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_34151,c_280]) ).

tcf(c_34572,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,sk4))))
      | ( cons(hd(sk3),app(sk3,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,sk4)))
      | ~ ssList(cons(hd(sk3),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_34151,c_279]) ).

tcf(c_34573,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,sk4))))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34572,c_17701,c_17697]) ).

tcf(c_34578,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,sk4))))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34571,c_17701,c_17697]) ).

tcf(c_34586,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,sk3))))
      | ( cons(hd(sk4),app(sk4,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,sk3)))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_34491,c_280]) ).

tcf(c_34587,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,sk3))))
      | ( cons(hd(sk4),app(sk4,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,sk3)))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_34491,c_279]) ).

tcf(c_34588,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,sk3))))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34587,c_7545,c_7540]) ).

tcf(c_34593,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,sk3))))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34586,c_7545,c_7540]) ).

tcf(c_34601,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,sk3))))
      | ( cons(hd(sk3),app(sk4,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,sk3)))
      | ~ ssList(cons(hd(sk3),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_34492,c_280]) ).

tcf(c_34602,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,sk3))))
      | ( cons(hd(sk3),app(sk4,sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,sk3)))
      | ~ ssList(cons(hd(sk3),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_34492,c_279]) ).

tcf(c_34603,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,sk3))))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34602,c_19513,c_19123]) ).

tcf(c_34608,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,sk3))))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34601,c_19513,c_19123]) ).

tcf(c_34626,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,sk4))))
      | ( cons(hd(sk4),app(sk4,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,sk4)))
      | ~ ssList(cons(hd(sk4),app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_34549,c_280]) ).

tcf(c_34627,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,sk4))))
      | ( cons(hd(sk4),app(sk4,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,sk4)))
      | ~ ssList(cons(hd(sk4),app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_34549,c_279]) ).

tcf(c_34628,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,sk4))))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34627,c_10611,c_10606]) ).

tcf(c_34633,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,sk4))))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_34626,c_10611,c_10606]) ).

tcf(c_34640,plain,
    app(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3),nil) = cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3),
    inference(global_subsumption_just,[status(thm)],[c_7594,c_7545,c_7594]) ).

tcf(c_34649,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,sk3))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_33403]) ).

tcf(c_34650,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,sk4))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_33403]) ).

tcf(c_34651,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,nil))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_33403]) ).

tcf(c_34652,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X1,app(nil,tl(X0)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_33403]) ).

tcf(c_34653,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(cons(X2,app(nil,app(X1,X0)))) = X2 )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_33403]) ).

tcf(c_34654,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(cons(X2,app(nil,cons(X1,X0)))) = X2 )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_33403]) ).

tcf(c_34655,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk3),sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_33403]) ).

tcf(c_34656,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk4),sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_33403]) ).

tcf(c_34657,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk3),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_33403]) ).

tcf(c_34658,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk4),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_33403]) ).

tcf(c_34659,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(cons(X0,app(nil,app(tl(sk3),sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_33403]) ).

tcf(c_34660,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(cons(X0,app(nil,app(tl(sk3),sk4)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_33403]) ).

tcf(c_34661,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(cons(X0,app(nil,app(tl(sk4),sk3)))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_33403]) ).

tcf(c_34662,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(cons(X0,app(nil,app(tl(sk4),sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_33403]) ).

tcf(c_34663,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk4),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_33403]) ).

tcf(c_34664,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_33403]) ).

tcf(c_34665,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_33403]) ).

tcf(c_34666,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_33403]) ).

tcf(c_34667,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk4),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_33403]) ).

tcf(c_34668,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_33403]) ).

tcf(c_34669,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_33403]) ).

tcf(c_34670,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_33403]) ).

tcf(c_34671,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_33403]) ).

tcf(c_34672,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_33403]) ).

tcf(c_34673,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk4),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_33403]) ).

tcf(c_34674,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk4),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_33403]) ).

tcf(c_34675,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_33403]) ).

tcf(c_34676,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_33403]) ).

tcf(c_34677,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_33403]) ).

tcf(c_34678,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk3),app(sk4,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_33403]) ).

tcf(c_34679,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk3),app(sk4,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_33403]) ).

tcf(c_34680,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk3),app(sk3,sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_33403]) ).

tcf(c_34681,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk3),app(sk3,sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_33403]) ).

tcf(c_34682,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_33403]) ).

tcf(c_34683,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_33403]) ).

tcf(c_34684,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_33403]) ).

tcf(c_34685,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_33403]) ).

tcf(c_34686,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_33403]) ).

tcf(c_34851,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,sk3))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_3155]) ).

tcf(c_34852,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,sk4))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_3155]) ).

tcf(c_34853,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,nil))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_3155]) ).

tcf(c_34854,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X2,cons(X1,tl(X0)))) = X2 )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3155]) ).

tcf(c_34855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hd(cons(X3,cons(X2,app(X1,X0)))) = X3 )
      | ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3155]) ).

tcf(c_34856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( hd(cons(X3,cons(X2,cons(X1,X0)))) = X3 )
      | ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3155]) ).

tcf(c_34857,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk3),sk3)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3155]) ).

tcf(c_34858,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk4),sk3)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3155]) ).

tcf(c_34859,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk3),sk4)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3155]) ).

tcf(c_34860,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk4),sk4)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3155]) ).

tcf(c_34861,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(cons(X1,cons(X0,app(tl(sk3),sk3)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3155]) ).

tcf(c_34862,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(cons(X1,cons(X0,app(tl(sk3),sk4)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3155]) ).

tcf(c_34863,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(cons(X1,cons(X0,app(tl(sk4),sk3)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3155]) ).

tcf(c_34864,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(cons(X1,cons(X0,app(tl(sk4),sk4)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3155]) ).

tcf(c_34865,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk4),app(sk3,sk3))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3155]) ).

tcf(c_34866,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk3,sk3))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3155]) ).

tcf(c_34867,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk3,sk4))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3155]) ).

tcf(c_34868,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk3,sk3))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3155]) ).

tcf(c_34869,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk4),app(sk4,sk3))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3155]) ).

tcf(c_34870,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk3,sk4))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3155]) ).

tcf(c_34871,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk4,sk3))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3155]) ).

tcf(c_34872,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk4,sk4))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3155]) ).

tcf(c_34873,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk4,sk3))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3155]) ).

tcf(c_34874,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk4,sk4))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3155]) ).

tcf(c_34875,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk4),app(sk3,sk4))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3155]) ).

tcf(c_34876,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk4),app(sk4,sk4))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3155]) ).

tcf(c_34877,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3155]) ).

tcf(c_34878,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3155]) ).

tcf(c_34879,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3155]) ).

tcf(c_34880,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk3),app(sk4,sk4))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3155]) ).

tcf(c_34881,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk3),app(sk4,sk3))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3155]) ).

tcf(c_34882,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk3),app(sk3,sk4))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3155]) ).

tcf(c_34883,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk3),app(sk3,sk3))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3155]) ).

tcf(c_34884,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3155]) ).

tcf(c_34885,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3155]) ).

tcf(c_34886,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3155]) ).

tcf(c_34887,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3155]) ).

tcf(c_34888,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3155]) ).

tcf(c_35140,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X1,cons(hd(X0),sk3))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34851]) ).

tcf(c_35163,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X1,cons(hd(X0),sk4))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34852]) ).

tcf(c_35171,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,sk4))))
      | ( cons(hd(sk3),app(sk4,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,sk4)))
      | ~ ssList(cons(hd(sk3),app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_34550,c_280]) ).

tcf(c_35172,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,sk4))))
      | ( cons(hd(sk3),app(sk4,sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,sk4)))
      | ~ ssList(cons(hd(sk3),app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_34550,c_279]) ).

tcf(c_35173,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,sk4))))
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_35172,c_16926,c_16922]) ).

tcf(c_35178,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,sk4))))
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_35171,c_16926,c_16922]) ).

tcf(c_35186,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),cons(hd(sk3),sk3)))))
      | ( app(sk4,cons(hd(sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_33089,c_280]) ).

tcf(c_35187,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),cons(hd(sk3),sk3)))))
      | ( app(sk4,cons(hd(sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_33089,c_279]) ).

tcf(c_35203,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),cons(hd(sk3),sk3)))))
      | ( app(sk4,cons(hd(sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_33090,c_280]) ).

tcf(c_35204,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),cons(hd(sk3),sk3)))))
      | ( app(sk4,cons(hd(sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_33090,c_279]) ).

tcf(c_35220,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),cons(hd(sk4),sk3)))))
      | ( app(sk4,cons(hd(sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_33113,c_280]) ).

tcf(c_35221,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),cons(hd(sk4),sk3)))))
      | ( app(sk4,cons(hd(sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_33113,c_279]) ).

tcf(c_35256,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk3),sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33745]) ).

tcf(c_35257,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33745]) ).

tcf(c_35258,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33745]) ).

tcf(c_35266,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk4),sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33746]) ).

tcf(c_35267,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33746]) ).

tcf(c_35268,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33746]) ).

tcf(c_35280,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk3),sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33747]) ).

tcf(c_35281,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33747]) ).

tcf(c_35282,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33747]) ).

tcf(c_35345,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk4),sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33748]) ).

tcf(c_35346,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33748]) ).

tcf(c_35347,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33748]) ).

tcf(c_35355,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk3),sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34168]) ).

tcf(c_35356,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34168]) ).

tcf(c_35357,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34168]) ).

tcf(c_35387,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk4),sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34169]) ).

tcf(c_35388,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34169]) ).

tcf(c_35389,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34169]) ).

tcf(c_35430,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk3),sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34170]) ).

tcf(c_35431,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34170]) ).

tcf(c_35432,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34170]) ).

tcf(c_35440,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk4),sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34171]) ).

tcf(c_35441,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34171]) ).

tcf(c_35442,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34171]) ).

tcf(c_35446,plain,
    app(tl(cons(hd(sk4),app(sk4,sk3))),nil) = tl(cons(hd(sk4),app(sk4,sk3))),
    inference(global_subsumption_just,[status(thm)],[c_7595,c_7545,c_7595]) ).

tcf(c_35456,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ( app(tl(cons(hd(sk4),app(sk4,sk3))),X0) != tl(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_35446,c_270]) ).

tcf(c_35457,plain,
    ! [X0: $i] :
      ( ( tl(cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ( tl(cons(hd(sk4),app(sk4,sk3))) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_35446,c_269]) ).

tcf(c_35458,plain,
    ! [X0: $i] :
      ( ( tl(cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ( tl(cons(hd(sk4),app(sk4,sk3))) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_35457,c_259]) ).

tcf(c_35463,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ( app(tl(cons(hd(sk4),app(sk4,sk3))),X0) != tl(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_35456,c_259]) ).

tcf(c_35475,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(cons(X1,cons(hd(X0),nil))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34853]) ).

tcf(c_35476,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk4),nil))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4059,c_34853]) ).

tcf(c_35477,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk3),nil))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10117,c_34853]) ).

tcf(c_35488,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4) ),
    inference(global_subsumption_just,[status(thm)],[c_4111,c_247,c_1242,c_3427,c_4111]) ).

tcf(c_35496,plain,
    ! [X0: $i] :
      ( lt(hd(sk4),X0)
      | ( tl(sk4) = nil )
      | ~ strictorderedP(sk4)
      | ~ ssItem(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssItem(hd(tl(sk4)))
      | ~ lt(hd(tl(sk4)),X0) ),
    inference(superposition,[status(thm)],[c_35488,c_292]) ).

tcf(c_35497,plain,
    ( ( tl(sk4) = nil )
    | ~ strictorderedP(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssItem(hd(tl(sk4)))
    | ~ lt(hd(tl(sk4)),hd(sk4)) ),
    inference(superposition,[status(thm)],[c_35488,c_296]) ).

tcf(c_35498,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssItem(hd(tl(sk4))) ),
    inference(superposition,[status(thm)],[c_35488,c_298]) ).

tcf(c_35499,plain,
    ( strictorderedP(cons(hd(sk4),tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4)
    | ~ strictorderedP(tl(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(superposition,[status(thm)],[c_35488,c_279]) ).

tcf(c_35500,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4)
    | ~ ssItem(hd(tl(sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_35498,c_4059]) ).

tcf(c_35505,plain,
    ( ( tl(sk4) = nil )
    | ~ strictorderedP(sk4)
    | ~ ssItem(hd(tl(sk4)))
    | ~ lt(hd(tl(sk4)),hd(sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_35497,c_4059]) ).

tcf(c_35511,plain,
    ! [X0: $i] :
      ( lt(hd(sk4),X0)
      | ( tl(sk4) = nil )
      | ~ strictorderedP(sk4)
      | ~ ssItem(X0)
      | ~ ssItem(hd(tl(sk4)))
      | ~ lt(hd(tl(sk4)),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_35496,c_4059]) ).

tcf(c_35525,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(sk3,nil)) = app(cons(X0,sk3),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_4463]) ).

tcf(c_35526,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(sk4,nil)) = app(cons(X0,sk4),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_4463]) ).

tcf(c_35527,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(nil,nil)) = app(cons(X0,nil),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_4463]) ).

tcf(c_35528,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( cons(X1,app(tl(X0),nil)) = app(cons(X1,tl(X0)),nil) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4463]) ).

tcf(c_35529,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X2,app(app(X1,X0),nil)) = app(cons(X2,app(X1,X0)),nil) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4463]) ).

tcf(c_35530,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X2,app(cons(X1,X0),nil)) = app(cons(X2,cons(X1,X0)),nil) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4463]) ).

tcf(c_35531,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),sk3),nil)) = app(cons(X0,cons(hd(sk3),sk3)),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_4463]) ).

tcf(c_35532,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),sk3),nil)) = app(cons(X0,cons(hd(sk4),sk3)),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_4463]) ).

tcf(c_35533,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),sk4),nil)) = app(cons(X0,cons(hd(sk3),sk4)),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_4463]) ).

tcf(c_35534,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),sk4),nil)) = app(cons(X0,cons(hd(sk4),sk4)),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_4463]) ).

tcf(c_35535,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( cons(X0,app(app(tl(sk3),sk3),nil)) = app(cons(X0,app(tl(sk3),sk3)),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4463]) ).

tcf(c_35536,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( cons(X0,app(app(tl(sk3),sk4),nil)) = app(cons(X0,app(tl(sk3),sk4)),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4463]) ).

tcf(c_35537,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( cons(X0,app(app(tl(sk4),sk3),nil)) = app(cons(X0,app(tl(sk4),sk3)),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4463]) ).

tcf(c_35538,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( cons(X0,app(app(tl(sk4),sk4),nil)) = app(cons(X0,app(tl(sk4),sk4)),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_4463]) ).

tcf(c_35539,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk3,sk3)),nil)) = app(cons(X0,cons(hd(sk4),app(sk3,sk3))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_4463]) ).

tcf(c_35540,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,sk3)),nil)) = app(cons(X0,app(sk3,app(sk3,sk3))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4463]) ).

tcf(c_35541,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,sk4)),nil)) = app(cons(X0,app(sk3,app(sk3,sk4))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4463]) ).

tcf(c_35542,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,sk3)),nil)) = app(cons(X0,app(sk4,app(sk3,sk3))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4463]) ).

tcf(c_35543,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk4,sk3)),nil)) = app(cons(X0,cons(hd(sk4),app(sk4,sk3))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_4463]) ).

tcf(c_35544,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,sk4)),nil)) = app(cons(X0,app(sk4,app(sk3,sk4))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4463]) ).

tcf(c_35545,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,sk3)),nil)) = app(cons(X0,app(sk3,app(sk4,sk3))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4463]) ).

tcf(c_35546,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,sk4)),nil)) = app(cons(X0,app(sk3,app(sk4,sk4))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4463]) ).

tcf(c_35547,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,sk3)),nil)) = app(cons(X0,app(sk4,app(sk4,sk3))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4463]) ).

tcf(c_35548,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,sk4)),nil)) = app(cons(X0,app(sk4,app(sk4,sk4))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4463]) ).

tcf(c_35549,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk3,sk4)),nil)) = app(cons(X0,cons(hd(sk4),app(sk3,sk4))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_4463]) ).

tcf(c_35550,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk4),app(sk4,sk4)),nil)) = app(cons(X0,cons(hd(sk4),app(sk4,sk4))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_4463]) ).

tcf(c_35551,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),nil)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4463]) ).

tcf(c_35552,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),nil)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4463]) ).

tcf(c_35553,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),nil)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4463]) ).

tcf(c_35554,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk4,sk4)),nil)) = app(cons(X0,cons(hd(sk3),app(sk4,sk4))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_4463]) ).

tcf(c_35555,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk4,sk3)),nil)) = app(cons(X0,cons(hd(sk3),app(sk4,sk3))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_4463]) ).

tcf(c_35556,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk3,sk4)),nil)) = app(cons(X0,cons(hd(sk3),app(sk3,sk4))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_4463]) ).

tcf(c_35557,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),app(sk3,sk3)),nil)) = app(cons(X0,cons(hd(sk3),app(sk3,sk3))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_4463]) ).

tcf(c_35558,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),nil)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4463]) ).

tcf(c_35559,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),nil)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4463]) ).

tcf(c_35560,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),nil)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4463]) ).

tcf(c_35561,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),nil)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4463]) ).

tcf(c_35562,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),nil)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4463]) ).

tcf(c_35748,plain,
    ! [X0: $i] :
      ( ( app(app(sk3,nil),X0) = app(sk3,app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_4541]) ).

tcf(c_35749,plain,
    ! [X0: $i] :
      ( ( app(app(sk4,nil),X0) = app(sk4,app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_4541]) ).

tcf(c_35750,plain,
    ! [X0: $i] :
      ( ( app(app(nil,nil),X0) = app(nil,app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_4541]) ).

tcf(c_35751,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( app(app(tl(X0),nil),X1) = app(tl(X0),app(nil,X1)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4541]) ).

tcf(c_35752,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(app(app(X1,X0),nil),X2) = app(app(X1,X0),app(nil,X2)) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4541]) ).

tcf(c_35753,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(app(cons(X2,X0),nil),X1) = app(cons(X2,X0),app(nil,X1)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4541]) ).

tcf(c_35754,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),sk3),nil),X0) = app(cons(hd(sk3),sk3),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_4541]) ).

tcf(c_35755,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),sk3),nil),X0) = app(cons(hd(sk4),sk3),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_4541]) ).

tcf(c_35756,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),sk4),nil),X0) = app(cons(hd(sk3),sk4),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_4541]) ).

tcf(c_35757,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),sk4),nil),X0) = app(cons(hd(sk4),sk4),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_4541]) ).

tcf(c_35758,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(app(app(tl(sk3),sk3),nil),X0) = app(app(tl(sk3),sk3),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4541]) ).

tcf(c_35759,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(app(app(tl(sk3),sk4),nil),X0) = app(app(tl(sk3),sk4),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4541]) ).

tcf(c_35760,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(app(app(tl(sk4),sk3),nil),X0) = app(app(tl(sk4),sk3),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4541]) ).

tcf(c_35761,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(app(app(tl(sk4),sk4),nil),X0) = app(app(tl(sk4),sk4),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_4541]) ).

tcf(c_35762,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk3,sk3)),nil),X0) = app(cons(hd(sk4),app(sk3,sk3)),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_4541]) ).

tcf(c_35763,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,sk3)),nil),X0) = app(app(sk3,app(sk3,sk3)),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4541]) ).

tcf(c_35764,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,sk4)),nil),X0) = app(app(sk3,app(sk3,sk4)),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4541]) ).

tcf(c_35765,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,sk3)),nil),X0) = app(app(sk4,app(sk3,sk3)),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4541]) ).

tcf(c_35766,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk4,sk3)),nil),X0) = app(cons(hd(sk4),app(sk4,sk3)),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_4541]) ).

tcf(c_35767,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,sk4)),nil),X0) = app(app(sk4,app(sk3,sk4)),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4541]) ).

tcf(c_35768,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,sk3)),nil),X0) = app(app(sk3,app(sk4,sk3)),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4541]) ).

tcf(c_35769,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,sk4)),nil),X0) = app(app(sk3,app(sk4,sk4)),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4541]) ).

tcf(c_35770,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,sk3)),nil),X0) = app(app(sk4,app(sk4,sk3)),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4541]) ).

tcf(c_35771,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,sk4)),nil),X0) = app(app(sk4,app(sk4,sk4)),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4541]) ).

tcf(c_35772,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk3,sk4)),nil),X0) = app(cons(hd(sk4),app(sk3,sk4)),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_4541]) ).

tcf(c_35773,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk4),app(sk4,sk4)),nil),X0) = app(cons(hd(sk4),app(sk4,sk4)),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_4541]) ).

tcf(c_35774,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),nil),X0) = app(app(sk3,app(sk3,cons(hd(sk4),sk3))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4541]) ).

tcf(c_35775,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),nil),X0) = app(app(sk3,app(sk3,cons(hd(sk4),sk4))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4541]) ).

tcf(c_35776,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),nil),X0) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4541]) ).

tcf(c_35777,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk4,sk4)),nil),X0) = app(cons(hd(sk3),app(sk4,sk4)),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_4541]) ).

tcf(c_35778,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk4,sk3)),nil),X0) = app(cons(hd(sk3),app(sk4,sk3)),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_4541]) ).

tcf(c_35779,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk3,sk4)),nil),X0) = app(cons(hd(sk3),app(sk3,sk4)),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_4541]) ).

tcf(c_35780,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),app(sk3,sk3)),nil),X0) = app(cons(hd(sk3),app(sk3,sk3)),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_4541]) ).

tcf(c_35781,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),nil),X0) = app(app(sk4,app(sk3,cons(hd(sk4),sk3))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4541]) ).

tcf(c_35782,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),nil),X0) = app(app(sk4,app(sk3,cons(hd(sk4),sk4))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4541]) ).

tcf(c_35783,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),nil),X0) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4541]) ).

tcf(c_35784,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),nil),X0) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4541]) ).

tcf(c_35785,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),nil),X0) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4541]) ).

tcf(c_35787,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(nil,X0)) = app(sk4,X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35749,c_3010]) ).

tcf(c_35790,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(nil,X0)) = app(sk3,X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35748,c_3009]) ).

tcf(c_35793,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),sk4),app(nil,X0)) = app(cons(hd(sk4),sk4),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35757,c_3788]) ).

tcf(c_35796,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),sk4),app(nil,X0)) = app(cons(hd(sk3),sk4),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35756,c_3804]) ).

tcf(c_35799,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),sk3),app(nil,X0)) = app(cons(hd(sk4),sk3),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35755,c_3752]) ).

tcf(c_35802,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),sk3),app(nil,X0)) = app(cons(hd(sk3),sk3),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35754,c_3768]) ).

tcf(c_35809,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),app(sk3,sk3)),app(nil,X0)) = app(cons(hd(sk3),app(sk3,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35780,c_20590]) ).

tcf(c_35812,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),app(sk3,sk4)),app(nil,X0)) = app(cons(hd(sk3),app(sk3,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35779,c_17805]) ).

tcf(c_35815,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),app(sk4,sk3)),app(nil,X0)) = app(cons(hd(sk3),app(sk4,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35778,c_19280]) ).

tcf(c_35818,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk3),app(sk4,sk4)),app(nil,X0)) = app(cons(hd(sk3),app(sk4,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35777,c_17047]) ).

tcf(c_35821,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),app(sk4,sk4)),app(nil,X0)) = app(cons(hd(sk4),app(sk4,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35773,c_10698]) ).

tcf(c_35824,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),app(sk3,sk4)),app(nil,X0)) = app(cons(hd(sk4),app(sk3,sk4)),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35772,c_10232]) ).

tcf(c_35827,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),app(sk4,sk3)),app(nil,X0)) = app(cons(hd(sk4),app(sk4,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35766,c_7605]) ).

tcf(c_35830,plain,
    ! [X0: $i] :
      ( ( app(cons(hd(sk4),app(sk3,sk3)),app(nil,X0)) = app(cons(hd(sk4),app(sk3,sk3)),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_35762,c_6407]) ).

tcf(c_36032,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk4),nil))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_35476]) ).

tcf(c_36033,plain,
    hd(cons(hd(sk4),cons(hd(sk4),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_35476]) ).

tcf(c_36034,plain,
    hd(cons(hd(sk3),cons(hd(sk4),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_35476]) ).

tcf(c_36039,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),nil))))
      | ( cons(hd(sk4),cons(hd(sk4),nil)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),nil)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_36033,c_280]) ).

tcf(c_36040,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk4),nil))))
      | ( cons(hd(sk4),cons(hd(sk4),nil)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk4),nil)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_36033,c_279]) ).

tcf(c_36064,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),nil))))
      | ( cons(hd(sk3),cons(hd(sk4),nil)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),nil)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_36034,c_280]) ).

tcf(c_36065,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk4),nil))))
      | ( cons(hd(sk3),cons(hd(sk4),nil)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk4),nil)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_36034,c_279]) ).

tcf(c_36084,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk3),nil))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_35477]) ).

tcf(c_36085,plain,
    hd(cons(hd(sk4),cons(hd(sk3),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_35477]) ).

tcf(c_36086,plain,
    hd(cons(hd(sk3),cons(hd(sk3),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_35477]) ).

tcf(c_36094,plain,
    app(sk4,app(nil,sk3)) = app(sk4,sk3),
    inference(superposition,[status(thm)],[c_246,c_35787]) ).

tcf(c_36095,plain,
    app(sk4,app(nil,sk4)) = app(sk4,sk4),
    inference(superposition,[status(thm)],[c_247,c_35787]) ).

tcf(c_36096,plain,
    app(sk4,app(nil,nil)) = app(sk4,nil),
    inference(superposition,[status(thm)],[c_259,c_35787]) ).

tcf(c_36097,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,app(nil,tl(X0))) = app(sk4,tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_35787]) ).

tcf(c_36098,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,app(nil,app(X1,X0))) = app(sk4,app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_35787]) ).

tcf(c_36099,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk4,app(nil,cons(X1,X0))) = app(sk4,cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_35787]) ).

tcf(c_36100,plain,
    app(sk4,app(nil,cons(hd(sk3),sk3))) = app(sk4,cons(hd(sk3),sk3)),
    inference(superposition,[status(thm)],[c_13784,c_35787]) ).

tcf(c_36101,plain,
    app(sk4,app(nil,cons(hd(sk4),sk3))) = app(sk4,cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4358,c_35787]) ).

tcf(c_36102,plain,
    app(sk4,app(nil,cons(hd(sk3),sk4))) = app(sk4,cons(hd(sk3),sk4)),
    inference(superposition,[status(thm)],[c_12796,c_35787]) ).

tcf(c_36103,plain,
    app(sk4,app(nil,cons(hd(sk4),sk4))) = app(sk4,cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4223,c_35787]) ).

tcf(c_36104,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(sk4,app(nil,app(tl(sk3),sk3))) = app(sk4,app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_35787]) ).

tcf(c_36105,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(sk4,app(nil,app(tl(sk3),sk4))) = app(sk4,app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_35787]) ).

tcf(c_36106,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(sk4,app(nil,app(tl(sk4),sk3))) = app(sk4,app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_35787]) ).

tcf(c_36107,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(sk4,app(nil,app(tl(sk4),sk4))) = app(sk4,app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_35787]) ).

tcf(c_36108,plain,
    app(sk4,app(nil,cons(hd(sk4),app(sk3,sk3)))) = app(sk4,cons(hd(sk4),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_5886,c_35787]) ).

tcf(c_36109,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk3,sk3)))) = app(sk4,app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_35787]) ).

tcf(c_36110,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk3,sk4)))) = app(sk4,app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_35787]) ).

tcf(c_36111,plain,
    ( ( app(sk4,app(nil,app(sk4,app(sk3,sk3)))) = app(sk4,app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_35787]) ).

tcf(c_36112,plain,
    app(sk4,app(nil,cons(hd(sk4),app(sk4,sk3)))) = app(sk4,cons(hd(sk4),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_7540,c_35787]) ).

tcf(c_36113,plain,
    ( ( app(sk4,app(nil,app(sk4,app(sk3,sk4)))) = app(sk4,app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_35787]) ).

tcf(c_36114,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk4,sk3)))) = app(sk4,app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_35787]) ).

tcf(c_36115,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk4,sk4)))) = app(sk4,app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_35787]) ).

tcf(c_36116,plain,
    ( ( app(sk4,app(nil,app(sk4,app(sk4,sk3)))) = app(sk4,app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_35787]) ).

tcf(c_36117,plain,
    ( ( app(sk4,app(nil,app(sk4,app(sk4,sk4)))) = app(sk4,app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_35787]) ).

tcf(c_36118,plain,
    app(sk4,app(nil,cons(hd(sk4),app(sk3,sk4)))) = app(sk4,cons(hd(sk4),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_10188,c_35787]) ).

tcf(c_36119,plain,
    app(sk4,app(nil,cons(hd(sk4),app(sk4,sk4)))) = app(sk4,cons(hd(sk4),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_10606,c_35787]) ).

tcf(c_36120,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_35787]) ).

tcf(c_36121,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_35787]) ).

tcf(c_36122,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_35787]) ).

tcf(c_36123,plain,
    app(sk4,app(nil,cons(hd(sk3),app(sk4,sk4)))) = app(sk4,cons(hd(sk3),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_16922,c_35787]) ).

tcf(c_36124,plain,
    app(sk4,app(nil,cons(hd(sk3),app(sk4,sk3)))) = app(sk4,cons(hd(sk3),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_19123,c_35787]) ).

tcf(c_36125,plain,
    app(sk4,app(nil,cons(hd(sk3),app(sk3,sk4)))) = app(sk4,cons(hd(sk3),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_17697,c_35787]) ).

tcf(c_36126,plain,
    app(sk4,app(nil,cons(hd(sk3),app(sk3,sk3)))) = app(sk4,cons(hd(sk3),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_20483,c_35787]) ).

tcf(c_36127,plain,
    ( ( app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_35787]) ).

tcf(c_36128,plain,
    ( ( app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_35787]) ).

tcf(c_36129,plain,
    ( ( app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_35787]) ).

tcf(c_36130,plain,
    ( ( app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_35787]) ).

tcf(c_36131,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_35787]) ).

tcf(c_36497,plain,
    app(sk3,app(nil,sk3)) = app(sk3,sk3),
    inference(superposition,[status(thm)],[c_246,c_35790]) ).

tcf(c_36498,plain,
    app(sk3,app(nil,sk4)) = app(sk3,sk4),
    inference(superposition,[status(thm)],[c_247,c_35790]) ).

tcf(c_36499,plain,
    app(sk3,app(nil,nil)) = app(sk3,nil),
    inference(superposition,[status(thm)],[c_259,c_35790]) ).

tcf(c_36500,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,app(nil,tl(X0))) = app(sk3,tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_35790]) ).

tcf(c_36501,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,app(nil,app(X1,X0))) = app(sk3,app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_35790]) ).

tcf(c_36502,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sk3,app(nil,cons(X1,X0))) = app(sk3,cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_35790]) ).

tcf(c_36503,plain,
    app(sk3,app(nil,cons(hd(sk3),sk3))) = app(sk3,cons(hd(sk3),sk3)),
    inference(superposition,[status(thm)],[c_13784,c_35790]) ).

tcf(c_36504,plain,
    app(sk3,app(nil,cons(hd(sk4),sk3))) = app(sk3,cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4358,c_35790]) ).

tcf(c_36505,plain,
    app(sk3,app(nil,cons(hd(sk3),sk4))) = app(sk3,cons(hd(sk3),sk4)),
    inference(superposition,[status(thm)],[c_12796,c_35790]) ).

tcf(c_36506,plain,
    app(sk3,app(nil,cons(hd(sk4),sk4))) = app(sk3,cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4223,c_35790]) ).

tcf(c_36507,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(sk3,app(nil,app(tl(sk3),sk3))) = app(sk3,app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_35790]) ).

tcf(c_36508,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(sk3,app(nil,app(tl(sk3),sk4))) = app(sk3,app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_35790]) ).

tcf(c_36509,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(sk3,app(nil,app(tl(sk4),sk3))) = app(sk3,app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_35790]) ).

tcf(c_36510,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(sk3,app(nil,app(tl(sk4),sk4))) = app(sk3,app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_35790]) ).

tcf(c_36511,plain,
    app(sk3,app(nil,cons(hd(sk4),app(sk3,sk3)))) = app(sk3,cons(hd(sk4),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_5886,c_35790]) ).

tcf(c_36512,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk3,sk3)))) = app(sk3,app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_35790]) ).

tcf(c_36513,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk3,sk4)))) = app(sk3,app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_35790]) ).

tcf(c_36514,plain,
    ( ( app(sk3,app(nil,app(sk4,app(sk3,sk3)))) = app(sk3,app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_35790]) ).

tcf(c_36515,plain,
    app(sk3,app(nil,cons(hd(sk4),app(sk4,sk3)))) = app(sk3,cons(hd(sk4),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_7540,c_35790]) ).

tcf(c_36516,plain,
    ( ( app(sk3,app(nil,app(sk4,app(sk3,sk4)))) = app(sk3,app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_35790]) ).

tcf(c_36517,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk4,sk3)))) = app(sk3,app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_35790]) ).

tcf(c_36518,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk4,sk4)))) = app(sk3,app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_35790]) ).

tcf(c_36519,plain,
    ( ( app(sk3,app(nil,app(sk4,app(sk4,sk3)))) = app(sk3,app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_35790]) ).

tcf(c_36520,plain,
    ( ( app(sk3,app(nil,app(sk4,app(sk4,sk4)))) = app(sk3,app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_35790]) ).

tcf(c_36521,plain,
    app(sk3,app(nil,cons(hd(sk4),app(sk3,sk4)))) = app(sk3,cons(hd(sk4),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_10188,c_35790]) ).

tcf(c_36522,plain,
    app(sk3,app(nil,cons(hd(sk4),app(sk4,sk4)))) = app(sk3,cons(hd(sk4),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_10606,c_35790]) ).

tcf(c_36523,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_35790]) ).

tcf(c_36524,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_35790]) ).

tcf(c_36525,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_35790]) ).

tcf(c_36526,plain,
    app(sk3,app(nil,cons(hd(sk3),app(sk4,sk4)))) = app(sk3,cons(hd(sk3),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_16922,c_35790]) ).

tcf(c_36527,plain,
    app(sk3,app(nil,cons(hd(sk3),app(sk4,sk3)))) = app(sk3,cons(hd(sk3),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_19123,c_35790]) ).

tcf(c_36528,plain,
    app(sk3,app(nil,cons(hd(sk3),app(sk3,sk4)))) = app(sk3,cons(hd(sk3),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_17697,c_35790]) ).

tcf(c_36529,plain,
    app(sk3,app(nil,cons(hd(sk3),app(sk3,sk3)))) = app(sk3,cons(hd(sk3),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_20483,c_35790]) ).

tcf(c_36530,plain,
    ( ( app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_35790]) ).

tcf(c_36531,plain,
    ( ( app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_35790]) ).

tcf(c_36532,plain,
    ( ( app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_35790]) ).

tcf(c_36533,plain,
    ( ( app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_35790]) ).

tcf(c_36534,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_35790]) ).

tcf(c_36634,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_17997]) ).

tcf(c_36635,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_17997]) ).

tcf(c_36636,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_17997]) ).

tcf(c_36637,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(cons(hd(sk3),sk3),tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_17997]) ).

tcf(c_36638,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_17997]) ).

tcf(c_36639,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),sk3),cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_17997]) ).

tcf(c_36640,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_17997]) ).

tcf(c_36641,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_17997]) ).

tcf(c_36642,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_17997]) ).

tcf(c_36643,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_17997]) ).

tcf(c_36644,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(cons(hd(sk3),sk3),app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_17997]) ).

tcf(c_36645,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(cons(hd(sk3),sk3),app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_17997]) ).

tcf(c_36646,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(cons(hd(sk3),sk3),app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_17997]) ).

tcf(c_36647,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(cons(hd(sk3),sk3),app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_17997]) ).

tcf(c_36648,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_17997]) ).

tcf(c_36649,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_17997]) ).

tcf(c_36650,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_17997]) ).

tcf(c_36651,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_17997]) ).

tcf(c_36652,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_17997]) ).

tcf(c_36653,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_17997]) ).

tcf(c_36654,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_17997]) ).

tcf(c_36655,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_17997]) ).

tcf(c_36656,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_17997]) ).

tcf(c_36657,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_17997]) ).

tcf(c_36658,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_17997]) ).

tcf(c_36659,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_17997]) ).

tcf(c_36660,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_17997]) ).

tcf(c_36661,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_17997]) ).

tcf(c_36662,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_17997]) ).

tcf(c_36663,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_17997]) ).

tcf(c_36664,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_17997]) ).

tcf(c_36665,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_17997]) ).

tcf(c_36666,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_17997]) ).

tcf(c_36667,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_17997]) ).

tcf(c_36668,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_17997]) ).

tcf(c_36669,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_17997]) ).

tcf(c_36670,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_17997]) ).

tcf(c_36671,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_17997]) ).

tcf(c_36855,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_17998]) ).

tcf(c_36856,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_17998]) ).

tcf(c_36857,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_17998]) ).

tcf(c_36858,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(cons(hd(sk4),sk3),tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_17998]) ).

tcf(c_36859,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_17998]) ).

tcf(c_36860,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),sk3),cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_17998]) ).

tcf(c_36861,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_17998]) ).

tcf(c_36862,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_17998]) ).

tcf(c_36863,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_17998]) ).

tcf(c_36864,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_17998]) ).

tcf(c_36865,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(cons(hd(sk4),sk3),app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_17998]) ).

tcf(c_36866,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(cons(hd(sk4),sk3),app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_17998]) ).

tcf(c_36867,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(cons(hd(sk4),sk3),app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_17998]) ).

tcf(c_36868,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(cons(hd(sk4),sk3),app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_17998]) ).

tcf(c_36869,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_17998]) ).

tcf(c_36870,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_17998]) ).

tcf(c_36871,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_17998]) ).

tcf(c_36872,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_17998]) ).

tcf(c_36873,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_17998]) ).

tcf(c_36874,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_17998]) ).

tcf(c_36875,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_17998]) ).

tcf(c_36876,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_17998]) ).

tcf(c_36877,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_17998]) ).

tcf(c_36878,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_17998]) ).

tcf(c_36879,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_17998]) ).

tcf(c_36880,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_17998]) ).

tcf(c_36881,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_17998]) ).

tcf(c_36882,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_17998]) ).

tcf(c_36883,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_17998]) ).

tcf(c_36884,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_17998]) ).

tcf(c_36885,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_17998]) ).

tcf(c_36886,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_17998]) ).

tcf(c_36887,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_17998]) ).

tcf(c_36888,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_17998]) ).

tcf(c_36889,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_17998]) ).

tcf(c_36890,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_17998]) ).

tcf(c_36891,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_17998]) ).

tcf(c_36892,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_17998]) ).

tcf(c_37178,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_18000]) ).

tcf(c_37179,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_18000]) ).

tcf(c_37180,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_18000]) ).

tcf(c_37181,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(cons(hd(sk4),sk4),tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18000]) ).

tcf(c_37182,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18000]) ).

tcf(c_37183,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk4),sk4),cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18000]) ).

tcf(c_37184,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_18000]) ).

tcf(c_37185,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_18000]) ).

tcf(c_37186,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_18000]) ).

tcf(c_37187,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_18000]) ).

tcf(c_37188,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(cons(hd(sk4),sk4),app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18000]) ).

tcf(c_37189,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(cons(hd(sk4),sk4),app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18000]) ).

tcf(c_37190,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(cons(hd(sk4),sk4),app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18000]) ).

tcf(c_37191,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(cons(hd(sk4),sk4),app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_18000]) ).

tcf(c_37192,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_18000]) ).

tcf(c_37193,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18000]) ).

tcf(c_37194,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18000]) ).

tcf(c_37195,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18000]) ).

tcf(c_37196,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_18000]) ).

tcf(c_37197,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18000]) ).

tcf(c_37198,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18000]) ).

tcf(c_37199,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18000]) ).

tcf(c_37200,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18000]) ).

tcf(c_37201,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18000]) ).

tcf(c_37202,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_18000]) ).

tcf(c_37203,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_18000]) ).

tcf(c_37204,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18000]) ).

tcf(c_37205,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18000]) ).

tcf(c_37206,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18000]) ).

tcf(c_37207,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_18000]) ).

tcf(c_37208,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_18000]) ).

tcf(c_37209,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_18000]) ).

tcf(c_37210,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_18000]) ).

tcf(c_37211,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18000]) ).

tcf(c_37212,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18000]) ).

tcf(c_37213,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18000]) ).

tcf(c_37214,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18000]) ).

tcf(c_37215,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18000]) ).

tcf(c_37317,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,cons(hd(X0),cons(hd(sk3),sk3)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_18851]) ).

tcf(c_37318,plain,
    hd(app(sk3,cons(hd(sk4),cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4059,c_18851]) ).

tcf(c_37319,plain,
    hd(app(sk3,cons(hd(sk3),cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_18851]) ).

tcf(c_37365,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,cons(hd(X0),cons(hd(sk4),sk3)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_18852]) ).

tcf(c_37366,plain,
    hd(app(sk3,cons(hd(sk4),cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4059,c_18852]) ).

tcf(c_37367,plain,
    hd(app(sk3,cons(hd(sk3),cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_18852]) ).

tcf(c_37375,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,cons(hd(X0),cons(hd(sk4),sk4)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_18854]) ).

tcf(c_37376,plain,
    hd(app(sk3,cons(hd(sk4),cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4059,c_18854]) ).

tcf(c_37377,plain,
    hd(app(sk3,cons(hd(sk3),cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_18854]) ).

tcf(c_37381,plain,
    hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4)) = hd(cons(hd(sk4),app(sk4,sk3))),
    inference(global_subsumption_just,[status(thm)],[c_7596,c_7545,c_7596]) ).

tcf(c_37390,plain,
    ( ( sk3 = nil )
    | ( hd(app(sk4,app(sk3,tl(sk3)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_246,c_15592]) ).

tcf(c_37391,plain,
    ( ( sk4 = nil )
    | ( hd(app(sk4,app(sk3,tl(sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_15592]) ).

tcf(c_37393,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk4,app(sk3,tl(tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15592]) ).

tcf(c_37394,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk4,app(sk3,tl(app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15592]) ).

tcf(c_37395,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk4,app(sk3,tl(cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15592]) ).

tcf(c_37396,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk3),sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_15592]) ).

tcf(c_37397,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk4),sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_15592]) ).

tcf(c_37398,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk3),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_15592]) ).

tcf(c_37399,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_15592]) ).

tcf(c_37400,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15592]) ).

tcf(c_37401,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15592]) ).

tcf(c_37402,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15592]) ).

tcf(c_37403,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_15592]) ).

tcf(c_37404,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_15592]) ).

tcf(c_37405,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15592]) ).

tcf(c_37406,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15592]) ).

tcf(c_37407,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15592]) ).

tcf(c_37408,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_15592]) ).

tcf(c_37409,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15592]) ).

tcf(c_37410,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15592]) ).

tcf(c_37411,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15592]) ).

tcf(c_37412,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15592]) ).

tcf(c_37413,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15592]) ).

tcf(c_37414,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_15592]) ).

tcf(c_37415,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_15592]) ).

tcf(c_37416,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15592]) ).

tcf(c_37417,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15592]) ).

tcf(c_37418,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15592]) ).

tcf(c_37419,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_15592]) ).

tcf(c_37420,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_15592]) ).

tcf(c_37421,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_15592]) ).

tcf(c_37422,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_15592]) ).

tcf(c_37423,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15592]) ).

tcf(c_37424,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15592]) ).

tcf(c_37425,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15592]) ).

tcf(c_37426,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15592]) ).

tcf(c_37427,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15592]) ).

tcf(c_37428,plain,
    hd(app(sk4,app(sk3,tl(sk4)))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_37391,c_1243]) ).

tcf(c_37439,plain,
    hd(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_37422,c_20706]) ).

tcf(c_37440,plain,
    hd(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_37421,c_17701]) ).

tcf(c_37441,plain,
    hd(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_37420,c_19513]) ).

tcf(c_37442,plain,
    hd(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_37419,c_16926]) ).

tcf(c_37443,plain,
    hd(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_37415,c_10611]) ).

tcf(c_37444,plain,
    hd(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_37414,c_10190]) ).

tcf(c_37445,plain,
    hd(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_37408,c_7545]) ).

tcf(c_37446,plain,
    hd(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_37404,c_5891]) ).

tcf(c_37563,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(sk4)))))
      | ( app(sk4,app(sk3,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(sk4))))
      | ~ ssList(app(sk4,app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_37428,c_280]) ).

tcf(c_37564,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(sk4)))))
      | ( app(sk4,app(sk3,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(sk4))))
      | ~ ssList(app(sk4,app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_37428,c_279]) ).

tcf(c_37579,plain,
    hd(app(sk4,app(sk3,tl(sk3)))) = hd(sk4),
    inference(global_subsumption_just,[status(thm)],[c_37390,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_37390]) ).

tcf(c_37582,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(sk3)))))
      | ( app(sk4,app(sk3,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(sk3))))
      | ~ ssList(app(sk4,app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_37579,c_280]) ).

tcf(c_37583,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(sk3)))))
      | ( app(sk4,app(sk3,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(sk3))))
      | ~ ssList(app(sk4,app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_37579,c_279]) ).

tcf(c_37604,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(sk3,X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_15593]) ).

tcf(c_37605,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(sk4,X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_15593]) ).

tcf(c_37606,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(nil,X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_15593]) ).

tcf(c_37607,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk3,app(tl(X0),X1)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15593]) ).

tcf(c_37608,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(X1,X0),X2)))) = hd(sk4) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15593]) ).

tcf(c_37609,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(X2,X0),X1)))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15593]) ).

tcf(c_37610,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk3),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_15593]) ).

tcf(c_37611,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk4),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_15593]) ).

tcf(c_37612,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk3),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_15593]) ).

tcf(c_37613,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk4),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_15593]) ).

tcf(c_37614,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk4,app(sk3,app(app(tl(sk3),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15593]) ).

tcf(c_37615,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk4,app(sk3,app(app(tl(sk3),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15593]) ).

tcf(c_37616,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk4,app(sk3,app(app(tl(sk4),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15593]) ).

tcf(c_37617,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk4,app(sk3,app(app(tl(sk4),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_15593]) ).

tcf(c_37618,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk4),app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_15593]) ).

tcf(c_37619,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15593]) ).

tcf(c_37620,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15593]) ).

tcf(c_37621,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15593]) ).

tcf(c_37622,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk4),app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_15593]) ).

tcf(c_37623,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15593]) ).

tcf(c_37624,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15593]) ).

tcf(c_37625,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15593]) ).

tcf(c_37626,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15593]) ).

tcf(c_37627,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15593]) ).

tcf(c_37628,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk4),app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_15593]) ).

tcf(c_37629,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk4),app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_15593]) ).

tcf(c_37630,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15593]) ).

tcf(c_37631,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15593]) ).

tcf(c_37632,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15593]) ).

tcf(c_37633,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk3),app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_15593]) ).

tcf(c_37634,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk3),app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_15593]) ).

tcf(c_37635,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk3),app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_15593]) ).

tcf(c_37636,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk3),app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_15593]) ).

tcf(c_37637,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15593]) ).

tcf(c_37638,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15593]) ).

tcf(c_37639,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15593]) ).

tcf(c_37640,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15593]) ).

tcf(c_37641,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15593]) ).

tcf(c_37918,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),nil))))
      | ( cons(hd(sk4),cons(hd(sk3),nil)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),nil)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_36085,c_280]) ).

tcf(c_37919,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),nil))))
      | ( cons(hd(sk4),cons(hd(sk3),nil)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk3),nil)))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_36085,c_279]) ).

tcf(c_37935,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),nil))))
      | ( cons(hd(sk3),cons(hd(sk3),nil)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),nil)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_36086,c_280]) ).

tcf(c_37936,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),nil))))
      | ( cons(hd(sk3),cons(hd(sk3),nil)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk3),nil)))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_36086,c_279]) ).

tcf(c_37965,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),cons(hd(sk4),sk3)))))
      | ( app(sk4,cons(hd(sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_33114,c_280]) ).

tcf(c_37966,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),cons(hd(sk4),sk3)))))
      | ( app(sk4,cons(hd(sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_33114,c_279]) ).

tcf(c_37982,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),cons(hd(sk4),sk4)))))
      | ( app(sk4,cons(hd(sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_33123,c_280]) ).

tcf(c_37983,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),cons(hd(sk4),sk4)))))
      | ( app(sk4,cons(hd(sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_33123,c_279]) ).

tcf(c_38002,plain,
    hd(app(sk4,app(sk3,app(sk3,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_37604]) ).

tcf(c_38003,plain,
    hd(app(sk4,app(sk3,app(sk3,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_37604]) ).

tcf(c_38004,plain,
    hd(app(sk4,app(sk3,app(sk3,nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_37604]) ).

tcf(c_38005,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk3,app(sk3,tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_37604]) ).

tcf(c_38006,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk3,app(sk3,app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_37604]) ).

tcf(c_38007,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk3,app(sk3,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_37604]) ).

tcf(c_38008,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_37604]) ).

tcf(c_38009,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_37604]) ).

tcf(c_38010,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_37604]) ).

tcf(c_38011,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_37604]) ).

tcf(c_38012,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(sk3,app(sk3,app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_37604]) ).

tcf(c_38013,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(sk3,app(sk3,app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_37604]) ).

tcf(c_38014,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(sk3,app(sk3,app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_37604]) ).

tcf(c_38015,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(sk3,app(sk3,app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_37604]) ).

tcf(c_38016,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_37604]) ).

tcf(c_38017,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_37604]) ).

tcf(c_38018,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_37604]) ).

tcf(c_38019,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_37604]) ).

tcf(c_38020,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_37604]) ).

tcf(c_38021,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_37604]) ).

tcf(c_38022,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_37604]) ).

tcf(c_38023,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_37604]) ).

tcf(c_38024,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_37604]) ).

tcf(c_38025,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_37604]) ).

tcf(c_38026,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_37604]) ).

tcf(c_38027,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_37604]) ).

tcf(c_38028,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_37604]) ).

tcf(c_38029,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_37604]) ).

tcf(c_38030,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_37604]) ).

tcf(c_38031,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_37604]) ).

tcf(c_38032,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_37604]) ).

tcf(c_38033,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_37604]) ).

tcf(c_38034,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_37604]) ).

tcf(c_38035,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_37604]) ).

tcf(c_38036,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_37604]) ).

tcf(c_38037,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_37604]) ).

tcf(c_38038,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_37604]) ).

tcf(c_38039,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_37604]) ).

tcf(c_38581,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,sk3)))))
      | ( app(sk4,app(sk3,app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,sk3))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_38002,c_280]) ).

tcf(c_38582,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,sk3)))))
      | ( app(sk4,app(sk3,app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,sk3))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_38002,c_279]) ).

tcf(c_38598,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,sk4)))))
      | ( app(sk4,app(sk3,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,sk4))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_38003,c_280]) ).

tcf(c_38599,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,sk4)))))
      | ( app(sk4,app(sk3,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,sk4))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_38003,c_279]) ).

tcf(c_38633,plain,
    hd(app(sk4,app(sk3,app(sk4,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_37605]) ).

tcf(c_38634,plain,
    hd(app(sk4,app(sk3,app(sk4,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_37605]) ).

tcf(c_38635,plain,
    hd(app(sk4,app(sk3,app(sk4,nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_37605]) ).

tcf(c_38636,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk3,app(sk4,tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_37605]) ).

tcf(c_38637,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk3,app(sk4,app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_37605]) ).

tcf(c_38638,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk3,app(sk4,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_37605]) ).

tcf(c_38639,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_37605]) ).

tcf(c_38640,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_37605]) ).

tcf(c_38641,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_37605]) ).

tcf(c_38642,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_37605]) ).

tcf(c_38643,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(sk3,app(sk4,app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_37605]) ).

tcf(c_38644,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(sk3,app(sk4,app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_37605]) ).

tcf(c_38645,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(sk3,app(sk4,app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_37605]) ).

tcf(c_38646,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(sk3,app(sk4,app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_37605]) ).

tcf(c_38647,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_37605]) ).

tcf(c_38648,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_37605]) ).

tcf(c_38649,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_37605]) ).

tcf(c_38650,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_37605]) ).

tcf(c_38651,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_37605]) ).

tcf(c_38652,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_37605]) ).

tcf(c_38653,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_37605]) ).

tcf(c_38654,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_37605]) ).

tcf(c_38655,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_37605]) ).

tcf(c_38656,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_37605]) ).

tcf(c_38657,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_37605]) ).

tcf(c_38658,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_37605]) ).

tcf(c_38659,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_37605]) ).

tcf(c_38660,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_37605]) ).

tcf(c_38661,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_37605]) ).

tcf(c_38662,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_37605]) ).

tcf(c_38663,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_37605]) ).

tcf(c_38664,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_37605]) ).

tcf(c_38665,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_37605]) ).

tcf(c_38666,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_37605]) ).

tcf(c_38667,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_37605]) ).

tcf(c_38668,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_37605]) ).

tcf(c_38669,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_37605]) ).

tcf(c_38670,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_37605]) ).

tcf(c_38789,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,sk3)))))
      | ( app(sk4,app(sk3,app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,sk3))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_38633,c_280]) ).

tcf(c_38790,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,sk3)))))
      | ( app(sk4,app(sk3,app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,sk3))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_38633,c_279]) ).

tcf(c_38806,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,sk4)))))
      | ( app(sk4,app(sk3,app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,sk4))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_38634,c_280]) ).

tcf(c_38807,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,sk4)))))
      | ( app(sk4,app(sk3,app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,sk4))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_38634,c_279]) ).

tcf(c_38823,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_38008,c_280]) ).

tcf(c_38824,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_38008,c_279]) ).

tcf(c_38840,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_38009,c_280]) ).

tcf(c_38841,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_38009,c_279]) ).

tcf(c_38856,plain,
    hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3)) = hd(cons(hd(sk4),app(sk4,sk3))),
    inference(global_subsumption_just,[status(thm)],[c_7597,c_7545,c_7597]) ).

tcf(c_38863,plain,
    hd(app(sk4,app(sk3,app(nil,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_37606]) ).

tcf(c_38864,plain,
    hd(app(sk4,app(sk3,app(nil,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_37606]) ).

tcf(c_38865,plain,
    hd(app(sk4,app(sk3,app(nil,nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_37606]) ).

tcf(c_38866,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk3,app(nil,tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_37606]) ).

tcf(c_38867,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk3,app(nil,app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_37606]) ).

tcf(c_38868,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk3,app(nil,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_37606]) ).

tcf(c_38869,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk3),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_37606]) ).

tcf(c_38870,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_37606]) ).

tcf(c_38871,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk3),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_37606]) ).

tcf(c_38872,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_37606]) ).

tcf(c_38873,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(sk3,app(nil,app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_37606]) ).

tcf(c_38874,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(sk3,app(nil,app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_37606]) ).

tcf(c_38875,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(sk3,app(nil,app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_37606]) ).

tcf(c_38876,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(sk3,app(nil,app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_37606]) ).

tcf(c_38877,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_37606]) ).

tcf(c_38878,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_37606]) ).

tcf(c_38879,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_37606]) ).

tcf(c_38880,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_37606]) ).

tcf(c_38881,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_37606]) ).

tcf(c_38882,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_37606]) ).

tcf(c_38883,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_37606]) ).

tcf(c_38884,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_37606]) ).

tcf(c_38885,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_37606]) ).

tcf(c_38886,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_37606]) ).

tcf(c_38887,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_37606]) ).

tcf(c_38888,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_37606]) ).

tcf(c_38889,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_37606]) ).

tcf(c_38890,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_37606]) ).

tcf(c_38891,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_37606]) ).

tcf(c_38892,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_37606]) ).

tcf(c_38893,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_37606]) ).

tcf(c_38894,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_37606]) ).

tcf(c_38895,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_37606]) ).

tcf(c_38896,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_37606]) ).

tcf(c_38897,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_37606]) ).

tcf(c_38898,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_37606]) ).

tcf(c_38899,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_37606]) ).

tcf(c_38900,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_37606]) ).

tcf(c_39173,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,sk3)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_15594]) ).

tcf(c_39174,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,sk4)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_15594]) ).

tcf(c_39175,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,nil)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_15594]) ).

tcf(c_39176,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk3,cons(X1,tl(X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15594]) ).

tcf(c_39177,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X2,app(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15594]) ).

tcf(c_39178,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X2,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15594]) ).

tcf(c_39179,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk3),sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_15594]) ).

tcf(c_39180,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk4),sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_15594]) ).

tcf(c_39181,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk3),sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_15594]) ).

tcf(c_39182,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk4),sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_15594]) ).

tcf(c_39183,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk4,app(sk3,cons(X0,app(tl(sk3),sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15594]) ).

tcf(c_39184,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk4,app(sk3,cons(X0,app(tl(sk3),sk4))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15594]) ).

tcf(c_39185,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk4,app(sk3,cons(X0,app(tl(sk4),sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15594]) ).

tcf(c_39186,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk4,app(sk3,cons(X0,app(tl(sk4),sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_15594]) ).

tcf(c_39187,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_15594]) ).

tcf(c_39188,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15594]) ).

tcf(c_39189,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15594]) ).

tcf(c_39190,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15594]) ).

tcf(c_39191,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_15594]) ).

tcf(c_39192,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15594]) ).

tcf(c_39193,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15594]) ).

tcf(c_39194,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15594]) ).

tcf(c_39195,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15594]) ).

tcf(c_39196,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15594]) ).

tcf(c_39197,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_15594]) ).

tcf(c_39198,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_15594]) ).

tcf(c_39199,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15594]) ).

tcf(c_39200,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15594]) ).

tcf(c_39201,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15594]) ).

tcf(c_39202,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_15594]) ).

tcf(c_39203,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_15594]) ).

tcf(c_39204,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_15594]) ).

tcf(c_39205,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_15594]) ).

tcf(c_39206,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15594]) ).

tcf(c_39207,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15594]) ).

tcf(c_39208,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15594]) ).

tcf(c_39209,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15594]) ).

tcf(c_39210,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15594]) ).

tcf(c_39409,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk3,cons(hd(X0),sk3)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_39173]) ).

tcf(c_39419,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk3,cons(hd(X0),sk4)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_39174]) ).

tcf(c_39426,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),cons(hd(sk4),sk4)))))
      | ( app(sk4,cons(hd(sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_33124,c_280]) ).

tcf(c_39427,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),cons(hd(sk4),sk4)))))
      | ( app(sk4,cons(hd(sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_33124,c_279]) ).

tcf(c_39443,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,cons(hd(sk3),sk3)))))
      | ( cons(hd(sk4),app(sk3,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,cons(hd(sk3),sk3))))
      | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35257,c_280]) ).

tcf(c_39444,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,cons(hd(sk3),sk3)))))
      | ( cons(hd(sk4),app(sk3,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,cons(hd(sk3),sk3))))
      | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35257,c_279]) ).

tcf(c_39482,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,cons(hd(sk3),sk3)))))
      | ( cons(hd(sk3),app(sk3,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),sk3))))
      | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35258,c_280]) ).

tcf(c_39483,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,cons(hd(sk3),sk3)))))
      | ( cons(hd(sk3),app(sk3,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),sk3))))
      | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35258,c_279]) ).

tcf(c_39499,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,cons(hd(sk4),sk3)))))
      | ( cons(hd(sk4),app(sk3,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,cons(hd(sk4),sk3))))
      | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35267,c_280]) ).

tcf(c_39500,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,cons(hd(sk4),sk3)))))
      | ( cons(hd(sk4),app(sk3,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,cons(hd(sk4),sk3))))
      | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35267,c_279]) ).

tcf(c_39516,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_38010,c_280]) ).

tcf(c_39517,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_38010,c_279]) ).

tcf(c_39533,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_38011,c_280]) ).

tcf(c_39534,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_38011,c_279]) ).

tcf(c_39550,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_38639,c_280]) ).

tcf(c_39551,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_38639,c_279]) ).

tcf(c_39567,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_38640,c_280]) ).

tcf(c_39568,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_38640,c_279]) ).

tcf(c_39584,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_38641,c_280]) ).

tcf(c_39585,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_38641,c_279]) ).

tcf(c_39601,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_38642,c_280]) ).

tcf(c_39602,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_38642,c_279]) ).

tcf(c_39657,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(cons(hd(sk3),app(sk3,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_31835]) ).

tcf(c_39658,plain,
    hd(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_31835]) ).

tcf(c_39659,plain,
    hd(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_31835]) ).

tcf(c_39667,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(cons(hd(sk3),app(sk3,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_31838]) ).

tcf(c_39668,plain,
    hd(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_31838]) ).

tcf(c_39669,plain,
    hd(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_31838]) ).

tcf(c_39673,plain,
    cons(hd(cons(hd(sk4),app(sk4,sk3))),tl(cons(hd(sk4),app(sk4,sk3)))) = cons(hd(sk4),app(sk4,sk3)),
    inference(global_subsumption_just,[status(thm)],[c_7599,c_7545,c_7599]) ).

tcf(c_39675,plain,
    cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))) = cons(hd(sk4),app(sk4,sk3)),
    inference(light_normalisation,[status(thm)],[c_39673,c_34491]) ).

tcf(c_39677,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_23857]) ).

tcf(c_39678,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_23849]) ).

tcf(c_39679,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_23004]) ).

tcf(c_39680,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_22996]) ).

tcf(c_39681,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_12052]) ).

tcf(c_39682,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_12044]) ).

tcf(c_39683,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_11285]) ).

tcf(c_39684,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_11277]) ).

tcf(c_39685,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_12667]) ).

tcf(c_39686,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_12660]) ).

tcf(c_39687,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_12629]) ).

tcf(c_39688,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_12622]) ).

tcf(c_39689,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_6332]) ).

tcf(c_39690,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_6325]) ).

tcf(c_39691,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_6196]) ).

tcf(c_39692,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_6189]) ).

tcf(c_39695,plain,
    ( lt(hd(sk4),hd(tl(cons(hd(sk4),app(sk4,sk3)))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ ssItem(hd(sk4))
    | ~ strictorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_39675,c_282]) ).

tcf(c_39696,plain,
    ( leq(hd(sk4),hd(tl(cons(hd(sk4),app(sk4,sk3)))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ ssItem(hd(sk4))
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_39675,c_281]) ).

tcf(c_39697,plain,
    ( totalorderedP(tl(cons(hd(sk4),app(sk4,sk3))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ ssItem(hd(sk4))
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_39675,c_301]) ).

tcf(c_39698,plain,
    ( strictorderedP(tl(cons(hd(sk4),app(sk4,sk3))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ ssItem(hd(sk4))
    | ~ strictorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_39675,c_288]) ).

tcf(c_39699,plain,
    ( ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_39675,c_267]) ).

tcf(c_39701,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2)))
      | ~ totalorderedP(app(app(X0,cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3))))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_39675,c_300]) ).

tcf(c_39702,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2)))
      | ~ strictorderedP(app(app(X0,cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3))))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_39675,c_287]) ).

tcf(c_39703,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(sk4) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ( cons(hd(sk4),app(sk4,sk3)) != cons(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_39675,c_265]) ).

tcf(c_39704,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(cons(hd(sk4),app(sk4,sk3))) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ( cons(hd(sk4),app(sk4,sk3)) != cons(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_39675,c_264]) ).

tcf(c_39705,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3))))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_300]) ).

tcf(c_39706,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3))))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_287]) ).

tcf(c_39707,plain,
    ( ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) != cons(hd(sk4),app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39699,c_4059]) ).

tcf(c_39710,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(sk4) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ( cons(hd(sk4),app(sk4,sk3)) != cons(X0,X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39703,c_4059]) ).

tcf(c_39716,plain,
    ( strictorderedP(tl(cons(hd(sk4),app(sk4,sk3))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ strictorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39698,c_4059]) ).

tcf(c_39721,plain,
    ( totalorderedP(tl(cons(hd(sk4),app(sk4,sk3))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39697,c_4059]) ).

tcf(c_39726,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(cons(hd(sk4),app(sk4,sk3))) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ( cons(hd(sk4),app(sk4,sk3)) != cons(X0,X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39704,c_4059]) ).

tcf(c_39732,plain,
    ( leq(hd(sk4),hd(tl(cons(hd(sk4),app(sk4,sk3)))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39696,c_4059]) ).

tcf(c_39737,plain,
    ( lt(hd(sk4),hd(tl(cons(hd(sk4),app(sk4,sk3)))))
    | ( tl(cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ strictorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39695,c_4059]) ).

tcf(c_39742,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39692,c_39675]) ).

tcf(c_39743,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39742,c_4059]) ).

tcf(c_39748,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39691,c_39675]) ).

tcf(c_39749,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39748,c_4059]) ).

tcf(c_39754,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39690,c_39675]) ).

tcf(c_39755,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39754,c_4059]) ).

tcf(c_39760,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39689,c_39675]) ).

tcf(c_39761,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39760,c_4059]) ).

tcf(c_39766,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39688,c_39675]) ).

tcf(c_39767,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39766,c_4059]) ).

tcf(c_39772,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39687,c_39675]) ).

tcf(c_39773,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39772,c_4059]) ).

tcf(c_39778,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39686,c_39675]) ).

tcf(c_39779,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39778,c_4059]) ).

tcf(c_39784,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39685,c_39675]) ).

tcf(c_39785,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39784,c_4059]) ).

tcf(c_39790,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39706,c_39675]) ).

tcf(c_39791,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39790,c_4059]) ).

tcf(c_39799,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39705,c_39675]) ).

tcf(c_39800,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39799,c_4059]) ).

tcf(c_39808,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ strictorderedP(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2))) ),
    inference(light_normalisation,[status(thm)],[c_39702,c_39675]) ).

tcf(c_39809,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ strictorderedP(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39808,c_4059]) ).

tcf(c_39817,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ totalorderedP(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2))) ),
    inference(light_normalisation,[status(thm)],[c_39701,c_39675]) ).

tcf(c_39818,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
      | ~ totalorderedP(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk4,sk3))),cons(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39817,c_4059]) ).

tcf(c_39826,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39684,c_39675]) ).

tcf(c_39827,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39826,c_4059]) ).

tcf(c_39833,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39683,c_39675]) ).

tcf(c_39834,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39833,c_4059]) ).

tcf(c_39840,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39682,c_39675]) ).

tcf(c_39841,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39840,c_4059]) ).

tcf(c_39847,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39681,c_39675]) ).

tcf(c_39848,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39847,c_4059]) ).

tcf(c_39854,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39680,c_39675]) ).

tcf(c_39855,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39854,c_4059]) ).

tcf(c_39861,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39679,c_39675]) ).

tcf(c_39862,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39861,c_4059]) ).

tcf(c_39868,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39678,c_39675]) ).

tcf(c_39869,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39868,c_4059]) ).

tcf(c_39875,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_39677,c_39675]) ).

tcf(c_39876,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_39875,c_4059]) ).

tcf(c_39918,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk3,cons(hd(X0),nil)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_39175]) ).

tcf(c_39919,plain,
    hd(app(sk4,app(sk3,cons(hd(sk4),nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_39175]) ).

tcf(c_39920,plain,
    hd(app(sk4,app(sk3,cons(hd(sk3),nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10117,c_39175]) ).

tcf(c_39930,plain,
    ( ( sk3 = nil )
    | ( hd(app(sk4,app(sk4,tl(sk3)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_246,c_15965]) ).

tcf(c_39931,plain,
    ( ( sk4 = nil )
    | ( hd(app(sk4,app(sk4,tl(sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_15965]) ).

tcf(c_39933,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk4,app(sk4,tl(tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15965]) ).

tcf(c_39934,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk4,app(sk4,tl(app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15965]) ).

tcf(c_39935,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk4,app(sk4,tl(cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15965]) ).

tcf(c_39936,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk3),sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_15965]) ).

tcf(c_39937,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk4),sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_15965]) ).

tcf(c_39938,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk3),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_15965]) ).

tcf(c_39939,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_15965]) ).

tcf(c_39940,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15965]) ).

tcf(c_39941,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15965]) ).

tcf(c_39942,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15965]) ).

tcf(c_39943,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_15965]) ).

tcf(c_39944,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_15965]) ).

tcf(c_39945,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15965]) ).

tcf(c_39946,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15965]) ).

tcf(c_39947,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15965]) ).

tcf(c_39948,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_15965]) ).

tcf(c_39949,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15965]) ).

tcf(c_39950,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15965]) ).

tcf(c_39951,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15965]) ).

tcf(c_39952,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15965]) ).

tcf(c_39953,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15965]) ).

tcf(c_39954,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_15965]) ).

tcf(c_39955,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_15965]) ).

tcf(c_39956,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15965]) ).

tcf(c_39957,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15965]) ).

tcf(c_39958,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15965]) ).

tcf(c_39959,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_15965]) ).

tcf(c_39960,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_15965]) ).

tcf(c_39961,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_15965]) ).

tcf(c_39962,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_15965]) ).

tcf(c_39963,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15965]) ).

tcf(c_39964,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15965]) ).

tcf(c_39965,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15965]) ).

tcf(c_39966,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15965]) ).

tcf(c_39967,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15965]) ).

tcf(c_39968,plain,
    hd(app(sk4,app(sk4,tl(sk4)))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_39931,c_1243]) ).

tcf(c_39979,plain,
    hd(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_39962,c_20706]) ).

tcf(c_39980,plain,
    hd(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_39961,c_17701]) ).

tcf(c_39981,plain,
    hd(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_39960,c_19513]) ).

tcf(c_39982,plain,
    hd(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_39959,c_16926]) ).

tcf(c_39983,plain,
    hd(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_39955,c_10611]) ).

tcf(c_39984,plain,
    hd(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_39954,c_10190]) ).

tcf(c_39985,plain,
    hd(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_39948,c_7545]) ).

tcf(c_39986,plain,
    hd(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_39944,c_5891]) ).

tcf(c_40126,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(sk4)))))
      | ( app(sk4,app(sk4,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(sk4))))
      | ~ ssList(app(sk4,app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_39968,c_280]) ).

tcf(c_40127,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(sk4)))))
      | ( app(sk4,app(sk4,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(sk4))))
      | ~ ssList(app(sk4,app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_39968,c_279]) ).

tcf(c_40142,plain,
    hd(app(sk4,app(sk4,tl(sk3)))) = hd(sk4),
    inference(global_subsumption_just,[status(thm)],[c_39930,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_39930]) ).

tcf(c_40145,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(sk3)))))
      | ( app(sk4,app(sk4,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(sk3))))
      | ~ ssList(app(sk4,app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_40142,c_280]) ).

tcf(c_40146,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(sk3)))))
      | ( app(sk4,app(sk4,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(sk3))))
      | ~ ssList(app(sk4,app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_40142,c_279]) ).

tcf(c_40185,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),nil)))))
      | ( app(sk4,app(sk3,cons(hd(sk4),nil))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),nil))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_39919,c_280]) ).

tcf(c_40186,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk4),nil)))))
      | ( app(sk4,app(sk3,cons(hd(sk4),nil))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk4),nil))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_39919,c_279]) ).

tcf(c_40202,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),nil)))))
      | ( app(sk4,app(sk3,cons(hd(sk3),nil))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),nil))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_39920,c_280]) ).

tcf(c_40203,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),nil)))))
      | ( app(sk4,app(sk3,cons(hd(sk3),nil))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk3),nil))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_39920,c_279]) ).

tcf(c_40223,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,cons(hd(sk4),sk3)))))
      | ( cons(hd(sk3),app(sk3,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),sk3))))
      | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35268,c_280]) ).

tcf(c_40224,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,cons(hd(sk4),sk3)))))
      | ( cons(hd(sk3),app(sk3,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),sk3))))
      | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35268,c_279]) ).

tcf(c_40251,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,cons(hd(sk3),sk4)))))
      | ( cons(hd(sk4),app(sk3,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,cons(hd(sk3),sk4))))
      | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35281,c_280]) ).

tcf(c_40252,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,cons(hd(sk3),sk4)))))
      | ( cons(hd(sk4),app(sk3,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,cons(hd(sk3),sk4))))
      | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35281,c_279]) ).

tcf(c_40282,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(cons(hd(sk3),app(sk4,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_31841]) ).

tcf(c_40283,plain,
    hd(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_31841]) ).

tcf(c_40284,plain,
    hd(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_31841]) ).

tcf(c_40330,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(cons(hd(sk3),app(sk4,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_31844]) ).

tcf(c_40331,plain,
    hd(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_31844]) ).

tcf(c_40332,plain,
    hd(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_31844]) ).

tcf(c_40340,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(cons(hd(sk4),app(sk4,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_31847]) ).

tcf(c_40341,plain,
    hd(cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_31847]) ).

tcf(c_40342,plain,
    hd(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_31847]) ).

tcf(c_40350,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(cons(hd(sk4),app(sk3,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_31850]) ).

tcf(c_40351,plain,
    hd(cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_31850]) ).

tcf(c_40352,plain,
    hd(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_31850]) ).

tcf(c_40360,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(cons(hd(sk4),app(sk4,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_31853]) ).

tcf(c_40361,plain,
    hd(cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_31853]) ).

tcf(c_40362,plain,
    hd(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_31853]) ).

tcf(c_40371,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),tl(cons(hd(sk4),app(sk3,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_31856]) ).

tcf(c_40372,plain,
    hd(cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_31856]) ).

tcf(c_40373,plain,
    hd(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_31856]) ).

tcf(c_40400,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_32313,c_280]) ).

tcf(c_40401,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_32313,c_279]) ).

tcf(c_40417,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_32314,c_280]) ).

tcf(c_40418,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_32314,c_279]) ).

tcf(c_40456,plain,
    tl(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4)) = sk4,
    inference(global_subsumption_just,[status(thm)],[c_7601,c_7545,c_7601]) ).

tcf(c_40465,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(sk3,X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_15966]) ).

tcf(c_40466,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(sk4,X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_15966]) ).

tcf(c_40467,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(nil,X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_15966]) ).

tcf(c_40468,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk4,app(tl(X0),X1)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15966]) ).

tcf(c_40469,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(X1,X0),X2)))) = hd(sk4) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15966]) ).

tcf(c_40470,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(X2,X0),X1)))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15966]) ).

tcf(c_40471,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk3),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_15966]) ).

tcf(c_40472,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk4),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_15966]) ).

tcf(c_40473,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk3),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_15966]) ).

tcf(c_40474,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk4),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_15966]) ).

tcf(c_40475,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk4,app(sk4,app(app(tl(sk3),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15966]) ).

tcf(c_40476,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk4,app(sk4,app(app(tl(sk3),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15966]) ).

tcf(c_40477,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk4,app(sk4,app(app(tl(sk4),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15966]) ).

tcf(c_40478,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk4,app(sk4,app(app(tl(sk4),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_15966]) ).

tcf(c_40479,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk4),app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_15966]) ).

tcf(c_40480,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15966]) ).

tcf(c_40481,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15966]) ).

tcf(c_40482,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15966]) ).

tcf(c_40483,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk4),app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_15966]) ).

tcf(c_40484,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15966]) ).

tcf(c_40485,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15966]) ).

tcf(c_40486,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15966]) ).

tcf(c_40487,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15966]) ).

tcf(c_40488,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15966]) ).

tcf(c_40489,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk4),app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_15966]) ).

tcf(c_40490,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk4),app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_15966]) ).

tcf(c_40491,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15966]) ).

tcf(c_40492,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15966]) ).

tcf(c_40493,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15966]) ).

tcf(c_40494,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk3),app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_15966]) ).

tcf(c_40495,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk3),app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_15966]) ).

tcf(c_40496,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk3),app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_15966]) ).

tcf(c_40497,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk3),app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_15966]) ).

tcf(c_40498,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15966]) ).

tcf(c_40499,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15966]) ).

tcf(c_40500,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15966]) ).

tcf(c_40501,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15966]) ).

tcf(c_40502,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15966]) ).

tcf(c_40727,plain,
    hd(app(sk4,app(sk4,app(sk3,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_40465]) ).

tcf(c_40728,plain,
    hd(app(sk4,app(sk4,app(sk3,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_40465]) ).

tcf(c_40729,plain,
    hd(app(sk4,app(sk4,app(sk3,nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_40465]) ).

tcf(c_40730,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk4,app(sk3,tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_40465]) ).

tcf(c_40731,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk4,app(sk3,app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_40465]) ).

tcf(c_40732,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk4,app(sk3,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_40465]) ).

tcf(c_40733,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_40465]) ).

tcf(c_40734,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_40465]) ).

tcf(c_40735,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_40465]) ).

tcf(c_40736,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_40465]) ).

tcf(c_40737,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(sk4,app(sk3,app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_40465]) ).

tcf(c_40738,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(sk4,app(sk3,app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_40465]) ).

tcf(c_40739,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(sk4,app(sk3,app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_40465]) ).

tcf(c_40740,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(sk4,app(sk3,app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_40465]) ).

tcf(c_40741,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_40465]) ).

tcf(c_40742,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_40465]) ).

tcf(c_40743,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_40465]) ).

tcf(c_40744,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_40465]) ).

tcf(c_40745,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_40465]) ).

tcf(c_40746,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_40465]) ).

tcf(c_40747,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_40465]) ).

tcf(c_40748,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_40465]) ).

tcf(c_40749,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_40465]) ).

tcf(c_40750,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_40465]) ).

tcf(c_40751,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_40465]) ).

tcf(c_40752,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_40465]) ).

tcf(c_40753,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_40465]) ).

tcf(c_40754,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_40465]) ).

tcf(c_40755,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_40465]) ).

tcf(c_40756,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_40465]) ).

tcf(c_40757,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_40465]) ).

tcf(c_40758,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_40465]) ).

tcf(c_40759,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_40465]) ).

tcf(c_40760,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_40465]) ).

tcf(c_40761,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_40465]) ).

tcf(c_40762,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_40465]) ).

tcf(c_40763,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_40465]) ).

tcf(c_40764,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_40465]) ).

tcf(c_40989,plain,
    ( totalorderedP(tl(sk4))
    | ( tl(sk4) = nil )
    | ~ totalorderedP(sk4) ),
    inference(global_subsumption_just,[status(thm)],[c_27808,c_247,c_1242,c_3427,c_3439,c_3859]) ).

tcf(c_40997,plain,
    ( strictorderedP(tl(sk4))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4) ),
    inference(global_subsumption_just,[status(thm)],[c_27809,c_247,c_1242,c_3427,c_3439,c_3622]) ).

tcf(c_41076,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,sk3)))))
      | ( app(sk4,app(sk4,app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,sk3))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_40727,c_280]) ).

tcf(c_41077,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,sk3)))))
      | ( app(sk4,app(sk4,app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,sk3))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_40727,c_279]) ).

tcf(c_41093,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,sk4)))))
      | ( app(sk4,app(sk4,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,sk4))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_40728,c_280]) ).

tcf(c_41094,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,sk4)))))
      | ( app(sk4,app(sk4,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,sk4))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_40728,c_279]) ).

tcf(c_41110,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,cons(hd(sk3),sk4)))))
      | ( cons(hd(sk3),app(sk3,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),sk4))))
      | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35282,c_280]) ).

tcf(c_41111,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,cons(hd(sk3),sk4)))))
      | ( cons(hd(sk3),app(sk3,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),sk4))))
      | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35282,c_279]) ).

tcf(c_41127,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,cons(hd(sk4),sk4)))))
      | ( cons(hd(sk4),app(sk3,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,cons(hd(sk4),sk4))))
      | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35346,c_280]) ).

tcf(c_41128,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,cons(hd(sk4),sk4)))))
      | ( cons(hd(sk4),app(sk3,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,cons(hd(sk4),sk4))))
      | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35346,c_279]) ).

tcf(c_41144,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,cons(hd(sk4),sk4)))))
      | ( cons(hd(sk3),app(sk3,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),sk4))))
      | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35347,c_280]) ).

tcf(c_41145,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,cons(hd(sk4),sk4)))))
      | ( cons(hd(sk3),app(sk3,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),sk4))))
      | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35347,c_279]) ).

tcf(c_41161,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,cons(hd(sk3),sk3)))))
      | ( cons(hd(sk4),app(sk4,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),sk3))))
      | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35356,c_280]) ).

tcf(c_41162,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,cons(hd(sk3),sk3)))))
      | ( cons(hd(sk4),app(sk4,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),sk3))))
      | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35356,c_279]) ).

tcf(c_41208,plain,
    hd(app(sk4,app(sk4,app(sk4,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_40466]) ).

tcf(c_41209,plain,
    hd(app(sk4,app(sk4,app(sk4,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_40466]) ).

tcf(c_41210,plain,
    hd(app(sk4,app(sk4,app(sk4,nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_40466]) ).

tcf(c_41211,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk4,app(sk4,tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_40466]) ).

tcf(c_41212,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk4,app(sk4,app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_40466]) ).

tcf(c_41213,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk4,app(sk4,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_40466]) ).

tcf(c_41214,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_40466]) ).

tcf(c_41215,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_40466]) ).

tcf(c_41216,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_40466]) ).

tcf(c_41217,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_40466]) ).

tcf(c_41218,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(sk4,app(sk4,app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_40466]) ).

tcf(c_41219,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(sk4,app(sk4,app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_40466]) ).

tcf(c_41220,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(sk4,app(sk4,app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_40466]) ).

tcf(c_41221,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(sk4,app(sk4,app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_40466]) ).

tcf(c_41222,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_40466]) ).

tcf(c_41223,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_40466]) ).

tcf(c_41224,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_40466]) ).

tcf(c_41225,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_40466]) ).

tcf(c_41226,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_40466]) ).

tcf(c_41227,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_40466]) ).

tcf(c_41228,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_40466]) ).

tcf(c_41229,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_40466]) ).

tcf(c_41230,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_40466]) ).

tcf(c_41231,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_40466]) ).

tcf(c_41232,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_40466]) ).

tcf(c_41233,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_40466]) ).

tcf(c_41234,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_40466]) ).

tcf(c_41235,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_40466]) ).

tcf(c_41236,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_40466]) ).

tcf(c_41237,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_40466]) ).

tcf(c_41238,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_40466]) ).

tcf(c_41239,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_40466]) ).

tcf(c_41240,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_40466]) ).

tcf(c_41241,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_40466]) ).

tcf(c_41242,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_40466]) ).

tcf(c_41243,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_40466]) ).

tcf(c_41244,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_40466]) ).

tcf(c_41245,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_40466]) ).

tcf(c_41580,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,sk3)))))
      | ( app(sk4,app(sk4,app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,sk3))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_41208,c_280]) ).

tcf(c_41581,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,sk3)))))
      | ( app(sk4,app(sk4,app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,sk3))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_41208,c_279]) ).

tcf(c_41597,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,sk4)))))
      | ( app(sk4,app(sk4,app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,sk4))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_41209,c_280]) ).

tcf(c_41598,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,sk4)))))
      | ( app(sk4,app(sk4,app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,sk4))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_41209,c_279]) ).

tcf(c_41614,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3))))))
      | ( app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_40733,c_280]) ).

tcf(c_41615,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3))))))
      | ( app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_40733,c_279]) ).

tcf(c_41631,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))))
      | ( app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_40734,c_280]) ).

tcf(c_41632,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))))
      | ( app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_40734,c_279]) ).

tcf(c_41648,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4))))))
      | ( app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_40735,c_280]) ).

tcf(c_41649,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4))))))
      | ( app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_40735,c_279]) ).

tcf(c_41665,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))))
      | ( app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_40736,c_280]) ).

tcf(c_41666,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))))
      | ( app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_40736,c_279]) ).

tcf(c_41682,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3))))))
      | ( app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_41214,c_280]) ).

tcf(c_41683,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3))))))
      | ( app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_41214,c_279]) ).

tcf(c_41698,plain,
    tl(cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3)) = sk3,
    inference(global_subsumption_just,[status(thm)],[c_7602,c_7545,c_7602]) ).

tcf(c_41705,plain,
    hd(app(sk4,app(sk4,app(nil,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_40467]) ).

tcf(c_41706,plain,
    hd(app(sk4,app(sk4,app(nil,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_40467]) ).

tcf(c_41707,plain,
    hd(app(sk4,app(sk4,app(nil,nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_40467]) ).

tcf(c_41708,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk4,app(nil,tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_40467]) ).

tcf(c_41709,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk4,app(nil,app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_40467]) ).

tcf(c_41710,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(sk4,app(nil,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_40467]) ).

tcf(c_41711,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk3),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_40467]) ).

tcf(c_41712,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_40467]) ).

tcf(c_41713,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk3),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_40467]) ).

tcf(c_41714,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_40467]) ).

tcf(c_41715,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(sk4,app(nil,app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_40467]) ).

tcf(c_41716,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(sk4,app(nil,app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_40467]) ).

tcf(c_41717,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(sk4,app(nil,app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_40467]) ).

tcf(c_41718,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(sk4,app(nil,app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_40467]) ).

tcf(c_41719,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_40467]) ).

tcf(c_41720,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_40467]) ).

tcf(c_41721,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_40467]) ).

tcf(c_41722,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_40467]) ).

tcf(c_41723,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_40467]) ).

tcf(c_41724,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_40467]) ).

tcf(c_41725,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_40467]) ).

tcf(c_41726,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_40467]) ).

tcf(c_41727,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_40467]) ).

tcf(c_41728,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_40467]) ).

tcf(c_41729,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_40467]) ).

tcf(c_41730,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_40467]) ).

tcf(c_41731,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_40467]) ).

tcf(c_41732,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_40467]) ).

tcf(c_41733,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_40467]) ).

tcf(c_41734,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_40467]) ).

tcf(c_41735,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_40467]) ).

tcf(c_41736,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_40467]) ).

tcf(c_41737,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_40467]) ).

tcf(c_41738,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_40467]) ).

tcf(c_41739,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_40467]) ).

tcf(c_41740,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_40467]) ).

tcf(c_41741,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_40467]) ).

tcf(c_41742,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_40467]) ).

tcf(c_41957,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,sk3)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_15967]) ).

tcf(c_41958,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,sk4)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_15967]) ).

tcf(c_41959,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,nil)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_15967]) ).

tcf(c_41960,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk4,cons(X1,tl(X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15967]) ).

tcf(c_41961,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X2,app(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15967]) ).

tcf(c_41962,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X2,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15967]) ).

tcf(c_41963,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk3),sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_15967]) ).

tcf(c_41964,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk4),sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_15967]) ).

tcf(c_41965,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk3),sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_15967]) ).

tcf(c_41966,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk4),sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_15967]) ).

tcf(c_41967,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk4,app(sk4,cons(X0,app(tl(sk3),sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15967]) ).

tcf(c_41968,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk4,app(sk4,cons(X0,app(tl(sk3),sk4))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15967]) ).

tcf(c_41969,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk4,app(sk4,cons(X0,app(tl(sk4),sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15967]) ).

tcf(c_41970,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk4,app(sk4,cons(X0,app(tl(sk4),sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_15967]) ).

tcf(c_41971,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_15967]) ).

tcf(c_41972,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15967]) ).

tcf(c_41973,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15967]) ).

tcf(c_41974,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15967]) ).

tcf(c_41975,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_15967]) ).

tcf(c_41976,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15967]) ).

tcf(c_41977,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15967]) ).

tcf(c_41978,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15967]) ).

tcf(c_41979,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15967]) ).

tcf(c_41980,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15967]) ).

tcf(c_41981,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_15967]) ).

tcf(c_41982,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_15967]) ).

tcf(c_41983,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15967]) ).

tcf(c_41984,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15967]) ).

tcf(c_41985,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15967]) ).

tcf(c_41986,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_15967]) ).

tcf(c_41987,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_15967]) ).

tcf(c_41988,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_15967]) ).

tcf(c_41989,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_15967]) ).

tcf(c_41990,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15967]) ).

tcf(c_41991,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15967]) ).

tcf(c_41992,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15967]) ).

tcf(c_41993,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15967]) ).

tcf(c_41994,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15967]) ).

tcf(c_42153,plain,
    ( ssList(app(sk3,sk4))
    | ~ ssList(sk4)
    | ~ ssList(sk3) ),
    inference(instantiation,[status(thm)],[c_6088]) ).

tcf(c_42211,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk4,cons(hd(X0),sk3)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_41957]) ).

tcf(c_42221,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk4,cons(hd(X0),sk4)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_41958]) ).

tcf(c_42228,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,cons(hd(sk3),sk3)))))
      | ( cons(hd(sk3),app(sk4,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,cons(hd(sk3),sk3))))
      | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35357,c_280]) ).

tcf(c_42229,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,cons(hd(sk3),sk3)))))
      | ( cons(hd(sk3),app(sk4,cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,cons(hd(sk3),sk3))))
      | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35357,c_279]) ).

tcf(c_42310,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,cons(hd(sk4),sk3)))))
      | ( cons(hd(sk4),app(sk4,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),sk3))))
      | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35388,c_280]) ).

tcf(c_42311,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,cons(hd(sk4),sk3)))))
      | ( cons(hd(sk4),app(sk4,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),sk3))))
      | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35388,c_279]) ).

tcf(c_42327,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,cons(hd(sk4),sk3)))))
      | ( cons(hd(sk3),app(sk4,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,cons(hd(sk4),sk3))))
      | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35389,c_280]) ).

tcf(c_42328,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,cons(hd(sk4),sk3)))))
      | ( cons(hd(sk3),app(sk4,cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,cons(hd(sk4),sk3))))
      | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35389,c_279]) ).

tcf(c_42344,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,cons(hd(sk3),sk4)))))
      | ( cons(hd(sk4),app(sk4,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),sk4))))
      | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35431,c_280]) ).

tcf(c_42345,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,cons(hd(sk3),sk4)))))
      | ( cons(hd(sk4),app(sk4,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),sk4))))
      | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35431,c_279]) ).

tcf(c_42361,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))))
      | ( app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_41215,c_280]) ).

tcf(c_42362,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))))
      | ( app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_41215,c_279]) ).

tcf(c_42378,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4))))))
      | ( app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_41216,c_280]) ).

tcf(c_42379,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4))))))
      | ( app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_41216,c_279]) ).

tcf(c_42425,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))))
      | ( app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_41217,c_280]) ).

tcf(c_42426,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))))
      | ( app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_41217,c_279]) ).

tcf(c_42442,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_32316,c_280]) ).

tcf(c_42443,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_32316,c_279]) ).

tcf(c_42463,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_32561,c_280]) ).

tcf(c_42464,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_32561,c_279]) ).

tcf(c_42496,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_32562,c_280]) ).

tcf(c_42497,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_32562,c_279]) ).

tcf(c_42513,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_32564,c_280]) ).

tcf(c_42514,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_32564,c_279]) ).

tcf(c_42530,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_32970,c_280]) ).

tcf(c_42531,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_32970,c_279]) ).

tcf(c_42548,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_8164,c_255]) ).

tcf(c_42549,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_8164,c_254]) ).

tcf(c_42550,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_8164,c_272]) ).

tcf(c_42551,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != app(app(sk3,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_8164,c_270]) ).

tcf(c_42552,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != app(X0,cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_8164,c_269]) ).

tcf(c_42553,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(app(sk3,sk4),cons(hd(sk4),sk3)),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_8164,c_300]) ).

tcf(c_42554,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(app(sk3,sk4),cons(hd(sk4),sk3)),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_8164,c_287]) ).

tcf(c_42555,plain,
    ( ( cons(hd(sk4),sk3) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_8164,c_8552]) ).

tcf(c_42556,plain,
    ( ( cons(hd(sk4),sk3) = sk3 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_8164,c_8271]) ).

tcf(c_42557,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_42550,c_4358]) ).

tcf(c_42564,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_42549,c_4430,c_4358]) ).

tcf(c_42567,plain,
    ( ( cons(hd(sk4),sk3) = sk3 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_42556,c_4358]) ).

tcf(c_42571,plain,
    ( ( cons(hd(sk4),sk3) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_42555,c_4358]) ).

tcf(c_42575,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != app(X0,cons(hd(sk4),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_42552,c_4358]) ).

tcf(c_42580,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) != app(app(sk3,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_42551,c_4358]) ).

tcf(c_42585,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_42554,c_8164]) ).

tcf(c_42586,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_42585,c_246,c_4059]) ).

tcf(c_42593,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_42553,c_8164]) ).

tcf(c_42594,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_42593,c_246,c_4059]) ).

tcf(c_42609,plain,
    ssList(app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(global_subsumption_just,[status(thm)],[c_42557,c_247,c_246,c_42153,c_42557]) ).

tcf(c_42611,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_15966]) ).

tcf(c_42612,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_15593]) ).

tcf(c_42613,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),nil),X0) = app(app(sk3,app(sk4,cons(hd(sk4),sk3))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_4541]) ).

tcf(c_42614,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3154]) ).

tcf(c_42615,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_4037]) ).

tcf(c_42616,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3952]) ).

tcf(c_42617,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)) = app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3050]) ).

tcf(c_42618,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0),nil) = app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3049]) ).

tcf(c_42619,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4),X0) = app(app(sk3,app(sk4,cons(hd(sk4),sk3))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_4540]) ).

tcf(c_42620,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk3),X0) = app(app(sk3,app(sk4,cons(hd(sk4),sk3))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_4539]) ).

tcf(c_42621,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk4,cons(hd(sk4),sk3)))),X0) = app(X1,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_271]) ).

tcf(c_42622,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(cons(X1,X0),app(sk3,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_266]) ).

tcf(c_42623,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))),X0) = tl(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_274]) ).

tcf(c_42624,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_283]) ).

tcf(c_42625,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_15967]) ).

tcf(c_42626,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_40467]) ).

tcf(c_42627,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_40466]) ).

tcf(c_42628,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_40465]) ).

tcf(c_42629,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_15965]) ).

tcf(c_42630,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_15594]) ).

tcf(c_42631,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_37606]) ).

tcf(c_42632,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_37605]) ).

tcf(c_42633,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_37604]) ).

tcf(c_42634,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_15592]) ).

tcf(c_42635,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_18000]) ).

tcf(c_42636,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_17998]) ).

tcf(c_42637,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_17997]) ).

tcf(c_42638,plain,
    app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_42609,c_35790]) ).

tcf(c_42639,plain,
    app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_42609,c_35787]) ).

tcf(c_42640,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),nil)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_4463]) ).

tcf(c_42641,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3155]) ).

tcf(c_42642,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_33403]) ).

tcf(c_42643,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_33402]) ).

tcf(c_42644,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_33401]) ).

tcf(c_42645,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),tl(sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_32111]) ).

tcf(c_42646,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),tl(sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_32098]) ).

tcf(c_42647,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_15410]) ).

tcf(c_42648,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_15408]) ).

tcf(c_42649,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_15407]) ).

tcf(c_42650,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3153]) ).

tcf(c_42651,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_4038]) ).

tcf(c_42652,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_17993]) ).

tcf(c_42653,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_17992]) ).

tcf(c_42654,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_17991]) ).

tcf(c_42655,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_4036]) ).

tcf(c_42656,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3953]) ).

tcf(c_42657,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_15403]) ).

tcf(c_42658,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_15402]) ).

tcf(c_42659,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_15401]) ).

tcf(c_42660,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3951]) ).

tcf(c_42661,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil)) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3423]) ).

tcf(c_42662,plain,
    app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_42609,c_13452]) ).

tcf(c_42663,plain,
    app(app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil) = app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_42609,c_12354]) ).

tcf(c_42664,plain,
    app(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_42609,c_12353]) ).

tcf(c_42665,plain,
    app(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_42609,c_12352]) ).

tcf(c_42666,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_42609,c_3199]) ).

tcf(c_42667,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3066]) ).

tcf(c_42668,plain,
    app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_42609,c_8061]) ).

tcf(c_42669,plain,
    app(app(sk4,sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_42609,c_8048]) ).

tcf(c_42670,plain,
    app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_42609,c_5745]) ).

tcf(c_42671,plain,
    app(app(sk3,sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_42609,c_8047]) ).

tcf(c_42672,plain,
    app(app(sk4,sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_42609,c_5738]) ).

tcf(c_42673,plain,
    app(app(sk3,sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_42609,c_5737]) ).

tcf(c_42674,plain,
    app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = tl(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_42609,c_4136]) ).

tcf(c_42675,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_4462]) ).

tcf(c_42676,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk3)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_4461]) ).

tcf(c_42677,plain,
    app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = tl(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_42609,c_4284]) ).

tcf(c_42678,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_4027]) ).

tcf(c_42680,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3019]) ).

tcf(c_42681,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3452]) ).

tcf(c_42682,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3444]) ).

tcf(c_42683,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil) = tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3065]) ).

tcf(c_42684,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4)) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3215]) ).

tcf(c_42685,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3)) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3207]) ).

tcf(c_42686,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_253]) ).

tcf(c_42687,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(sk3,app(sk4,cons(hd(sk4),sk3))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_275]) ).

tcf(c_42688,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3018]) ).

tcf(c_42689,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_42609,c_3191]) ).

tcf(c_42690,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_42609,c_3183]) ).

tcf(c_42691,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_284]) ).

tcf(c_42692,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(sk3,app(sk4,cons(hd(sk4),sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_276]) ).

tcf(c_42693,plain,
    app(app(sk3,app(sk4,cons(hd(sk4),sk3))),nil) = app(sk3,app(sk4,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_42609,c_258]) ).

tcf(c_42694,plain,
    app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3)))) = app(sk3,app(sk4,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_42609,c_257]) ).

tcf(c_42778,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_42624,c_18500]) ).

tcf(c_42787,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(sk3,app(sk4,cons(hd(sk4),sk3))) ) ),
    inference(light_normalisation,[status(thm)],[c_42687,c_18500]) ).

tcf(c_43032,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(sk4,cons(hd(X0),nil)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_41959]) ).

tcf(c_43033,plain,
    hd(app(sk4,app(sk4,cons(hd(sk4),nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_41959]) ).

tcf(c_43034,plain,
    hd(app(sk4,app(sk4,cons(hd(sk3),nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10117,c_41959]) ).

tcf(c_43038,plain,
    app(sk3,app(sk4,cons(hd(sk4),sk3))) != nil,
    inference(global_subsumption_just,[status(thm)],[c_42564,c_247,c_246,c_42153,c_42564]) ).

tcf(c_43044,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,app(sk4,cons(hd(sk4),sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_42691]) ).

tcf(c_43045,plain,
    hd(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_42691]) ).

tcf(c_43046,plain,
    hd(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_42691]) ).

tcf(c_43051,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),nil)))))
      | ( app(sk4,app(sk4,cons(hd(sk4),nil))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),nil))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_43033,c_280]) ).

tcf(c_43052,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk4),nil)))))
      | ( app(sk4,app(sk4,cons(hd(sk4),nil))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk4),nil))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_43033,c_279]) ).

tcf(c_43068,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),nil)))))
      | ( app(sk4,app(sk4,cons(hd(sk3),nil))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),nil))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_43034,c_280]) ).

tcf(c_43069,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),nil)))))
      | ( app(sk4,app(sk4,cons(hd(sk3),nil))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk3),nil))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_43034,c_279]) ).

tcf(c_43085,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,cons(hd(sk3),sk4)))))
      | ( cons(hd(sk3),app(sk4,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,cons(hd(sk3),sk4))))
      | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35432,c_280]) ).

tcf(c_43086,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,cons(hd(sk3),sk4)))))
      | ( cons(hd(sk3),app(sk4,cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,cons(hd(sk3),sk4))))
      | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35432,c_279]) ).

tcf(c_43102,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,cons(hd(sk4),sk4)))))
      | ( cons(hd(sk4),app(sk4,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),sk4))))
      | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35441,c_280]) ).

tcf(c_43103,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,cons(hd(sk4),sk4)))))
      | ( cons(hd(sk4),app(sk4,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),sk4))))
      | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35441,c_279]) ).

tcf(c_43118,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_42586,c_247,c_246,c_42153,c_42586]) ).

tcf(c_43119,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(renaming,[status(thm)],[c_43118]) ).

tcf(c_43131,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk3))))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_43119]) ).

tcf(c_43132,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk3))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_43119]) ).

tcf(c_43133,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_43119]) ).

tcf(c_43134,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_43119]) ).

tcf(c_43135,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43131,c_42609]) ).

tcf(c_43141,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_43133,c_3365]) ).

tcf(c_43142,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43141,c_4059]) ).

tcf(c_43147,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk3))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43132,c_10117]) ).

tcf(c_43153,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_43134,c_39675]) ).

tcf(c_43154,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43153,c_4059]) ).

tcf(c_43160,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_42594,c_247,c_246,c_42153,c_42594]) ).

tcf(c_43161,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(renaming,[status(thm)],[c_43160]) ).

tcf(c_43173,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk3))))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_43161]) ).

tcf(c_43174,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk3))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_43161]) ).

tcf(c_43175,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_43161]) ).

tcf(c_43176,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_43161]) ).

tcf(c_43177,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43173,c_42609]) ).

tcf(c_43183,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_43175,c_3365]) ).

tcf(c_43184,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43183,c_4059]) ).

tcf(c_43189,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),sk3))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43174,c_10117]) ).

tcf(c_43195,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_43176,c_39675]) ).

tcf(c_43196,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43195,c_4059]) ).

tcf(c_43234,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_42678,c_280]) ).

tcf(c_43235,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_42678,c_279]) ).

tcf(c_43251,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_32971,c_280]) ).

tcf(c_43252,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_32971,c_279]) ).

tcf(c_43268,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_32973,c_280]) ).

tcf(c_43269,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_32973,c_279]) ).

tcf(c_43312,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_36640,c_280]) ).

tcf(c_43313,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_36640,c_279]) ).

tcf(c_43329,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_36641,c_280]) ).

tcf(c_43330,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_36641,c_279]) ).

tcf(c_43350,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_36643,c_280]) ).

tcf(c_43351,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_36643,c_279]) ).

tcf(c_43368,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_8165,c_255]) ).

tcf(c_43369,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_8165,c_254]) ).

tcf(c_43370,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_8165,c_272]) ).

tcf(c_43371,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != app(app(sk3,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_8165,c_270]) ).

tcf(c_43372,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != app(X0,cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_8165,c_269]) ).

tcf(c_43373,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(app(sk3,sk4),cons(hd(sk4),sk4)),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_8165,c_300]) ).

tcf(c_43374,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(app(sk3,sk4),cons(hd(sk4),sk4)),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_8165,c_287]) ).

tcf(c_43375,plain,
    ( ( cons(hd(sk4),sk4) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_8165,c_8552]) ).

tcf(c_43376,plain,
    ( ( cons(hd(sk4),sk4) = sk3 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_8165,c_8271]) ).

tcf(c_43377,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43370,c_4223]) ).

tcf(c_43384,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43369,c_4281,c_4223]) ).

tcf(c_43387,plain,
    ( ( cons(hd(sk4),sk4) = sk3 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43376,c_4223]) ).

tcf(c_43391,plain,
    ( ( cons(hd(sk4),sk4) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43375,c_4223]) ).

tcf(c_43395,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != app(X0,cons(hd(sk4),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43372,c_4223]) ).

tcf(c_43400,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) != app(app(sk3,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43371,c_4223]) ).

tcf(c_43405,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_43374,c_8165]) ).

tcf(c_43406,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43405,c_247,c_4059]) ).

tcf(c_43413,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_43373,c_8165]) ).

tcf(c_43414,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_43413,c_247,c_4059]) ).

tcf(c_43441,plain,
    ssList(app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(global_subsumption_just,[status(thm)],[c_43377,c_247,c_246,c_42153,c_43377]) ).

tcf(c_43443,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_15966]) ).

tcf(c_43444,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_15593]) ).

tcf(c_43445,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),nil),X0) = app(app(sk3,app(sk4,cons(hd(sk4),sk4))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_4541]) ).

tcf(c_43446,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3154]) ).

tcf(c_43447,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_4037]) ).

tcf(c_43448,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3952]) ).

tcf(c_43449,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)) = app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3050]) ).

tcf(c_43450,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0),nil) = app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3049]) ).

tcf(c_43451,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4),X0) = app(app(sk3,app(sk4,cons(hd(sk4),sk4))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_4540]) ).

tcf(c_43452,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk3),X0) = app(app(sk3,app(sk4,cons(hd(sk4),sk4))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_4539]) ).

tcf(c_43453,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk4,cons(hd(sk4),sk4)))),X0) = app(X1,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_271]) ).

tcf(c_43454,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(cons(X1,X0),app(sk3,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_266]) ).

tcf(c_43455,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))),X0) = tl(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_274]) ).

tcf(c_43456,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_283]) ).

tcf(c_43457,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_15967]) ).

tcf(c_43458,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_40467]) ).

tcf(c_43459,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_40466]) ).

tcf(c_43460,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_40465]) ).

tcf(c_43461,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_15965]) ).

tcf(c_43462,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_15594]) ).

tcf(c_43463,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_37606]) ).

tcf(c_43464,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_37605]) ).

tcf(c_43465,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_37604]) ).

tcf(c_43466,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_15592]) ).

tcf(c_43467,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_18000]) ).

tcf(c_43468,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_17998]) ).

tcf(c_43469,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_17997]) ).

tcf(c_43470,plain,
    app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_43441,c_35790]) ).

tcf(c_43471,plain,
    app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_43441,c_35787]) ).

tcf(c_43472,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),nil)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_4463]) ).

tcf(c_43473,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3155]) ).

tcf(c_43474,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_33403]) ).

tcf(c_43475,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_33402]) ).

tcf(c_43476,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_33401]) ).

tcf(c_43477,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),tl(sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_32111]) ).

tcf(c_43478,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),tl(sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_32098]) ).

tcf(c_43479,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_15410]) ).

tcf(c_43480,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_15408]) ).

tcf(c_43481,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_15407]) ).

tcf(c_43482,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3153]) ).

tcf(c_43483,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_4038]) ).

tcf(c_43484,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_17993]) ).

tcf(c_43485,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_17992]) ).

tcf(c_43486,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_17991]) ).

tcf(c_43487,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_4036]) ).

tcf(c_43488,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3953]) ).

tcf(c_43489,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_15403]) ).

tcf(c_43490,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_15402]) ).

tcf(c_43491,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_15401]) ).

tcf(c_43492,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3951]) ).

tcf(c_43493,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil)) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3423]) ).

tcf(c_43494,plain,
    app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_43441,c_13452]) ).

tcf(c_43495,plain,
    app(app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil) = app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_43441,c_12354]) ).

tcf(c_43496,plain,
    app(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_43441,c_12353]) ).

tcf(c_43497,plain,
    app(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_43441,c_12352]) ).

tcf(c_43498,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_43441,c_3199]) ).

tcf(c_43499,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3066]) ).

tcf(c_43500,plain,
    app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_43441,c_8061]) ).

tcf(c_43501,plain,
    app(app(sk4,sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_43441,c_8048]) ).

tcf(c_43502,plain,
    app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_43441,c_5745]) ).

tcf(c_43503,plain,
    app(app(sk3,sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_43441,c_8047]) ).

tcf(c_43504,plain,
    app(app(sk4,sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_43441,c_5738]) ).

tcf(c_43505,plain,
    app(app(sk3,sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_43441,c_5737]) ).

tcf(c_43506,plain,
    app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = tl(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_43441,c_4136]) ).

tcf(c_43507,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_4462]) ).

tcf(c_43508,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk3)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_4461]) ).

tcf(c_43509,plain,
    app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = tl(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_43441,c_4284]) ).

tcf(c_43510,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_4027]) ).

tcf(c_43512,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3019]) ).

tcf(c_43513,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3452]) ).

tcf(c_43514,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3444]) ).

tcf(c_43515,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil) = tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3065]) ).

tcf(c_43516,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4)) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3215]) ).

tcf(c_43517,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3)) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3207]) ).

tcf(c_43518,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_253]) ).

tcf(c_43519,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(sk3,app(sk4,cons(hd(sk4),sk4))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_275]) ).

tcf(c_43520,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3018]) ).

tcf(c_43521,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_43441,c_3191]) ).

tcf(c_43522,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_43441,c_3183]) ).

tcf(c_43523,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_284]) ).

tcf(c_43524,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(sk3,app(sk4,cons(hd(sk4),sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_276]) ).

tcf(c_43525,plain,
    app(app(sk3,app(sk4,cons(hd(sk4),sk4))),nil) = app(sk3,app(sk4,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_43441,c_258]) ).

tcf(c_43526,plain,
    app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4)))) = app(sk3,app(sk4,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_43441,c_257]) ).

tcf(c_43610,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_43456,c_18502]) ).

tcf(c_43619,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(sk3,app(sk4,cons(hd(sk4),sk4))) ) ),
    inference(light_normalisation,[status(thm)],[c_43519,c_18502]) ).

tcf(c_44126,plain,
    app(sk3,app(sk4,cons(hd(sk4),sk4))) != nil,
    inference(global_subsumption_just,[status(thm)],[c_43384,c_247,c_246,c_42153,c_43384]) ).

tcf(c_44132,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,app(sk4,cons(hd(sk4),sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_43523]) ).

tcf(c_44133,plain,
    hd(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_43523]) ).

tcf(c_44134,plain,
    hd(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_43523]) ).

tcf(c_44144,plain,
    ( ( sk3 = nil )
    | ( hd(app(sk4,app(nil,tl(sk3)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_246,c_16329]) ).

tcf(c_44145,plain,
    ( ( sk4 = nil )
    | ( hd(app(sk4,app(nil,tl(sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_16329]) ).

tcf(c_44147,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk4,app(nil,tl(tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_16329]) ).

tcf(c_44148,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk4,app(nil,tl(app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_16329]) ).

tcf(c_44149,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk4,app(nil,tl(cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_16329]) ).

tcf(c_44150,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk3),sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_16329]) ).

tcf(c_44151,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk4),sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_16329]) ).

tcf(c_44152,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk3),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_16329]) ).

tcf(c_44153,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_16329]) ).

tcf(c_44154,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk4,app(nil,tl(app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_16329]) ).

tcf(c_44155,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk4,app(nil,tl(app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_16329]) ).

tcf(c_44156,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk4,app(nil,tl(app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_16329]) ).

tcf(c_44157,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk4,app(nil,tl(app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_16329]) ).

tcf(c_44158,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_16329]) ).

tcf(c_44159,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_16329]) ).

tcf(c_44160,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_16329]) ).

tcf(c_44161,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_16329]) ).

tcf(c_44162,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_16329]) ).

tcf(c_44163,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_16329]) ).

tcf(c_44164,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_16329]) ).

tcf(c_44165,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_16329]) ).

tcf(c_44166,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_16329]) ).

tcf(c_44167,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_16329]) ).

tcf(c_44168,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_16329]) ).

tcf(c_44169,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_16329]) ).

tcf(c_44170,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_16329]) ).

tcf(c_44171,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_16329]) ).

tcf(c_44172,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_16329]) ).

tcf(c_44173,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_16329]) ).

tcf(c_44174,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_16329]) ).

tcf(c_44175,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_16329]) ).

tcf(c_44176,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_16329]) ).

tcf(c_44177,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_16329]) ).

tcf(c_44178,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_16329]) ).

tcf(c_44179,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_16329]) ).

tcf(c_44180,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_16329]) ).

tcf(c_44181,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_16329]) ).

tcf(c_44182,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_16329]) ).

tcf(c_44183,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_16329]) ).

tcf(c_44194,plain,
    hd(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_44176,c_20706]) ).

tcf(c_44195,plain,
    hd(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_44175,c_17701]) ).

tcf(c_44196,plain,
    hd(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_44174,c_19513]) ).

tcf(c_44197,plain,
    hd(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_44173,c_16926]) ).

tcf(c_44237,plain,
    hd(app(sk4,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_44180,c_44126]) ).

tcf(c_44238,plain,
    hd(app(sk4,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(forward_subsumption_resolution,[status(thm)],[c_44179,c_43038]) ).

tcf(c_44323,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,cons(hd(sk4),sk4)))))
      | ( cons(hd(sk3),app(sk4,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,cons(hd(sk4),sk4))))
      | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35442,c_280]) ).

tcf(c_44324,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,cons(hd(sk4),sk4)))))
      | ( cons(hd(sk3),app(sk4,cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,cons(hd(sk4),sk4))))
      | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35442,c_279]) ).

tcf(c_44340,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),cons(hd(sk3),sk3)))))
      | ( app(sk3,cons(hd(sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_37318,c_280]) ).

tcf(c_44341,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),cons(hd(sk3),sk3)))))
      | ( app(sk3,cons(hd(sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_37318,c_279]) ).

tcf(c_44402,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),cons(hd(sk3),sk3)))))
      | ( app(sk3,cons(hd(sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_37319,c_280]) ).

tcf(c_44403,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),cons(hd(sk3),sk3)))))
      | ( app(sk3,cons(hd(sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_37319,c_279]) ).

tcf(c_44419,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),cons(hd(sk4),sk3)))))
      | ( app(sk3,cons(hd(sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_37366,c_280]) ).

tcf(c_44420,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),cons(hd(sk4),sk3)))))
      | ( app(sk3,cons(hd(sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_37366,c_279]) ).

tcf(c_44435,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_43406,c_247,c_246,c_42153,c_43406]) ).

tcf(c_44436,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(renaming,[status(thm)],[c_44435]) ).

tcf(c_44448,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk4))))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_44436]) ).

tcf(c_44449,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk3))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_44436]) ).

tcf(c_44450,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_44436]) ).

tcf(c_44451,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_44436]) ).

tcf(c_44452,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44448,c_43441]) ).

tcf(c_44458,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_44450,c_3365]) ).

tcf(c_44459,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44458,c_4059]) ).

tcf(c_44464,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk3))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44449,c_10117]) ).

tcf(c_44470,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_44451,c_39675]) ).

tcf(c_44471,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44470,c_4059]) ).

tcf(c_44477,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_43414,c_247,c_246,c_42153,c_43414]) ).

tcf(c_44478,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(renaming,[status(thm)],[c_44477]) ).

tcf(c_44490,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk4))))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_44478]) ).

tcf(c_44491,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk3))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_44478]) ).

tcf(c_44492,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_44478]) ).

tcf(c_44493,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_44478]) ).

tcf(c_44494,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44490,c_43441]) ).

tcf(c_44500,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_44492,c_3365]) ).

tcf(c_44501,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44500,c_4059]) ).

tcf(c_44506,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),sk3))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44491,c_10117]) ).

tcf(c_44512,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_44493,c_39675]) ).

tcf(c_44513,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44512,c_4059]) ).

tcf(c_44520,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_43510,c_280]) ).

tcf(c_44521,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_43510,c_279]) ).

tcf(c_44537,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_36861,c_280]) ).

tcf(c_44538,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_36861,c_279]) ).

tcf(c_44554,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_36862,c_280]) ).

tcf(c_44555,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_36862,c_279]) ).

tcf(c_44594,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_36864,c_280]) ).

tcf(c_44595,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_36864,c_279]) ).

tcf(c_44611,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_37184,c_280]) ).

tcf(c_44612,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_37184,c_279]) ).

tcf(c_44628,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_37185,c_280]) ).

tcf(c_44629,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_37185,c_279]) ).

tcf(c_44646,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_8166,c_255]) ).

tcf(c_44647,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_8166,c_254]) ).

tcf(c_44648,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_8166,c_272]) ).

tcf(c_44649,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(app(sk3,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_8166,c_270]) ).

tcf(c_44650,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(X0,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_8166,c_269]) ).

tcf(c_44651,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(app(sk3,sk4),cons(hd(sk4),app(sk3,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_8166,c_300]) ).

tcf(c_44652,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(app(sk3,sk4),cons(hd(sk4),app(sk3,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_8166,c_287]) ).

tcf(c_44653,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_8166,c_8552]) ).

tcf(c_44654,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk3 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_8166,c_8271]) ).

tcf(c_44655,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk3,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44648,c_5886]) ).

tcf(c_44662,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44647,c_5891,c_5886]) ).

tcf(c_44665,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44654,c_5887,c_5886]) ).

tcf(c_44668,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44653,c_5886]) ).

tcf(c_44672,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(X0,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44650,c_5886]) ).

tcf(c_44677,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(app(sk3,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44649,c_5886]) ).

tcf(c_44682,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_44652,c_8166]) ).

tcf(c_44683,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44682,c_4059]) ).

tcf(c_44691,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_44651,c_8166]) ).

tcf(c_44692,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_44691,c_4059]) ).

tcf(c_44714,plain,
    ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(global_subsumption_just,[status(thm)],[c_44655,c_247,c_246,c_42153,c_44655]) ).

tcf(c_44716,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_15966]) ).

tcf(c_44717,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_15593]) ).

tcf(c_44718,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),nil),X0) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_4541]) ).

tcf(c_44719,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3154]) ).

tcf(c_44720,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_4037]) ).

tcf(c_44721,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3952]) ).

tcf(c_44722,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3050]) ).

tcf(c_44723,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0),nil) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3049]) ).

tcf(c_44724,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),sk4),X0) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_4540]) ).

tcf(c_44725,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),sk3),X0) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_4539]) ).

tcf(c_44726,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),X0) = app(X1,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_271]) ).

tcf(c_44727,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(cons(X1,X0),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_266]) ).

tcf(c_44728,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),X0) = tl(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_274]) ).

tcf(c_44729,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_283]) ).

tcf(c_44730,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_16329]) ).

tcf(c_44731,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_15967]) ).

tcf(c_44732,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_40467]) ).

tcf(c_44733,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_40466]) ).

tcf(c_44734,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_40465]) ).

tcf(c_44735,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_15965]) ).

tcf(c_44736,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_15594]) ).

tcf(c_44737,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_37606]) ).

tcf(c_44738,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_37605]) ).

tcf(c_44739,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_37604]) ).

tcf(c_44740,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_15592]) ).

tcf(c_44741,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_18000]) ).

tcf(c_44742,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_17998]) ).

tcf(c_44743,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_17997]) ).

tcf(c_44744,plain,
    app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_44714,c_35790]) ).

tcf(c_44745,plain,
    app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_44714,c_35787]) ).

tcf(c_44746,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),nil)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_4463]) ).

tcf(c_44747,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3155]) ).

tcf(c_44748,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_33403]) ).

tcf(c_44749,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_33402]) ).

tcf(c_44750,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_33401]) ).

tcf(c_44751,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_32111]) ).

tcf(c_44752,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_32098]) ).

tcf(c_44753,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_15410]) ).

tcf(c_44754,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_15408]) ).

tcf(c_44755,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_15407]) ).

tcf(c_44756,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3153]) ).

tcf(c_44757,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_4038]) ).

tcf(c_44758,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_17993]) ).

tcf(c_44759,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_17992]) ).

tcf(c_44760,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_17991]) ).

tcf(c_44761,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_4036]) ).

tcf(c_44762,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3953]) ).

tcf(c_44763,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_15403]) ).

tcf(c_44764,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_15402]) ).

tcf(c_44765,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_15401]) ).

tcf(c_44766,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3951]) ).

tcf(c_44767,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3423]) ).

tcf(c_44768,plain,
    app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_44714,c_13452]) ).

tcf(c_44769,plain,
    app(app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_44714,c_12354]) ).

tcf(c_44770,plain,
    app(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_44714,c_12353]) ).

tcf(c_44771,plain,
    app(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_44714,c_12352]) ).

tcf(c_44772,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_44714,c_3199]) ).

tcf(c_44773,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3066]) ).

tcf(c_44774,plain,
    app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_44714,c_8061]) ).

tcf(c_44775,plain,
    app(app(sk4,sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_44714,c_8048]) ).

tcf(c_44776,plain,
    app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_44714,c_5745]) ).

tcf(c_44777,plain,
    app(app(sk3,sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_44714,c_8047]) ).

tcf(c_44778,plain,
    app(app(sk4,sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_44714,c_5738]) ).

tcf(c_44779,plain,
    app(app(sk3,sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_44714,c_5737]) ).

tcf(c_44780,plain,
    app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = tl(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_44714,c_4136]) ).

tcf(c_44781,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),sk4)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_4462]) ).

tcf(c_44782,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),sk3)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_4461]) ).

tcf(c_44783,plain,
    app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = tl(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_44714,c_4284]) ).

tcf(c_44784,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_4027]) ).

tcf(c_44786,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3019]) ).

tcf(c_44787,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3452]) ).

tcf(c_44788,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3444]) ).

tcf(c_44789,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3065]) ).

tcf(c_44790,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3215]) ).

tcf(c_44791,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3207]) ).

tcf(c_44792,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_253]) ).

tcf(c_44793,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_275]) ).

tcf(c_44794,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3018]) ).

tcf(c_44795,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_44714,c_3191]) ).

tcf(c_44796,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_44714,c_3183]) ).

tcf(c_44797,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_284]) ).

tcf(c_44798,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_276]) ).

tcf(c_44799,plain,
    app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),nil) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_44714,c_258]) ).

tcf(c_44800,plain,
    app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_44714,c_257]) ).

tcf(c_44886,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_44729,c_18503]) ).

tcf(c_44895,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) ) ),
    inference(light_normalisation,[status(thm)],[c_44793,c_18503]) ).

tcf(c_44932,plain,
    ( ( sk4 = nil )
    | ~ ssList(sk4)
    | ( app(sk4,sk4) != nil ) ),
    inference(instantiation,[status(thm)],[c_3464]) ).

tcf(c_45258,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(sk3,X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_16330]) ).

tcf(c_45259,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(sk4,X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_16330]) ).

tcf(c_45260,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(nil,X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_16330]) ).

tcf(c_45261,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(nil,app(tl(X0),X1)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_16330]) ).

tcf(c_45262,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(nil,app(app(X1,X0),X2)))) = hd(sk4) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_16330]) ).

tcf(c_45263,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(X2,X0),X1)))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_16330]) ).

tcf(c_45264,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk3),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_16330]) ).

tcf(c_45265,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk4),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_16330]) ).

tcf(c_45266,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk3),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_16330]) ).

tcf(c_45267,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk4),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_16330]) ).

tcf(c_45268,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk4,app(nil,app(app(tl(sk3),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_16330]) ).

tcf(c_45269,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk4,app(nil,app(app(tl(sk3),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_16330]) ).

tcf(c_45270,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk4,app(nil,app(app(tl(sk4),sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_16330]) ).

tcf(c_45271,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk4,app(nil,app(app(tl(sk4),sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_16330]) ).

tcf(c_45272,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk4),app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_16330]) ).

tcf(c_45273,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_16330]) ).

tcf(c_45274,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_16330]) ).

tcf(c_45275,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_16330]) ).

tcf(c_45276,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk4),app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_16330]) ).

tcf(c_45277,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_16330]) ).

tcf(c_45278,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_16330]) ).

tcf(c_45279,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_16330]) ).

tcf(c_45280,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_16330]) ).

tcf(c_45281,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_16330]) ).

tcf(c_45282,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk4),app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_16330]) ).

tcf(c_45283,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk4),app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_16330]) ).

tcf(c_45284,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_16330]) ).

tcf(c_45285,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_16330]) ).

tcf(c_45286,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_16330]) ).

tcf(c_45287,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk3),app(sk4,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_16330]) ).

tcf(c_45288,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk3),app(sk4,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_16330]) ).

tcf(c_45289,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk3),app(sk3,sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_16330]) ).

tcf(c_45290,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk3),app(sk3,sk3)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_16330]) ).

tcf(c_45291,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_16330]) ).

tcf(c_45292,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_16330]) ).

tcf(c_45293,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_16330]) ).

tcf(c_45294,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_16330]) ).

tcf(c_45295,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_16330]) ).

tcf(c_45296,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_16330]) ).

tcf(c_45297,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_16330]) ).

tcf(c_45298,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_16330]) ).

tcf(c_45653,plain,
    hd(app(sk4,app(nil,app(sk3,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_45258]) ).

tcf(c_45654,plain,
    hd(app(sk4,app(nil,app(sk3,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_45258]) ).

tcf(c_45655,plain,
    hd(app(sk4,app(nil,app(sk3,nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_45258]) ).

tcf(c_45656,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(nil,app(sk3,tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_45258]) ).

tcf(c_45657,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(nil,app(sk3,app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_45258]) ).

tcf(c_45658,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(nil,app(sk3,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_45258]) ).

tcf(c_45659,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk3),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_45258]) ).

tcf(c_45660,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_45258]) ).

tcf(c_45661,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk3),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_45258]) ).

tcf(c_45662,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_45258]) ).

tcf(c_45663,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(nil,app(sk3,app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_45258]) ).

tcf(c_45664,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(nil,app(sk3,app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_45258]) ).

tcf(c_45665,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(nil,app(sk3,app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_45258]) ).

tcf(c_45666,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(nil,app(sk3,app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_45258]) ).

tcf(c_45667,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_45258]) ).

tcf(c_45668,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_45258]) ).

tcf(c_45669,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_45258]) ).

tcf(c_45670,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_45258]) ).

tcf(c_45671,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_45258]) ).

tcf(c_45672,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_45258]) ).

tcf(c_45673,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_45258]) ).

tcf(c_45674,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_45258]) ).

tcf(c_45675,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_45258]) ).

tcf(c_45676,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_45258]) ).

tcf(c_45677,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_45258]) ).

tcf(c_45678,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_45258]) ).

tcf(c_45679,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_45258]) ).

tcf(c_45680,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_45258]) ).

tcf(c_45681,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_45258]) ).

tcf(c_45682,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_45258]) ).

tcf(c_45683,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_45258]) ).

tcf(c_45684,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_45258]) ).

tcf(c_45685,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_45258]) ).

tcf(c_45686,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_45258]) ).

tcf(c_45687,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_45258]) ).

tcf(c_45688,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_45258]) ).

tcf(c_45689,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_45258]) ).

tcf(c_45690,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_45258]) ).

tcf(c_45691,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_45258]) ).

tcf(c_45692,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_45258]) ).

tcf(c_45693,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_45258]) ).

tcf(c_45841,plain,
    hd(app(sk4,app(nil,app(sk4,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_45259]) ).

tcf(c_45842,plain,
    hd(app(sk4,app(nil,app(sk4,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_45259]) ).

tcf(c_45843,plain,
    hd(app(sk4,app(nil,app(sk4,nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_45259]) ).

tcf(c_45844,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(nil,app(sk4,tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_45259]) ).

tcf(c_45845,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(nil,app(sk4,app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_45259]) ).

tcf(c_45846,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(nil,app(sk4,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_45259]) ).

tcf(c_45847,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk3),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_45259]) ).

tcf(c_45848,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_45259]) ).

tcf(c_45849,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk3),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_45259]) ).

tcf(c_45850,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_45259]) ).

tcf(c_45851,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(nil,app(sk4,app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_45259]) ).

tcf(c_45852,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(nil,app(sk4,app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_45259]) ).

tcf(c_45853,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(nil,app(sk4,app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_45259]) ).

tcf(c_45854,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(nil,app(sk4,app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_45259]) ).

tcf(c_45855,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_45259]) ).

tcf(c_45856,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_45259]) ).

tcf(c_45857,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_45259]) ).

tcf(c_45858,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_45259]) ).

tcf(c_45859,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_45259]) ).

tcf(c_45860,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_45259]) ).

tcf(c_45861,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_45259]) ).

tcf(c_45862,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_45259]) ).

tcf(c_45863,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_45259]) ).

tcf(c_45864,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_45259]) ).

tcf(c_45865,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_45259]) ).

tcf(c_45866,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_45259]) ).

tcf(c_45867,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_45259]) ).

tcf(c_45868,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_45259]) ).

tcf(c_45869,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_45259]) ).

tcf(c_45870,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_45259]) ).

tcf(c_45871,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_45259]) ).

tcf(c_45872,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_45259]) ).

tcf(c_45873,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_45259]) ).

tcf(c_45874,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_45259]) ).

tcf(c_45875,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_45259]) ).

tcf(c_45876,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_45259]) ).

tcf(c_45877,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_45259]) ).

tcf(c_45878,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_45259]) ).

tcf(c_45879,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_45259]) ).

tcf(c_45880,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_45259]) ).

tcf(c_45881,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_45259]) ).

tcf(c_45996,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),cons(hd(sk4),sk3)))))
      | ( app(sk3,cons(hd(sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_37367,c_280]) ).

tcf(c_45997,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),cons(hd(sk4),sk3)))))
      | ( app(sk3,cons(hd(sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_37367,c_279]) ).

tcf(c_46013,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),cons(hd(sk4),sk4)))))
      | ( app(sk3,cons(hd(sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_37376,c_280]) ).

tcf(c_46014,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),cons(hd(sk4),sk4)))))
      | ( app(sk3,cons(hd(sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_37376,c_279]) ).

tcf(c_46030,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),cons(hd(sk4),sk4)))))
      | ( app(sk3,cons(hd(sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_37377,c_280]) ).

tcf(c_46031,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),cons(hd(sk4),sk4)))))
      | ( app(sk3,cons(hd(sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_37377,c_279]) ).

tcf(c_46047,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3))))))
      | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_39658,c_280]) ).

tcf(c_46048,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3))))))
      | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_39658,c_279]) ).

tcf(c_46064,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_37187,c_280]) ).

tcf(c_46065,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_37187,c_279]) ).

tcf(c_46197,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37439,c_280]) ).

tcf(c_46198,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37439,c_279]) ).

tcf(c_46214,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37440,c_280]) ).

tcf(c_46215,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37440,c_279]) ).

tcf(c_46231,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37441,c_280]) ).

tcf(c_46232,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37441,c_279]) ).

tcf(c_46248,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37442,c_280]) ).

tcf(c_46249,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37442,c_279]) ).

tcf(c_46265,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37443,c_280]) ).

tcf(c_46266,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37443,c_279]) ).

tcf(c_46282,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37444,c_280]) ).

tcf(c_46283,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37444,c_279]) ).

tcf(c_46299,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37445,c_280]) ).

tcf(c_46300,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37445,c_279]) ).

tcf(c_46317,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_8170,c_255]) ).

tcf(c_46318,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_8170,c_254]) ).

tcf(c_46319,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_8170,c_272]) ).

tcf(c_46320,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(app(sk3,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_8170,c_270]) ).

tcf(c_46321,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(X0,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_8170,c_269]) ).

tcf(c_46322,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(app(sk3,sk4),cons(hd(sk4),app(sk4,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_8170,c_300]) ).

tcf(c_46323,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(app(sk3,sk4),cons(hd(sk4),app(sk4,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_8170,c_287]) ).

tcf(c_46324,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_8170,c_8552]) ).

tcf(c_46325,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk3 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_8170,c_8271]) ).

tcf(c_46326,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk3,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46319,c_7540]) ).

tcf(c_46333,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46318,c_7545,c_7540]) ).

tcf(c_46336,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46325,c_7541,c_7540]) ).

tcf(c_46339,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46324,c_7540]) ).

tcf(c_46343,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(X0,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46321,c_7540]) ).

tcf(c_46348,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(app(sk3,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46320,c_7540]) ).

tcf(c_46353,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_46323,c_8170]) ).

tcf(c_46354,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46353,c_4059]) ).

tcf(c_46362,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_46322,c_8170]) ).

tcf(c_46363,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46362,c_4059]) ).

tcf(c_46398,plain,
    hd(app(sk4,app(nil,app(nil,sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_45260]) ).

tcf(c_46399,plain,
    hd(app(sk4,app(nil,app(nil,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_45260]) ).

tcf(c_46400,plain,
    hd(app(sk4,app(nil,app(nil,nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_45260]) ).

tcf(c_46401,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(nil,app(nil,tl(X0))))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_45260]) ).

tcf(c_46402,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(nil,app(nil,app(X1,X0))))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_45260]) ).

tcf(c_46403,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(nil,app(nil,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_45260]) ).

tcf(c_46404,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk3),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_45260]) ).

tcf(c_46405,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_45260]) ).

tcf(c_46406,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk3),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_45260]) ).

tcf(c_46407,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_45260]) ).

tcf(c_46408,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(nil,app(nil,app(tl(sk3),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_45260]) ).

tcf(c_46409,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(nil,app(nil,app(tl(sk3),sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_45260]) ).

tcf(c_46410,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(nil,app(nil,app(tl(sk4),sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_45260]) ).

tcf(c_46411,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(nil,app(nil,app(tl(sk4),sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_45260]) ).

tcf(c_46412,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_45260]) ).

tcf(c_46413,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_45260]) ).

tcf(c_46414,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_45260]) ).

tcf(c_46415,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_45260]) ).

tcf(c_46416,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_45260]) ).

tcf(c_46417,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_45260]) ).

tcf(c_46418,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_45260]) ).

tcf(c_46419,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_45260]) ).

tcf(c_46420,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_45260]) ).

tcf(c_46421,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_45260]) ).

tcf(c_46422,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_45260]) ).

tcf(c_46423,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_45260]) ).

tcf(c_46424,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_45260]) ).

tcf(c_46425,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_45260]) ).

tcf(c_46426,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_45260]) ).

tcf(c_46427,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_45260]) ).

tcf(c_46428,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_45260]) ).

tcf(c_46429,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_45260]) ).

tcf(c_46430,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_45260]) ).

tcf(c_46431,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_45260]) ).

tcf(c_46432,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_45260]) ).

tcf(c_46433,plain,
    hd(app(sk4,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_45260]) ).

tcf(c_46434,plain,
    hd(app(sk4,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_45260]) ).

tcf(c_46435,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_45260]) ).

tcf(c_46436,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_45260]) ).

tcf(c_46437,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_45260]) ).

tcf(c_46438,plain,
    hd(app(sk4,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_45260]) ).

tcf(c_46613,plain,
    ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(global_subsumption_just,[status(thm)],[c_46326,c_247,c_246,c_42153,c_46326]) ).

tcf(c_46615,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_16330]) ).

tcf(c_46616,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_15966]) ).

tcf(c_46617,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_15593]) ).

tcf(c_46618,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),nil),X0) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_4541]) ).

tcf(c_46619,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3154]) ).

tcf(c_46620,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_4037]) ).

tcf(c_46621,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3952]) ).

tcf(c_46622,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3050]) ).

tcf(c_46623,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0),nil) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3049]) ).

tcf(c_46624,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),sk4),X0) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_4540]) ).

tcf(c_46625,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),sk3),X0) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_4539]) ).

tcf(c_46626,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),X0) = app(X1,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_271]) ).

tcf(c_46627,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(cons(X1,X0),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_266]) ).

tcf(c_46628,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),X0) = tl(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_274]) ).

tcf(c_46629,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_283]) ).

tcf(c_46630,plain,
    hd(app(sk4,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_45260]) ).

tcf(c_46631,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_45259]) ).

tcf(c_46632,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_45258]) ).

tcf(c_46633,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_16329]) ).

tcf(c_46634,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_15967]) ).

tcf(c_46635,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_40467]) ).

tcf(c_46636,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_40466]) ).

tcf(c_46637,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_40465]) ).

tcf(c_46638,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_15965]) ).

tcf(c_46639,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_15594]) ).

tcf(c_46640,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_37606]) ).

tcf(c_46641,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_37605]) ).

tcf(c_46642,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_37604]) ).

tcf(c_46643,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_15592]) ).

tcf(c_46644,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_18000]) ).

tcf(c_46645,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_17998]) ).

tcf(c_46646,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_17997]) ).

tcf(c_46647,plain,
    app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_46613,c_35790]) ).

tcf(c_46648,plain,
    app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_46613,c_35787]) ).

tcf(c_46649,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),nil)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_4463]) ).

tcf(c_46650,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3155]) ).

tcf(c_46651,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_33403]) ).

tcf(c_46652,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_33402]) ).

tcf(c_46653,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_33401]) ).

tcf(c_46654,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_32111]) ).

tcf(c_46655,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_32098]) ).

tcf(c_46656,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_15410]) ).

tcf(c_46657,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_15408]) ).

tcf(c_46658,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_15407]) ).

tcf(c_46659,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3153]) ).

tcf(c_46660,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_4038]) ).

tcf(c_46661,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_17993]) ).

tcf(c_46662,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_17992]) ).

tcf(c_46663,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_17991]) ).

tcf(c_46664,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_4036]) ).

tcf(c_46665,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3953]) ).

tcf(c_46666,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_15403]) ).

tcf(c_46667,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_15402]) ).

tcf(c_46668,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_15401]) ).

tcf(c_46669,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3951]) ).

tcf(c_46670,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3423]) ).

tcf(c_46671,plain,
    app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_46613,c_13452]) ).

tcf(c_46672,plain,
    app(app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_46613,c_12354]) ).

tcf(c_46673,plain,
    app(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_46613,c_12353]) ).

tcf(c_46674,plain,
    app(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_46613,c_12352]) ).

tcf(c_46675,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_46613,c_3199]) ).

tcf(c_46676,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3066]) ).

tcf(c_46677,plain,
    app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_46613,c_8061]) ).

tcf(c_46678,plain,
    app(app(sk4,sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_46613,c_8048]) ).

tcf(c_46679,plain,
    app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_46613,c_5745]) ).

tcf(c_46680,plain,
    app(app(sk3,sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_46613,c_8047]) ).

tcf(c_46681,plain,
    app(app(sk4,sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_46613,c_5738]) ).

tcf(c_46682,plain,
    app(app(sk3,sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_46613,c_5737]) ).

tcf(c_46683,plain,
    app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = tl(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_46613,c_4136]) ).

tcf(c_46684,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),sk4)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_4462]) ).

tcf(c_46685,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),sk3)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_4461]) ).

tcf(c_46686,plain,
    app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = tl(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_46613,c_4284]) ).

tcf(c_46687,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_4027]) ).

tcf(c_46689,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3019]) ).

tcf(c_46690,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3452]) ).

tcf(c_46691,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3444]) ).

tcf(c_46692,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3065]) ).

tcf(c_46693,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3215]) ).

tcf(c_46694,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3207]) ).

tcf(c_46695,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_253]) ).

tcf(c_46696,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_275]) ).

tcf(c_46697,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3018]) ).

tcf(c_46698,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_46613,c_3191]) ).

tcf(c_46699,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_46613,c_3183]) ).

tcf(c_46700,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_284]) ).

tcf(c_46701,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_276]) ).

tcf(c_46702,plain,
    app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),nil) = app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_46613,c_258]) ).

tcf(c_46703,plain,
    app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_46613,c_257]) ).

tcf(c_46791,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_46629,c_18507]) ).

tcf(c_46800,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) ) ),
    inference(light_normalisation,[status(thm)],[c_46696,c_18507]) ).

tcf(c_47137,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,sk3)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_16331]) ).

tcf(c_47138,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,sk4)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_16331]) ).

tcf(c_47139,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,nil)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_16331]) ).

tcf(c_47140,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(nil,cons(X1,tl(X0))))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_16331]) ).

tcf(c_47141,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(nil,cons(X2,app(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_16331]) ).

tcf(c_47142,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk4,app(nil,cons(X2,cons(X1,X0))))) = hd(sk4) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_16331]) ).

tcf(c_47143,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk3),sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_16331]) ).

tcf(c_47144,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk4),sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_16331]) ).

tcf(c_47145,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk3),sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_16331]) ).

tcf(c_47146,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk4),sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_16331]) ).

tcf(c_47147,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk4,app(nil,cons(X0,app(tl(sk3),sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_16331]) ).

tcf(c_47148,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk4,app(nil,cons(X0,app(tl(sk3),sk4))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_16331]) ).

tcf(c_47149,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk4,app(nil,cons(X0,app(tl(sk4),sk3))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_16331]) ).

tcf(c_47150,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk4,app(nil,cons(X0,app(tl(sk4),sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_16331]) ).

tcf(c_47151,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_16331]) ).

tcf(c_47152,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_16331]) ).

tcf(c_47153,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_16331]) ).

tcf(c_47154,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_16331]) ).

tcf(c_47155,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_16331]) ).

tcf(c_47156,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_16331]) ).

tcf(c_47157,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_16331]) ).

tcf(c_47158,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_16331]) ).

tcf(c_47159,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_16331]) ).

tcf(c_47160,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_16331]) ).

tcf(c_47161,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_16331]) ).

tcf(c_47162,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_16331]) ).

tcf(c_47163,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_16331]) ).

tcf(c_47164,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_16331]) ).

tcf(c_47165,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_16331]) ).

tcf(c_47166,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_16331]) ).

tcf(c_47167,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_16331]) ).

tcf(c_47168,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_16331]) ).

tcf(c_47169,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_16331]) ).

tcf(c_47170,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_16331]) ).

tcf(c_47171,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_16331]) ).

tcf(c_47172,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_16331]) ).

tcf(c_47173,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_16331]) ).

tcf(c_47174,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_16331]) ).

tcf(c_47175,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_16331]) ).

tcf(c_47176,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_16331]) ).

tcf(c_47177,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_16331]) ).

tcf(c_47178,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_16331]) ).

tcf(c_47392,plain,
    hd(app(sk3,sk3)) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_25250]) ).

tcf(c_47393,plain,
    hd(app(sk3,sk4)) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_25250]) ).

tcf(c_47465,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(nil,cons(hd(X0),sk3)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_47137]) ).

tcf(c_47472,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3))))))
      | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_39659,c_280]) ).

tcf(c_47473,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3))))))
      | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_39659,c_279]) ).

tcf(c_47489,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4))))))
      | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_39668,c_280]) ).

tcf(c_47490,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4))))))
      | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_39668,c_279]) ).

tcf(c_47506,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4))))))
      | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_39669,c_280]) ).

tcf(c_47507,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4))))))
      | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_39669,c_279]) ).

tcf(c_47523,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3))))))
      | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_40283,c_280]) ).

tcf(c_47524,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3))))))
      | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_40283,c_279]) ).

tcf(c_47543,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(nil,cons(hd(X0),sk4)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_47138]) ).

tcf(c_47550,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37446,c_280]) ).

tcf(c_47551,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37446,c_279]) ).

tcf(c_47567,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39979,c_280]) ).

tcf(c_47568,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39979,c_279]) ).

tcf(c_47584,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39980,c_280]) ).

tcf(c_47585,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39980,c_279]) ).

tcf(c_47601,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39981,c_280]) ).

tcf(c_47602,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39981,c_279]) ).

tcf(c_47632,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39982,c_280]) ).

tcf(c_47633,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39982,c_279]) ).

tcf(c_47649,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39983,c_280]) ).

tcf(c_47650,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39983,c_279]) ).

tcf(c_47666,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39984,c_280]) ).

tcf(c_47667,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39984,c_279]) ).

tcf(c_47690,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3))))
      | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_8854,c_270]) ).

tcf(c_47691,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3))))
      | ( app(X0,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_8854,c_269]) ).

tcf(c_47692,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3))))
      | ( app(X0,app(sk3,cons(hd(sk4),app(sk3,sk3)))) != app(sk3,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_47691,c_259]) ).

tcf(c_47697,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3))))
      | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_47690,c_259]) ).

tcf(c_47707,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(nil,cons(hd(X0),nil)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_47139]) ).

tcf(c_47708,plain,
    hd(app(sk4,app(nil,cons(hd(sk4),nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_47139]) ).

tcf(c_47709,plain,
    hd(app(sk4,app(nil,cons(hd(sk3),nil)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10117,c_47139]) ).

tcf(c_47751,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk4,cons(hd(tl(X0)),sk3))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_16670]) ).

tcf(c_47752,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk4,cons(hd(app(X1,X0)),sk3))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_16670]) ).

tcf(c_47753,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk4,cons(hd(cons(X1,X0)),sk3))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_16670]) ).

tcf(c_47754,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),sk3)),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_16670]) ).

tcf(c_47755,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),sk3)),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_16670]) ).

tcf(c_47756,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),sk4)),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_16670]) ).

tcf(c_47757,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),sk4)),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_16670]) ).

tcf(c_47758,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk3),sk3)),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_16670]) ).

tcf(c_47759,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk3),sk4)),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_16670]) ).

tcf(c_47760,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk4),sk3)),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_16670]) ).

tcf(c_47761,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk4),sk4)),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_16670]) ).

tcf(c_47762,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_16670]) ).

tcf(c_47763,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,sk3))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_16670]) ).

tcf(c_47764,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,sk4))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_16670]) ).

tcf(c_47765,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,sk3))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_16670]) ).

tcf(c_47766,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_16670]) ).

tcf(c_47767,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,sk4))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_16670]) ).

tcf(c_47768,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,sk3))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_16670]) ).

tcf(c_47769,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,sk4))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_16670]) ).

tcf(c_47770,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,sk3))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_16670]) ).

tcf(c_47771,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,sk4))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_16670]) ).

tcf(c_47772,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_16670]) ).

tcf(c_47773,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk4,sk4))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_16670]) ).

tcf(c_47774,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_16670]) ).

tcf(c_47775,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_16670]) ).

tcf(c_47776,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_16670]) ).

tcf(c_47777,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk4,sk4))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_16670]) ).

tcf(c_47778,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk4,sk3))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_16670]) ).

tcf(c_47779,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk3,sk4))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_16670]) ).

tcf(c_47780,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk3,sk3))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_16670]) ).

tcf(c_47781,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_16670]) ).

tcf(c_47782,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_16670]) ).

tcf(c_47783,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_16670]) ).

tcf(c_47784,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_16670]) ).

tcf(c_47785,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_16670]) ).

tcf(c_47786,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_16670]) ).

tcf(c_47787,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_16670]) ).

tcf(c_47788,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_16670]) ).

tcf(c_47789,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_16670]) ).

tcf(c_47894,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk4,cons(hd(tl(X0)),sk4))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_16680]) ).

tcf(c_47895,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk4,cons(hd(app(X1,X0)),sk4))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_16680]) ).

tcf(c_47896,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk4,cons(hd(cons(X1,X0)),sk4))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_16680]) ).

tcf(c_47897,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),sk3)),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_16680]) ).

tcf(c_47898,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),sk3)),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_16680]) ).

tcf(c_47899,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),sk4)),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_16680]) ).

tcf(c_47900,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),sk4)),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_16680]) ).

tcf(c_47901,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk3),sk3)),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_16680]) ).

tcf(c_47902,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk3),sk4)),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_16680]) ).

tcf(c_47903,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk4),sk3)),sk4))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_16680]) ).

tcf(c_47904,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk4),sk4)),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_16680]) ).

tcf(c_47905,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_16680]) ).

tcf(c_47906,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,sk3))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_16680]) ).

tcf(c_47907,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,sk4))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_16680]) ).

tcf(c_47908,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,sk3))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_16680]) ).

tcf(c_47909,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_16680]) ).

tcf(c_47910,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,sk4))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_16680]) ).

tcf(c_47911,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,sk3))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_16680]) ).

tcf(c_47912,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,sk4))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_16680]) ).

tcf(c_47913,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,sk3))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_16680]) ).

tcf(c_47914,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,sk4))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_16680]) ).

tcf(c_47915,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_16680]) ).

tcf(c_47916,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk4,sk4))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_16680]) ).

tcf(c_47917,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_16680]) ).

tcf(c_47918,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_16680]) ).

tcf(c_47919,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_16680]) ).

tcf(c_47920,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk4,sk4))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_16680]) ).

tcf(c_47921,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk4,sk3))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_16680]) ).

tcf(c_47922,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk3,sk4))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_16680]) ).

tcf(c_47923,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk3,sk3))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_16680]) ).

tcf(c_47924,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_16680]) ).

tcf(c_47925,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_16680]) ).

tcf(c_47926,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_16680]) ).

tcf(c_47927,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_16680]) ).

tcf(c_47928,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_16680]) ).

tcf(c_47929,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_16680]) ).

tcf(c_47930,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_16680]) ).

tcf(c_47931,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_16680]) ).

tcf(c_47932,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_16680]) ).

tcf(c_48002,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk4,cons(hd(tl(X0)),nil))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_17287]) ).

tcf(c_48003,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk4,cons(hd(app(X1,X0)),nil))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_17287]) ).

tcf(c_48004,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk4,cons(hd(cons(X1,X0)),nil))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_17287]) ).

tcf(c_48005,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),sk3)),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_17287]) ).

tcf(c_48006,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),sk3)),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_17287]) ).

tcf(c_48007,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),sk4)),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_17287]) ).

tcf(c_48008,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),sk4)),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_17287]) ).

tcf(c_48009,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk3),sk3)),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_17287]) ).

tcf(c_48010,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk3),sk4)),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_17287]) ).

tcf(c_48011,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk4),sk3)),nil))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_17287]) ).

tcf(c_48012,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk4,cons(hd(app(tl(sk4),sk4)),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_17287]) ).

tcf(c_48013,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk3,sk3))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_17287]) ).

tcf(c_48014,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,sk3))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_17287]) ).

tcf(c_48015,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,sk4))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_17287]) ).

tcf(c_48016,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,sk3))),nil))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_17287]) ).

tcf(c_48017,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk4,sk3))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_17287]) ).

tcf(c_48018,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,sk4))),nil))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_17287]) ).

tcf(c_48019,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,sk3))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_17287]) ).

tcf(c_48020,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,sk4))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_17287]) ).

tcf(c_48021,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,sk3))),nil))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_17287]) ).

tcf(c_48022,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,sk4))),nil))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_17287]) ).

tcf(c_48023,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk3,sk4))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_17287]) ).

tcf(c_48024,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk4),app(sk4,sk4))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_17287]) ).

tcf(c_48025,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_17287]) ).

tcf(c_48026,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_17287]) ).

tcf(c_48027,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_17287]) ).

tcf(c_48028,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk4,sk4))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_17287]) ).

tcf(c_48029,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk4,sk3))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_17287]) ).

tcf(c_48030,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk3,sk4))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_17287]) ).

tcf(c_48031,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),app(sk3,sk3))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_17287]) ).

tcf(c_48032,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_17287]) ).

tcf(c_48033,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_17287]) ).

tcf(c_48034,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_17287]) ).

tcf(c_48035,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_17287]) ).

tcf(c_48036,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_17287]) ).

tcf(c_48037,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_17287]) ).

tcf(c_48038,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_17287]) ).

tcf(c_48039,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_17287]) ).

tcf(c_48040,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_17287]) ).

tcf(c_48149,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3))))))
      | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_40284,c_280]) ).

tcf(c_48150,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3))))))
      | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_40284,c_279]) ).

tcf(c_48166,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4))))))
      | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40331,c_280]) ).

tcf(c_48167,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4))))))
      | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40331,c_279]) ).

tcf(c_48183,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4))))))
      | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40332,c_280]) ).

tcf(c_48184,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4))))))
      | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40332,c_279]) ).

tcf(c_48216,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4))))))
      | ( cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40341,c_280]) ).

tcf(c_48217,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4))))))
      | ( cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40341,c_279]) ).

tcf(c_48233,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39985,c_280]) ).

tcf(c_48234,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39985,c_279]) ).

tcf(c_48250,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39986,c_280]) ).

tcf(c_48251,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39986,c_279]) ).

tcf(c_48267,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_44194,c_280]) ).

tcf(c_48268,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_44194,c_279]) ).

tcf(c_48284,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_44195,c_280]) ).

tcf(c_48285,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_44195,c_279]) ).

tcf(c_48301,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_44196,c_280]) ).

tcf(c_48302,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_44196,c_279]) ).

tcf(c_48346,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_44197,c_280]) ).

tcf(c_48347,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_44197,c_279]) ).

tcf(c_48372,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3))))
      | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_8858,c_270]) ).

tcf(c_48373,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3))))
      | ( app(X0,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_8858,c_269]) ).

tcf(c_48374,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3))))
      | ( app(X0,app(sk3,cons(hd(sk4),app(sk4,sk3)))) != app(sk3,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_48373,c_259]) ).

tcf(c_48379,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3))))
      | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_48372,c_259]) ).

tcf(c_48391,plain,
    ( ( sk3 = nil )
    | ( hd(app(sk3,app(sk3,tl(sk3)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_18184]) ).

tcf(c_48392,plain,
    ( ( sk4 = nil )
    | ( hd(app(sk3,app(sk3,tl(sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_247,c_18184]) ).

tcf(c_48394,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk3,app(sk3,tl(tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18184]) ).

tcf(c_48395,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk3,app(sk3,tl(app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18184]) ).

tcf(c_48396,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk3,app(sk3,tl(cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18184]) ).

tcf(c_48397,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk3),sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_18184]) ).

tcf(c_48398,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk4),sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_18184]) ).

tcf(c_48399,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk3),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_18184]) ).

tcf(c_48400,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_18184]) ).

tcf(c_48401,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18184]) ).

tcf(c_48402,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18184]) ).

tcf(c_48403,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18184]) ).

tcf(c_48404,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_18184]) ).

tcf(c_48405,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_18184]) ).

tcf(c_48406,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18184]) ).

tcf(c_48407,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18184]) ).

tcf(c_48408,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18184]) ).

tcf(c_48409,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_18184]) ).

tcf(c_48410,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18184]) ).

tcf(c_48411,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18184]) ).

tcf(c_48412,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18184]) ).

tcf(c_48413,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18184]) ).

tcf(c_48414,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18184]) ).

tcf(c_48415,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_18184]) ).

tcf(c_48416,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_18184]) ).

tcf(c_48417,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18184]) ).

tcf(c_48418,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18184]) ).

tcf(c_48419,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18184]) ).

tcf(c_48420,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_18184]) ).

tcf(c_48421,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_18184]) ).

tcf(c_48422,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_18184]) ).

tcf(c_48423,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_18184]) ).

tcf(c_48424,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18184]) ).

tcf(c_48425,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18184]) ).

tcf(c_48426,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_18184]) ).

tcf(c_48427,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_18184]) ).

tcf(c_48428,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18184]) ).

tcf(c_48429,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18184]) ).

tcf(c_48430,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18184]) ).

tcf(c_48431,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_18184]) ).

tcf(c_48432,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_18184]) ).

tcf(c_48433,plain,
    hd(app(sk3,app(sk3,tl(sk4)))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48392,c_1243]) ).

tcf(c_48444,plain,
    hd(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48423,c_20706]) ).

tcf(c_48445,plain,
    hd(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48422,c_17701]) ).

tcf(c_48446,plain,
    hd(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48421,c_19513]) ).

tcf(c_48447,plain,
    hd(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48420,c_16926]) ).

tcf(c_48448,plain,
    hd(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48416,c_10611]) ).

tcf(c_48449,plain,
    hd(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48415,c_10190]) ).

tcf(c_48450,plain,
    hd(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48409,c_7545]) ).

tcf(c_48451,plain,
    hd(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48405,c_5891]) ).

tcf(c_48487,plain,
    hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48427,c_44126]) ).

tcf(c_48488,plain,
    hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_48426,c_43038]) ).

tcf(c_48773,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(sk4)))))
      | ( app(sk3,app(sk3,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(sk4))))
      | ~ ssList(app(sk3,app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_48433,c_280]) ).

tcf(c_48774,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(sk4)))))
      | ( app(sk3,app(sk3,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(sk4))))
      | ~ ssList(app(sk3,app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_48433,c_279]) ).

tcf(c_48789,plain,
    hd(app(sk3,app(sk3,tl(sk3)))) = hd(sk3),
    inference(global_subsumption_just,[status(thm)],[c_48391,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_48391]) ).

tcf(c_48792,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(sk3)))))
      | ( app(sk3,app(sk3,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(sk3))))
      | ~ ssList(app(sk3,app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_48789,c_280]) ).

tcf(c_48793,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(sk3)))))
      | ( app(sk3,app(sk3,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(sk3))))
      | ~ ssList(app(sk3,app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_48789,c_279]) ).

tcf(c_48817,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(sk3,X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_18185]) ).

tcf(c_48818,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(sk4,X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_18185]) ).

tcf(c_48819,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(nil,X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_18185]) ).

tcf(c_48820,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk3,app(tl(X0),X1)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18185]) ).

tcf(c_48821,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(X1,X0),X2)))) = hd(sk3) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18185]) ).

tcf(c_48822,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(X2,X0),X1)))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18185]) ).

tcf(c_48823,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk3),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_18185]) ).

tcf(c_48824,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk4),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_18185]) ).

tcf(c_48825,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk3),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_18185]) ).

tcf(c_48826,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk4),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_18185]) ).

tcf(c_48827,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk3,app(sk3,app(app(tl(sk3),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18185]) ).

tcf(c_48828,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk3,app(sk3,app(app(tl(sk3),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18185]) ).

tcf(c_48829,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk3,app(sk3,app(app(tl(sk4),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18185]) ).

tcf(c_48830,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk3,app(sk3,app(app(tl(sk4),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_18185]) ).

tcf(c_48831,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk4),app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_18185]) ).

tcf(c_48832,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18185]) ).

tcf(c_48833,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18185]) ).

tcf(c_48834,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18185]) ).

tcf(c_48835,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk4),app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_18185]) ).

tcf(c_48836,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18185]) ).

tcf(c_48837,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18185]) ).

tcf(c_48838,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18185]) ).

tcf(c_48839,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18185]) ).

tcf(c_48840,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18185]) ).

tcf(c_48841,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk4),app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_18185]) ).

tcf(c_48842,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk4),app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_18185]) ).

tcf(c_48843,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18185]) ).

tcf(c_48844,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18185]) ).

tcf(c_48845,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18185]) ).

tcf(c_48846,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk3),app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_18185]) ).

tcf(c_48847,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk3),app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_18185]) ).

tcf(c_48848,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk3),app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_18185]) ).

tcf(c_48849,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk3),app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_18185]) ).

tcf(c_48850,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18185]) ).

tcf(c_48851,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18185]) ).

tcf(c_48852,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_18185]) ).

tcf(c_48853,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_18185]) ).

tcf(c_48854,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18185]) ).

tcf(c_48855,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18185]) ).

tcf(c_48856,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18185]) ).

tcf(c_48857,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_18185]) ).

tcf(c_48858,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_18185]) ).

tcf(c_49059,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4))))))
      | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40342,c_280]) ).

tcf(c_49060,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4))))))
      | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40342,c_279]) ).

tcf(c_49117,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4))))))
      | ( cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_40351,c_280]) ).

tcf(c_49118,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4))))))
      | ( cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_40351,c_279]) ).

tcf(c_49134,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4))))))
      | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_40352,c_280]) ).

tcf(c_49135,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4))))))
      | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_40352,c_279]) ).

tcf(c_49171,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3))))))
      | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_40362,c_280]) ).

tcf(c_49172,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3))))))
      | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_40362,c_279]) ).

tcf(c_49210,plain,
    hd(app(sk3,app(sk3,app(sk3,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_48817]) ).

tcf(c_49211,plain,
    hd(app(sk3,app(sk3,app(sk3,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_48817]) ).

tcf(c_49212,plain,
    hd(app(sk3,app(sk3,app(sk3,nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_48817]) ).

tcf(c_49213,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk3,app(sk3,tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_48817]) ).

tcf(c_49214,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk3,app(sk3,app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_48817]) ).

tcf(c_49215,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk3,app(sk3,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_48817]) ).

tcf(c_49216,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_48817]) ).

tcf(c_49217,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_48817]) ).

tcf(c_49218,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_48817]) ).

tcf(c_49219,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_48817]) ).

tcf(c_49220,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(sk3,app(sk3,app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_48817]) ).

tcf(c_49221,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(sk3,app(sk3,app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_48817]) ).

tcf(c_49222,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(sk3,app(sk3,app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_48817]) ).

tcf(c_49223,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(sk3,app(sk3,app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_48817]) ).

tcf(c_49224,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_48817]) ).

tcf(c_49225,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_48817]) ).

tcf(c_49226,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_48817]) ).

tcf(c_49227,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_48817]) ).

tcf(c_49228,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_48817]) ).

tcf(c_49229,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_48817]) ).

tcf(c_49230,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_48817]) ).

tcf(c_49231,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_48817]) ).

tcf(c_49232,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_48817]) ).

tcf(c_49233,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_48817]) ).

tcf(c_49234,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_48817]) ).

tcf(c_49235,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_48817]) ).

tcf(c_49236,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_48817]) ).

tcf(c_49237,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_48817]) ).

tcf(c_49238,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_48817]) ).

tcf(c_49239,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_48817]) ).

tcf(c_49240,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_48817]) ).

tcf(c_49241,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_48817]) ).

tcf(c_49242,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_48817]) ).

tcf(c_49243,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_48817]) ).

tcf(c_49244,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_48817]) ).

tcf(c_49245,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_48817]) ).

tcf(c_49246,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_48817]) ).

tcf(c_49247,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_48817]) ).

tcf(c_49248,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_48817]) ).

tcf(c_49249,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_48817]) ).

tcf(c_49250,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_48817]) ).

tcf(c_49251,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_48817]) ).

tcf(c_49465,plain,
    ( ssItem(hd(sk3))
    | ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_47392,c_286]) ).

tcf(c_49497,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,sk3)))))
      | ( app(sk3,app(sk3,app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,sk3))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_49210,c_280]) ).

tcf(c_49498,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,sk3)))))
      | ( app(sk3,app(sk3,app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,sk3))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_49210,c_279]) ).

tcf(c_49514,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,sk4)))))
      | ( app(sk3,app(sk3,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,sk4))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_49211,c_280]) ).

tcf(c_49515,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,sk4)))))
      | ( app(sk3,app(sk3,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,sk4))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_49211,c_279]) ).

tcf(c_49543,plain,
    hd(app(sk3,app(sk3,app(sk4,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_48818]) ).

tcf(c_49544,plain,
    hd(app(sk3,app(sk3,app(sk4,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_48818]) ).

tcf(c_49545,plain,
    hd(app(sk3,app(sk3,app(sk4,nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_48818]) ).

tcf(c_49546,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk3,app(sk4,tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_48818]) ).

tcf(c_49547,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk3,app(sk4,app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_48818]) ).

tcf(c_49548,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk3,app(sk4,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_48818]) ).

tcf(c_49549,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_48818]) ).

tcf(c_49551,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_48818]) ).

tcf(c_49553,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(sk3,app(sk4,app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_48818]) ).

tcf(c_49554,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(sk3,app(sk4,app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_48818]) ).

tcf(c_49555,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(sk3,app(sk4,app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_48818]) ).

tcf(c_49556,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(sk3,app(sk4,app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_48818]) ).

tcf(c_49558,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_48818]) ).

tcf(c_49559,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_48818]) ).

tcf(c_49560,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_48818]) ).

tcf(c_49562,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_48818]) ).

tcf(c_49563,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_48818]) ).

tcf(c_49564,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_48818]) ).

tcf(c_49565,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_48818]) ).

tcf(c_49566,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_48818]) ).

tcf(c_49567,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_48818]) ).

tcf(c_49568,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_48818]) ).

tcf(c_49569,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_48818]) ).

tcf(c_49570,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_48818]) ).

tcf(c_49571,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_48818]) ).

tcf(c_49572,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_48818]) ).

tcf(c_49573,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_48818]) ).

tcf(c_49574,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_48818]) ).

tcf(c_49575,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_48818]) ).

tcf(c_49576,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_48818]) ).

tcf(c_49577,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_48818]) ).

tcf(c_49578,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_48818]) ).

tcf(c_49579,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_48818]) ).

tcf(c_49580,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_48818]) ).

tcf(c_49581,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_48818]) ).

tcf(c_49582,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_48818]) ).

tcf(c_49583,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_48818]) ).

tcf(c_49584,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_48818]) ).

tcf(c_49973,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,sk3)))))
      | ( app(sk3,app(sk3,app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,sk3))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_49543,c_280]) ).

tcf(c_49974,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,sk3)))))
      | ( app(sk3,app(sk3,app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,sk3))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_49543,c_279]) ).

tcf(c_49990,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,sk4)))))
      | ( app(sk3,app(sk3,app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,sk4))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_49544,c_280]) ).

tcf(c_49991,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,sk4)))))
      | ( app(sk3,app(sk3,app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,sk4))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_49544,c_279]) ).

tcf(c_50007,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3))))))
      | ( app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_49216,c_280]) ).

tcf(c_50008,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3))))))
      | ( app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_49216,c_279]) ).

tcf(c_50024,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))))
      | ( app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_49217,c_280]) ).

tcf(c_50025,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))))
      | ( app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_49217,c_279]) ).

tcf(c_50042,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_9166,c_255]) ).

tcf(c_50043,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_9166,c_254]) ).

tcf(c_50044,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_9166,c_272]) ).

tcf(c_50045,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != app(app(sk4,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_9166,c_270]) ).

tcf(c_50046,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),sk3))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != app(X0,cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_9166,c_269]) ).

tcf(c_50047,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(app(app(sk4,sk4),cons(hd(sk4),sk3)),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_9166,c_300]) ).

tcf(c_50048,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(app(app(sk4,sk4),cons(hd(sk4),sk3)),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_9166,c_287]) ).

tcf(c_50049,plain,
    ( ( cons(hd(sk4),sk3) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9166,c_9527]) ).

tcf(c_50050,plain,
    ( ( cons(hd(sk4),sk3) = sk3 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk3))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_9166,c_9248]) ).

tcf(c_50051,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50044,c_4358]) ).

tcf(c_50058,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50043,c_4430,c_4358]) ).

tcf(c_50061,plain,
    ( ( cons(hd(sk4),sk3) = sk3 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50050,c_4358]) ).

tcf(c_50065,plain,
    ( ( cons(hd(sk4),sk3) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50049,c_4358]) ).

tcf(c_50069,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != app(X0,cons(hd(sk4),sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50046,c_4358]) ).

tcf(c_50074,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) != app(app(sk4,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50045,c_4358]) ).

tcf(c_50079,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_50048,c_9166]) ).

tcf(c_50080,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50079,c_246,c_4059]) ).

tcf(c_50087,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk3)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_50047,c_9166]) ).

tcf(c_50088,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50087,c_246,c_4059]) ).

tcf(c_50099,plain,
    ssList(app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(global_subsumption_just,[status(thm)],[c_50051,c_247,c_20236,c_50051]) ).

tcf(c_50101,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_18185]) ).

tcf(c_50102,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_16330]) ).

tcf(c_50103,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_15966]) ).

tcf(c_50104,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_15593]) ).

tcf(c_50105,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),nil),X0) = app(app(sk4,app(sk4,cons(hd(sk4),sk3))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_4541]) ).

tcf(c_50106,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3154]) ).

tcf(c_50107,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_4037]) ).

tcf(c_50108,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3952]) ).

tcf(c_50109,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)) = app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3050]) ).

tcf(c_50110,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0),nil) = app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3049]) ).

tcf(c_50111,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4),X0) = app(app(sk4,app(sk4,cons(hd(sk4),sk3))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_4540]) ).

tcf(c_50112,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk3),X0) = app(app(sk4,app(sk4,cons(hd(sk4),sk3))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_4539]) ).

tcf(c_50113,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk4,cons(hd(sk4),sk3)))),X0) = app(X1,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_271]) ).

tcf(c_50114,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(cons(X1,X0),app(sk4,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_266]) ).

tcf(c_50115,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))),X0) = tl(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_274]) ).

tcf(c_50116,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_283]) ).

tcf(c_50117,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_48818]) ).

tcf(c_50118,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_48817]) ).

tcf(c_50119,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_18184]) ).

tcf(c_50120,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_17287]) ).

tcf(c_50121,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_16680]) ).

tcf(c_50122,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_16670]) ).

tcf(c_50123,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_16331]) ).

tcf(c_50124,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_45260]) ).

tcf(c_50125,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_45259]) ).

tcf(c_50126,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_45258]) ).

tcf(c_50127,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_16329]) ).

tcf(c_50128,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_15967]) ).

tcf(c_50129,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_40467]) ).

tcf(c_50130,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_40466]) ).

tcf(c_50131,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_40465]) ).

tcf(c_50132,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_15965]) ).

tcf(c_50133,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_15594]) ).

tcf(c_50134,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_37606]) ).

tcf(c_50135,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_37605]) ).

tcf(c_50136,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_37604]) ).

tcf(c_50137,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_15592]) ).

tcf(c_50138,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_18000]) ).

tcf(c_50139,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_17998]) ).

tcf(c_50140,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_17997]) ).

tcf(c_50141,plain,
    app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_50099,c_35790]) ).

tcf(c_50142,plain,
    app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_50099,c_35787]) ).

tcf(c_50143,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),nil)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_4463]) ).

tcf(c_50144,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3155]) ).

tcf(c_50145,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_33403]) ).

tcf(c_50146,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_33402]) ).

tcf(c_50147,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_33401]) ).

tcf(c_50148,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),tl(sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_32111]) ).

tcf(c_50149,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),tl(sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_32098]) ).

tcf(c_50150,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_15410]) ).

tcf(c_50151,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_15408]) ).

tcf(c_50152,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_15407]) ).

tcf(c_50153,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3153]) ).

tcf(c_50154,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_4038]) ).

tcf(c_50155,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_17993]) ).

tcf(c_50156,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_17992]) ).

tcf(c_50157,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_17991]) ).

tcf(c_50158,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_4036]) ).

tcf(c_50159,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3953]) ).

tcf(c_50160,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_15403]) ).

tcf(c_50161,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_15402]) ).

tcf(c_50162,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_15401]) ).

tcf(c_50163,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3951]) ).

tcf(c_50164,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil)) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3423]) ).

tcf(c_50165,plain,
    app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_50099,c_13452]) ).

tcf(c_50166,plain,
    app(app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil) = app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_50099,c_12354]) ).

tcf(c_50167,plain,
    app(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_50099,c_12353]) ).

tcf(c_50168,plain,
    app(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_50099,c_12352]) ).

tcf(c_50169,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_50099,c_3199]) ).

tcf(c_50170,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3066]) ).

tcf(c_50171,plain,
    app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_50099,c_8061]) ).

tcf(c_50172,plain,
    app(app(sk4,sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))) = app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_50099,c_8048]) ).

tcf(c_50173,plain,
    app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_50099,c_5745]) ).

tcf(c_50174,plain,
    app(app(sk3,sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))) = app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_50099,c_8047]) ).

tcf(c_50175,plain,
    app(app(sk4,sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))) = app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_50099,c_5738]) ).

tcf(c_50176,plain,
    app(app(sk3,sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))) = app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_50099,c_5737]) ).

tcf(c_50177,plain,
    app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))) = tl(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_50099,c_4136]) ).

tcf(c_50178,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_4462]) ).

tcf(c_50179,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk3)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_4461]) ).

tcf(c_50180,plain,
    app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))) = tl(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))),
    inference(superposition,[status(thm)],[c_50099,c_4284]) ).

tcf(c_50181,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_4027]) ).

tcf(c_50183,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3019]) ).

tcf(c_50184,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3452]) ).

tcf(c_50185,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3444]) ).

tcf(c_50186,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil) = tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3065]) ).

tcf(c_50187,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4)) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3215]) ).

tcf(c_50188,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3)) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3207]) ).

tcf(c_50189,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk4,cons(hd(sk4),sk3)))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_253]) ).

tcf(c_50190,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(sk4,app(sk4,cons(hd(sk4),sk3))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_275]) ).

tcf(c_50191,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3018]) ).

tcf(c_50192,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_50099,c_3191]) ).

tcf(c_50193,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_50099,c_3183]) ).

tcf(c_50194,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_284]) ).

tcf(c_50195,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(sk4,app(sk4,cons(hd(sk4),sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_276]) ).

tcf(c_50196,plain,
    app(app(sk4,app(sk4,cons(hd(sk4),sk3))),nil) = app(sk4,app(sk4,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_50099,c_258]) ).

tcf(c_50197,plain,
    app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3)))) = app(sk4,app(sk4,cons(hd(sk4),sk3))),
    inference(superposition,[status(thm)],[c_50099,c_257]) ).

tcf(c_50294,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_50116,c_15969]) ).

tcf(c_50303,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(sk4,app(sk4,cons(hd(sk4),sk3))) ) ),
    inference(light_normalisation,[status(thm)],[c_50190,c_15969]) ).

tcf(c_50461,plain,
    hd(app(sk3,app(sk3,app(nil,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_48819]) ).

tcf(c_50462,plain,
    hd(app(sk3,app(sk3,app(nil,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_48819]) ).

tcf(c_50463,plain,
    hd(app(sk3,app(sk3,app(nil,nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_48819]) ).

tcf(c_50464,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk3,app(nil,tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_48819]) ).

tcf(c_50465,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk3,app(nil,app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_48819]) ).

tcf(c_50466,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk3,app(nil,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_48819]) ).

tcf(c_50467,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk3),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_48819]) ).

tcf(c_50468,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_48819]) ).

tcf(c_50469,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk3),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_48819]) ).

tcf(c_50470,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_48819]) ).

tcf(c_50471,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(sk3,app(nil,app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_48819]) ).

tcf(c_50472,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(sk3,app(nil,app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_48819]) ).

tcf(c_50473,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(sk3,app(nil,app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_48819]) ).

tcf(c_50474,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(sk3,app(nil,app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_48819]) ).

tcf(c_50475,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_48819]) ).

tcf(c_50476,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_48819]) ).

tcf(c_50477,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_48819]) ).

tcf(c_50478,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_48819]) ).

tcf(c_50479,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_48819]) ).

tcf(c_50480,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_48819]) ).

tcf(c_50481,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_48819]) ).

tcf(c_50482,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_48819]) ).

tcf(c_50483,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_48819]) ).

tcf(c_50484,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_48819]) ).

tcf(c_50485,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_48819]) ).

tcf(c_50486,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_48819]) ).

tcf(c_50487,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_48819]) ).

tcf(c_50488,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_48819]) ).

tcf(c_50489,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_48819]) ).

tcf(c_50490,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_48819]) ).

tcf(c_50491,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_48819]) ).

tcf(c_50492,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_48819]) ).

tcf(c_50493,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_48819]) ).

tcf(c_50494,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_48819]) ).

tcf(c_50495,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_48819]) ).

tcf(c_50496,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_48819]) ).

tcf(c_50497,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_48819]) ).

tcf(c_50498,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_48819]) ).

tcf(c_50499,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_48819]) ).

tcf(c_50500,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_48819]) ).

tcf(c_50501,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_48819]) ).

tcf(c_50502,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_48819]) ).

tcf(c_50503,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_48819]) ).

tcf(c_50642,plain,
    app(sk4,app(sk4,cons(hd(sk4),sk3))) != nil,
    inference(global_subsumption_just,[status(thm)],[c_50058,c_247,c_20236,c_50058]) ).

tcf(c_50648,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,app(sk4,cons(hd(sk4),sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_50194]) ).

tcf(c_50649,plain,
    hd(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_50194]) ).

tcf(c_50650,plain,
    hd(cons(hd(sk3),app(sk4,app(sk4,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_50194]) ).

tcf(c_50655,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3))))))
      | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_40373,c_280]) ).

tcf(c_50656,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3))))))
      | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_40373,c_279]) ).

tcf(c_50709,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4))))))
      | ( app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_49218,c_280]) ).

tcf(c_50710,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4))))))
      | ( app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_49218,c_279]) ).

tcf(c_50726,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))))
      | ( app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_49219,c_280]) ).

tcf(c_50727,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))))
      | ( app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_49219,c_279]) ).

tcf(c_50743,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_49549,c_280]) ).

tcf(c_50744,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_49549,c_279]) ).

tcf(c_50770,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_50080,c_247,c_20236,c_50080]) ).

tcf(c_50771,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(renaming,[status(thm)],[c_50770]) ).

tcf(c_50783,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk3))))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_50771]) ).

tcf(c_50784,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk3))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_50771]) ).

tcf(c_50785,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_50771]) ).

tcf(c_50786,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_50771]) ).

tcf(c_50787,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50783,c_50099]) ).

tcf(c_50793,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_50785,c_3365]) ).

tcf(c_50794,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50793,c_4059]) ).

tcf(c_50799,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk3))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50784,c_10117]) ).

tcf(c_50805,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_50786,c_39675]) ).

tcf(c_50806,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50805,c_4059]) ).

tcf(c_50868,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_50088,c_247,c_20236,c_50088]) ).

tcf(c_50869,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(renaming,[status(thm)],[c_50868]) ).

tcf(c_50881,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk3))))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_50869]) ).

tcf(c_50882,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk3))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_50869]) ).

tcf(c_50883,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_50869]) ).

tcf(c_50884,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_50869]) ).

tcf(c_50885,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50881,c_50099]) ).

tcf(c_50891,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_50883,c_3365]) ).

tcf(c_50892,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50891,c_4059]) ).

tcf(c_50897,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),sk3))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50882,c_10117]) ).

tcf(c_50903,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_50884,c_39675]) ).

tcf(c_50904,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50903,c_4059]) ).

tcf(c_50911,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_49551,c_280]) ).

tcf(c_50912,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_49551,c_279]) ).

tcf(c_50928,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_50181,c_280]) ).

tcf(c_50929,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_50181,c_279]) ).

tcf(c_51006,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48444,c_280]) ).

tcf(c_51007,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48444,c_279]) ).

tcf(c_51023,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48445,c_280]) ).

tcf(c_51024,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48445,c_279]) ).

tcf(c_51040,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48446,c_280]) ).

tcf(c_51041,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48446,c_279]) ).

tcf(c_51057,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48447,c_280]) ).

tcf(c_51058,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48447,c_279]) ).

tcf(c_51075,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_9167,c_255]) ).

tcf(c_51076,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_9167,c_254]) ).

tcf(c_51077,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_9167,c_272]) ).

tcf(c_51078,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != app(app(sk4,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_9167,c_270]) ).

tcf(c_51079,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != app(X0,cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_9167,c_269]) ).

tcf(c_51080,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(app(app(sk4,sk4),cons(hd(sk4),sk4)),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_9167,c_300]) ).

tcf(c_51081,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(app(app(sk4,sk4),cons(hd(sk4),sk4)),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_9167,c_287]) ).

tcf(c_51082,plain,
    ( ( cons(hd(sk4),sk4) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9167,c_9527]) ).

tcf(c_51083,plain,
    ( ( cons(hd(sk4),sk4) = sk3 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_9167,c_9248]) ).

tcf(c_51084,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_51077,c_4223]) ).

tcf(c_51091,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_51076,c_4281,c_4223]) ).

tcf(c_51094,plain,
    ( ( cons(hd(sk4),sk4) = sk3 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_51083,c_4223]) ).

tcf(c_51098,plain,
    ( ( cons(hd(sk4),sk4) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_51082,c_4223]) ).

tcf(c_51102,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != app(X0,cons(hd(sk4),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_51079,c_4223]) ).

tcf(c_51107,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) != app(app(sk4,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_51078,c_4223]) ).

tcf(c_51112,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_51081,c_9167]) ).

tcf(c_51113,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_51112,c_247,c_4059]) ).

tcf(c_51120,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssList(sk4)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_51080,c_9167]) ).

tcf(c_51121,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_51120,c_247,c_4059]) ).

tcf(c_51167,plain,
    ssList(app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(global_subsumption_just,[status(thm)],[c_51084,c_247,c_20236,c_51084]) ).

tcf(c_51169,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_18185]) ).

tcf(c_51170,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_16330]) ).

tcf(c_51171,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_15966]) ).

tcf(c_51172,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_15593]) ).

tcf(c_51173,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),nil),X0) = app(app(sk4,app(sk4,cons(hd(sk4),sk4))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_4541]) ).

tcf(c_51174,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3154]) ).

tcf(c_51175,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_4037]) ).

tcf(c_51176,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3952]) ).

tcf(c_51177,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)) = app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3050]) ).

tcf(c_51178,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0),nil) = app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3049]) ).

tcf(c_51179,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4),X0) = app(app(sk4,app(sk4,cons(hd(sk4),sk4))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_4540]) ).

tcf(c_51180,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk3),X0) = app(app(sk4,app(sk4,cons(hd(sk4),sk4))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_4539]) ).

tcf(c_51181,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk4,cons(hd(sk4),sk4)))),X0) = app(X1,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_271]) ).

tcf(c_51182,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(cons(X1,X0),app(sk4,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_266]) ).

tcf(c_51183,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))),X0) = tl(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_274]) ).

tcf(c_51184,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_283]) ).

tcf(c_51185,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_48819]) ).

tcf(c_51186,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_48818]) ).

tcf(c_51187,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_48817]) ).

tcf(c_51188,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_18184]) ).

tcf(c_51189,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_17287]) ).

tcf(c_51190,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_16680]) ).

tcf(c_51191,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_16670]) ).

tcf(c_51192,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_16331]) ).

tcf(c_51193,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_45260]) ).

tcf(c_51194,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_45259]) ).

tcf(c_51195,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_45258]) ).

tcf(c_51196,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_16329]) ).

tcf(c_51197,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_15967]) ).

tcf(c_51198,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_40467]) ).

tcf(c_51199,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_40466]) ).

tcf(c_51200,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_40465]) ).

tcf(c_51201,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_15965]) ).

tcf(c_51202,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_15594]) ).

tcf(c_51203,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_37606]) ).

tcf(c_51204,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_37605]) ).

tcf(c_51205,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_37604]) ).

tcf(c_51206,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_15592]) ).

tcf(c_51207,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_18000]) ).

tcf(c_51208,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_17998]) ).

tcf(c_51209,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_17997]) ).

tcf(c_51210,plain,
    app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_51167,c_35790]) ).

tcf(c_51211,plain,
    app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_51167,c_35787]) ).

tcf(c_51212,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),nil)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_4463]) ).

tcf(c_51213,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3155]) ).

tcf(c_51214,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_33403]) ).

tcf(c_51215,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_33402]) ).

tcf(c_51216,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_33401]) ).

tcf(c_51217,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),tl(sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_32111]) ).

tcf(c_51218,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),tl(sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_32098]) ).

tcf(c_51219,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_15410]) ).

tcf(c_51220,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_15408]) ).

tcf(c_51221,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_15407]) ).

tcf(c_51222,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3153]) ).

tcf(c_51223,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_4038]) ).

tcf(c_51224,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_17993]) ).

tcf(c_51225,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_17992]) ).

tcf(c_51226,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_17991]) ).

tcf(c_51227,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_4036]) ).

tcf(c_51228,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3953]) ).

tcf(c_51229,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_15403]) ).

tcf(c_51230,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_15402]) ).

tcf(c_51231,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_15401]) ).

tcf(c_51232,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3951]) ).

tcf(c_51233,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil)) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3423]) ).

tcf(c_51234,plain,
    app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_51167,c_13452]) ).

tcf(c_51235,plain,
    app(app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil) = app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_51167,c_12354]) ).

tcf(c_51236,plain,
    app(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_51167,c_12353]) ).

tcf(c_51237,plain,
    app(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_51167,c_12352]) ).

tcf(c_51238,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_51167,c_3199]) ).

tcf(c_51239,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3066]) ).

tcf(c_51240,plain,
    app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_51167,c_8061]) ).

tcf(c_51241,plain,
    app(app(sk4,sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))) = app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_51167,c_8048]) ).

tcf(c_51242,plain,
    app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_51167,c_5745]) ).

tcf(c_51243,plain,
    app(app(sk3,sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))) = app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_51167,c_8047]) ).

tcf(c_51244,plain,
    app(app(sk4,sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))) = app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_51167,c_5738]) ).

tcf(c_51245,plain,
    app(app(sk3,sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))) = app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_51167,c_5737]) ).

tcf(c_51246,plain,
    app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))) = tl(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_51167,c_4136]) ).

tcf(c_51247,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_4462]) ).

tcf(c_51248,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk3)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_4461]) ).

tcf(c_51249,plain,
    app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))) = tl(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))),
    inference(superposition,[status(thm)],[c_51167,c_4284]) ).

tcf(c_51250,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_4027]) ).

tcf(c_51252,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3019]) ).

tcf(c_51253,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3452]) ).

tcf(c_51254,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3444]) ).

tcf(c_51255,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil) = tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3065]) ).

tcf(c_51256,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4)) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3215]) ).

tcf(c_51257,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3)) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3207]) ).

tcf(c_51258,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk4,cons(hd(sk4),sk4)))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_253]) ).

tcf(c_51259,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(sk4,app(sk4,cons(hd(sk4),sk4))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_275]) ).

tcf(c_51260,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3018]) ).

tcf(c_51261,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_51167,c_3191]) ).

tcf(c_51262,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_51167,c_3183]) ).

tcf(c_51263,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_284]) ).

tcf(c_51264,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(sk4,app(sk4,cons(hd(sk4),sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_276]) ).

tcf(c_51265,plain,
    app(app(sk4,app(sk4,cons(hd(sk4),sk4))),nil) = app(sk4,app(sk4,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_51167,c_258]) ).

tcf(c_51266,plain,
    app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4)))) = app(sk4,app(sk4,cons(hd(sk4),sk4))),
    inference(superposition,[status(thm)],[c_51167,c_257]) ).

tcf(c_51363,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_51184,c_15971]) ).

tcf(c_51372,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(sk4,app(sk4,cons(hd(sk4),sk4))) ) ),
    inference(light_normalisation,[status(thm)],[c_51259,c_15971]) ).

tcf(c_51895,plain,
    app(sk4,app(sk4,cons(hd(sk4),sk4))) != nil,
    inference(global_subsumption_just,[status(thm)],[c_51091,c_247,c_20236,c_51091]) ).

tcf(c_51901,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,app(sk4,cons(hd(sk4),sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_51263]) ).

tcf(c_51902,plain,
    hd(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_51263]) ).

tcf(c_51903,plain,
    hd(cons(hd(sk3),app(sk4,app(sk4,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_51263]) ).

tcf(c_51913,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,sk3)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_18186]) ).

tcf(c_51914,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,sk4)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_18186]) ).

tcf(c_51915,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,nil)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_18186]) ).

tcf(c_51916,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk3,cons(X1,tl(X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18186]) ).

tcf(c_51917,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X2,app(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18186]) ).

tcf(c_51918,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X2,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18186]) ).

tcf(c_51919,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk3),sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_18186]) ).

tcf(c_51920,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk4),sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_18186]) ).

tcf(c_51921,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk3),sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_18186]) ).

tcf(c_51922,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk4),sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_18186]) ).

tcf(c_51923,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk3,app(sk3,cons(X0,app(tl(sk3),sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18186]) ).

tcf(c_51924,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk3,app(sk3,cons(X0,app(tl(sk3),sk4))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18186]) ).

tcf(c_51925,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk3,app(sk3,cons(X0,app(tl(sk4),sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18186]) ).

tcf(c_51926,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk3,app(sk3,cons(X0,app(tl(sk4),sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_18186]) ).

tcf(c_51927,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_18186]) ).

tcf(c_51928,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18186]) ).

tcf(c_51929,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18186]) ).

tcf(c_51930,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18186]) ).

tcf(c_51931,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_18186]) ).

tcf(c_51932,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18186]) ).

tcf(c_51933,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18186]) ).

tcf(c_51934,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18186]) ).

tcf(c_51935,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18186]) ).

tcf(c_51936,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18186]) ).

tcf(c_51937,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_18186]) ).

tcf(c_51938,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_18186]) ).

tcf(c_51939,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18186]) ).

tcf(c_51940,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18186]) ).

tcf(c_51941,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18186]) ).

tcf(c_51942,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_18186]) ).

tcf(c_51943,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_18186]) ).

tcf(c_51944,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_18186]) ).

tcf(c_51945,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_18186]) ).

tcf(c_51946,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18186]) ).

tcf(c_51947,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18186]) ).

tcf(c_51948,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_18186]) ).

tcf(c_51949,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_18186]) ).

tcf(c_51950,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_18186]) ).

tcf(c_51951,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_18186]) ).

tcf(c_51952,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18186]) ).

tcf(c_51953,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18186]) ).

tcf(c_51954,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18186]) ).

tcf(c_51955,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_18186]) ).

tcf(c_51956,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_18186]) ).

tcf(c_52321,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_51250,c_280]) ).

tcf(c_52322,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_51250,c_279]) ).

tcf(c_52341,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk3,cons(hd(X0),sk3)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_51913]) ).

tcf(c_52380,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk3,cons(hd(X0),sk4)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_51914]) ).

tcf(c_52390,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk3,cons(hd(X0),nil)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_51915]) ).

tcf(c_52391,plain,
    hd(app(sk3,app(sk3,cons(hd(sk4),nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4059,c_51915]) ).

tcf(c_52392,plain,
    hd(app(sk3,app(sk3,cons(hd(sk3),nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_51915]) ).

tcf(c_52396,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_51113,c_247,c_20236,c_51113]) ).

tcf(c_52397,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(renaming,[status(thm)],[c_52396]) ).

tcf(c_52409,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk4))))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_52397]) ).

tcf(c_52410,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk3))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_52397]) ).

tcf(c_52411,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_52397]) ).

tcf(c_52412,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_52397]) ).

tcf(c_52413,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52409,c_51167]) ).

tcf(c_52419,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_52411,c_3365]) ).

tcf(c_52420,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52419,c_4059]) ).

tcf(c_52425,plain,
    ( lt(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk3))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52410,c_10117]) ).

tcf(c_52431,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_52412,c_39675]) ).

tcf(c_52432,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52431,c_4059]) ).

tcf(c_52450,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_51121,c_247,c_20236,c_51121]) ).

tcf(c_52451,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(renaming,[status(thm)],[c_52450]) ).

tcf(c_52463,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk4))))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_272,c_52451]) ).

tcf(c_52464,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk3))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_3359,c_52451]) ).

tcf(c_52465,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_3365,c_52451]) ).

tcf(c_52466,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39675,c_52451]) ).

tcf(c_52467,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(cons(X0,X1))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52463,c_51167]) ).

tcf(c_52473,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_52465,c_3365]) ).

tcf(c_52474,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(sk4))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52473,c_4059]) ).

tcf(c_52479,plain,
    ( leq(hd(sk4),hd(sk3))
    | ( sk3 = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),sk3))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk3),tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52464,c_10117]) ).

tcf(c_52485,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(light_normalisation,[status(thm)],[c_52466,c_39675]) ).

tcf(c_52486,plain,
    ( leq(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52485,c_4059]) ).

tcf(c_52493,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48448,c_280]) ).

tcf(c_52494,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48448,c_279]) ).

tcf(c_52520,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48449,c_280]) ).

tcf(c_52521,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48449,c_279]) ).

tcf(c_52548,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48450,c_280]) ).

tcf(c_52549,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48450,c_279]) ).

tcf(c_52577,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48451,c_280]) ).

tcf(c_52578,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48451,c_279]) ).

tcf(c_52599,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_9168,c_255]) ).

tcf(c_52600,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_9168,c_254]) ).

tcf(c_52601,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_9168,c_272]) ).

tcf(c_52602,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(app(sk4,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_9168,c_270]) ).

tcf(c_52603,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(X0,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_9168,c_269]) ).

tcf(c_52604,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(app(sk4,sk4),cons(hd(sk4),app(sk3,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_9168,c_300]) ).

tcf(c_52605,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(app(sk4,sk4),cons(hd(sk4),app(sk3,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_9168,c_287]) ).

tcf(c_52606,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9168,c_9527]) ).

tcf(c_52607,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk3 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_9168,c_9248]) ).

tcf(c_52608,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk4,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52601,c_5886]) ).

tcf(c_52615,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52600,c_5891,c_5886]) ).

tcf(c_52618,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52607,c_5887,c_5886]) ).

tcf(c_52621,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52606,c_5886]) ).

tcf(c_52625,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(X0,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52603,c_5886]) ).

tcf(c_52630,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(app(sk4,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52602,c_5886]) ).

tcf(c_52635,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_52605,c_9168]) ).

tcf(c_52636,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52635,c_4059]) ).

tcf(c_52644,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_52604,c_9168]) ).

tcf(c_52645,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_52644,c_4059]) ).

tcf(c_52696,plain,
    ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(global_subsumption_just,[status(thm)],[c_52608,c_247,c_20236,c_52608]) ).

tcf(c_52698,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_18185]) ).

tcf(c_52699,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_16330]) ).

tcf(c_52700,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_15966]) ).

tcf(c_52701,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_15593]) ).

tcf(c_52702,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),nil),X0) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_4541]) ).

tcf(c_52703,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3154]) ).

tcf(c_52704,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_4037]) ).

tcf(c_52705,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3952]) ).

tcf(c_52706,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3050]) ).

tcf(c_52707,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0),nil) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3049]) ).

tcf(c_52708,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),sk4),X0) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_4540]) ).

tcf(c_52709,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),sk3),X0) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_4539]) ).

tcf(c_52710,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),X0) = app(X1,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_271]) ).

tcf(c_52711,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(cons(X1,X0),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_266]) ).

tcf(c_52712,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),X0) = tl(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_274]) ).

tcf(c_52713,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_283]) ).

tcf(c_52714,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_18186]) ).

tcf(c_52715,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_48819]) ).

tcf(c_52716,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_48818]) ).

tcf(c_52717,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_48817]) ).

tcf(c_52718,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_18184]) ).

tcf(c_52719,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_17287]) ).

tcf(c_52720,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_16680]) ).

tcf(c_52721,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_16670]) ).

tcf(c_52722,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_16331]) ).

tcf(c_52723,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_45260]) ).

tcf(c_52724,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_45259]) ).

tcf(c_52725,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_45258]) ).

tcf(c_52726,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_16329]) ).

tcf(c_52727,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_15967]) ).

tcf(c_52728,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_40467]) ).

tcf(c_52729,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_40466]) ).

tcf(c_52730,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_40465]) ).

tcf(c_52731,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_15965]) ).

tcf(c_52732,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_15594]) ).

tcf(c_52733,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_37606]) ).

tcf(c_52734,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_37605]) ).

tcf(c_52735,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_37604]) ).

tcf(c_52736,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_15592]) ).

tcf(c_52737,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_18000]) ).

tcf(c_52738,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_17998]) ).

tcf(c_52739,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_17997]) ).

tcf(c_52740,plain,
    app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_52696,c_35790]) ).

tcf(c_52741,plain,
    app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_52696,c_35787]) ).

tcf(c_52742,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),nil)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_4463]) ).

tcf(c_52743,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3155]) ).

tcf(c_52744,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_33403]) ).

tcf(c_52745,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_33402]) ).

tcf(c_52746,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_33401]) ).

tcf(c_52747,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_32111]) ).

tcf(c_52748,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_32098]) ).

tcf(c_52749,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_15410]) ).

tcf(c_52750,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_15408]) ).

tcf(c_52751,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_15407]) ).

tcf(c_52752,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3153]) ).

tcf(c_52753,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_4038]) ).

tcf(c_52754,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_17993]) ).

tcf(c_52755,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_17992]) ).

tcf(c_52756,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_17991]) ).

tcf(c_52757,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_4036]) ).

tcf(c_52758,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3953]) ).

tcf(c_52759,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_15403]) ).

tcf(c_52760,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_15402]) ).

tcf(c_52761,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_15401]) ).

tcf(c_52762,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3951]) ).

tcf(c_52763,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3423]) ).

tcf(c_52764,plain,
    app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_52696,c_13452]) ).

tcf(c_52765,plain,
    app(app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_52696,c_12354]) ).

tcf(c_52766,plain,
    app(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_52696,c_12353]) ).

tcf(c_52767,plain,
    app(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_52696,c_12352]) ).

tcf(c_52768,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_52696,c_3199]) ).

tcf(c_52769,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3066]) ).

tcf(c_52770,plain,
    app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_52696,c_8061]) ).

tcf(c_52771,plain,
    app(app(sk4,sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_52696,c_8048]) ).

tcf(c_52772,plain,
    app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_52696,c_5745]) ).

tcf(c_52773,plain,
    app(app(sk3,sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_52696,c_8047]) ).

tcf(c_52774,plain,
    app(app(sk4,sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_52696,c_5738]) ).

tcf(c_52775,plain,
    app(app(sk3,sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_52696,c_5737]) ).

tcf(c_52776,plain,
    app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = tl(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_52696,c_4136]) ).

tcf(c_52777,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),sk4)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_4462]) ).

tcf(c_52778,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),sk3)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_4461]) ).

tcf(c_52779,plain,
    app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = tl(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))),
    inference(superposition,[status(thm)],[c_52696,c_4284]) ).

tcf(c_52780,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_4027]) ).

tcf(c_52782,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3019]) ).

tcf(c_52783,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3452]) ).

tcf(c_52784,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3444]) ).

tcf(c_52785,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3065]) ).

tcf(c_52786,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3215]) ).

tcf(c_52787,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3207]) ).

tcf(c_52788,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_253]) ).

tcf(c_52789,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_275]) ).

tcf(c_52790,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3018]) ).

tcf(c_52791,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_52696,c_3191]) ).

tcf(c_52792,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_52696,c_3183]) ).

tcf(c_52793,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_284]) ).

tcf(c_52794,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_276]) ).

tcf(c_52795,plain,
    app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),nil) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_52696,c_258]) ).

tcf(c_52796,plain,
    app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),
    inference(superposition,[status(thm)],[c_52696,c_257]) ).

tcf(c_52895,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_52713,c_15972]) ).

tcf(c_52904,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) ) ),
    inference(light_normalisation,[status(thm)],[c_52789,c_15972]) ).

tcf(c_53318,plain,
    ( ( sk3 = nil )
    | ( hd(app(sk3,app(sk4,tl(sk3)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_18496]) ).

tcf(c_53319,plain,
    ( ( sk4 = nil )
    | ( hd(app(sk3,app(sk4,tl(sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_247,c_18496]) ).

tcf(c_53321,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk3,app(sk4,tl(tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18496]) ).

tcf(c_53322,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk3,app(sk4,tl(app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18496]) ).

tcf(c_53323,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk3,app(sk4,tl(cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18496]) ).

tcf(c_53324,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk3),sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_18496]) ).

tcf(c_53325,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk4),sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_18496]) ).

tcf(c_53326,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk3),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_18496]) ).

tcf(c_53327,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_18496]) ).

tcf(c_53328,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18496]) ).

tcf(c_53329,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18496]) ).

tcf(c_53330,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18496]) ).

tcf(c_53331,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_18496]) ).

tcf(c_53332,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_18496]) ).

tcf(c_53333,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18496]) ).

tcf(c_53334,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18496]) ).

tcf(c_53335,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18496]) ).

tcf(c_53336,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_18496]) ).

tcf(c_53337,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18496]) ).

tcf(c_53338,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18496]) ).

tcf(c_53339,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18496]) ).

tcf(c_53340,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18496]) ).

tcf(c_53341,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18496]) ).

tcf(c_53342,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_18496]) ).

tcf(c_53343,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_18496]) ).

tcf(c_53344,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18496]) ).

tcf(c_53345,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18496]) ).

tcf(c_53346,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18496]) ).

tcf(c_53347,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_18496]) ).

tcf(c_53348,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_18496]) ).

tcf(c_53349,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_18496]) ).

tcf(c_53350,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_18496]) ).

tcf(c_53351,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18496]) ).

tcf(c_53352,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18496]) ).

tcf(c_53353,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_18496]) ).

tcf(c_53354,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_18496]) ).

tcf(c_53355,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_18496]) ).

tcf(c_53356,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_18496]) ).

tcf(c_53357,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18496]) ).

tcf(c_53358,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18496]) ).

tcf(c_53359,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_18496]) ).

tcf(c_53360,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18496]) ).

tcf(c_53361,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_18496]) ).

tcf(c_53362,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_18496]) ).

tcf(c_53363,plain,
    hd(app(sk3,app(sk4,tl(sk4)))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53319,c_1243]) ).

tcf(c_53374,plain,
    hd(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53350,c_20706]) ).

tcf(c_53375,plain,
    hd(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53349,c_17701]) ).

tcf(c_53376,plain,
    hd(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53348,c_19513]) ).

tcf(c_53377,plain,
    hd(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53347,c_16926]) ).

tcf(c_53378,plain,
    hd(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53343,c_10611]) ).

tcf(c_53379,plain,
    hd(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53342,c_10190]) ).

tcf(c_53380,plain,
    hd(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53336,c_7545]) ).

tcf(c_53381,plain,
    hd(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53332,c_5891]) ).

tcf(c_53417,plain,
    hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53356,c_44126]) ).

tcf(c_53418,plain,
    hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53355,c_43038]) ).

tcf(c_53419,plain,
    hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53354,c_51895]) ).

tcf(c_53420,plain,
    hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_53353,c_50642]) ).

tcf(c_53636,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(sk4)))))
      | ( app(sk3,app(sk4,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(sk4))))
      | ~ ssList(app(sk3,app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_53363,c_280]) ).

tcf(c_53637,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(sk4)))))
      | ( app(sk3,app(sk4,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(sk4))))
      | ~ ssList(app(sk3,app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_53363,c_279]) ).

tcf(c_53652,plain,
    hd(app(sk3,app(sk4,tl(sk3)))) = hd(sk3),
    inference(global_subsumption_just,[status(thm)],[c_53318,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_53318]) ).

tcf(c_53655,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(sk3)))))
      | ( app(sk3,app(sk4,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(sk3))))
      | ~ ssList(app(sk3,app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_53652,c_280]) ).

tcf(c_53656,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(sk3)))))
      | ( app(sk3,app(sk4,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(sk3))))
      | ~ ssList(app(sk3,app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_53652,c_279]) ).

tcf(c_53672,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),nil)))))
      | ( app(sk3,app(sk3,cons(hd(sk4),nil))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),nil))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_52391,c_280]) ).

tcf(c_53673,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk4),nil)))))
      | ( app(sk3,app(sk3,cons(hd(sk4),nil))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk4),nil))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_52391,c_279]) ).

tcf(c_53689,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),nil)))))
      | ( app(sk3,app(sk3,cons(hd(sk3),nil))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),nil))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_52392,c_280]) ).

tcf(c_53690,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),nil)))))
      | ( app(sk3,app(sk3,cons(hd(sk3),nil))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk3),nil))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_52392,c_279]) ).

tcf(c_53713,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( app(sk3,cons(hd(sk3),sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_13173,c_270]) ).

tcf(c_53714,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( app(X0,app(sk3,cons(hd(sk3),sk4))) != app(sk3,cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_13173,c_269]) ).

tcf(c_53715,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( app(X0,app(sk3,cons(hd(sk3),sk4))) != app(sk3,cons(hd(sk3),sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53714,c_259]) ).

tcf(c_53720,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk3),sk4)))
      | ( app(sk3,cons(hd(sk3),sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53713,c_259]) ).

tcf(c_53726,plain,
    ( ssList(app(tl(sk4),cons(hd(sk3),sk4)))
    | ( app(sk4,cons(hd(sk3),sk4)) = nil )
    | ~ ssList(app(sk4,cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13177,c_278]) ).

tcf(c_53727,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk3),sk4)) = nil )
      | ( app(sk4,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( hd(app(sk4,cons(hd(sk3),sk4))) != hd(X0) )
      | ( app(tl(sk4),cons(hd(sk3),sk4)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_13177,c_273]) ).

tcf(c_53731,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk3),sk4)) = nil )
      | ( app(sk4,cons(hd(sk3),sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk3),sk4)))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),cons(hd(sk3),sk4)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_53727,c_13182]) ).

tcf(c_53740,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53374,c_280]) ).

tcf(c_53741,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53374,c_279]) ).

tcf(c_53757,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53375,c_280]) ).

tcf(c_53758,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53375,c_279]) ).

tcf(c_53774,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53376,c_280]) ).

tcf(c_53775,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53376,c_279]) ).

tcf(c_53791,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53377,c_280]) ).

tcf(c_53792,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53377,c_279]) ).

tcf(c_53808,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53378,c_280]) ).

tcf(c_53809,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53378,c_279]) ).

tcf(c_53861,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53379,c_280]) ).

tcf(c_53862,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53379,c_279]) ).

tcf(c_53878,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53380,c_280]) ).

tcf(c_53879,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53380,c_279]) ).

tcf(c_53895,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53381,c_280]) ).

tcf(c_53896,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53381,c_279]) ).

tcf(c_53913,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_9172,c_255]) ).

tcf(c_53914,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(superposition,[status(thm)],[c_9172,c_254]) ).

tcf(c_53915,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_9172,c_272]) ).

tcf(c_53916,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(app(sk4,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_9172,c_270]) ).

tcf(c_53917,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(X0,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_9172,c_269]) ).

tcf(c_53918,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(app(sk4,sk4),cons(hd(sk4),app(sk4,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_9172,c_300]) ).

tcf(c_53919,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(app(sk4,sk4),cons(hd(sk4),app(sk4,sk3))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_9172,c_287]) ).

tcf(c_53920,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_9172,c_9527]) ).

tcf(c_53921,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk3 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_9172,c_9248]) ).

tcf(c_53922,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk4,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53915,c_7540]) ).

tcf(c_53929,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53914,c_7545,c_7540]) ).

tcf(c_53932,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53921,c_7541,c_7540]) ).

tcf(c_53935,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53920,c_7540]) ).

tcf(c_53939,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(X0,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53917,c_7540]) ).

tcf(c_53944,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(app(sk4,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53916,c_7540]) ).

tcf(c_53949,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_53919,c_9172]) ).

tcf(c_53950,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53949,c_4059]) ).

tcf(c_53958,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_53918,c_9172]) ).

tcf(c_53959,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_53958,c_4059]) ).

tcf(c_53971,plain,
    ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(global_subsumption_just,[status(thm)],[c_53922,c_247,c_20236,c_53922]) ).

tcf(c_53973,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_18185]) ).

tcf(c_53974,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_16330]) ).

tcf(c_53975,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_15966]) ).

tcf(c_53976,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_15593]) ).

tcf(c_53977,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),nil),X0) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_4541]) ).

tcf(c_53978,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3154]) ).

tcf(c_53979,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_4037]) ).

tcf(c_53980,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3952]) ).

tcf(c_53981,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3050]) ).

tcf(c_53982,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0),nil) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3049]) ).

tcf(c_53983,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),sk4),X0) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_4540]) ).

tcf(c_53984,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),sk3),X0) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_4539]) ).

tcf(c_53985,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),X0) = app(X1,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_271]) ).

tcf(c_53986,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(cons(X1,X0),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_266]) ).

tcf(c_53987,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),X0) = tl(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_274]) ).

tcf(c_53988,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_283]) ).

tcf(c_53989,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_18496]) ).

tcf(c_53990,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_18186]) ).

tcf(c_53991,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_48819]) ).

tcf(c_53992,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_48818]) ).

tcf(c_53993,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_48817]) ).

tcf(c_53994,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_18184]) ).

tcf(c_53995,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_17287]) ).

tcf(c_53996,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_16680]) ).

tcf(c_53997,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_16670]) ).

tcf(c_53998,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_16331]) ).

tcf(c_53999,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_45260]) ).

tcf(c_54000,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_45259]) ).

tcf(c_54001,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_45258]) ).

tcf(c_54002,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_16329]) ).

tcf(c_54003,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_15967]) ).

tcf(c_54004,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_40467]) ).

tcf(c_54005,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_40466]) ).

tcf(c_54006,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_40465]) ).

tcf(c_54007,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_15965]) ).

tcf(c_54008,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_15594]) ).

tcf(c_54009,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_37606]) ).

tcf(c_54010,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_37605]) ).

tcf(c_54011,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_37604]) ).

tcf(c_54012,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_15592]) ).

tcf(c_54013,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_18000]) ).

tcf(c_54014,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_17998]) ).

tcf(c_54015,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_17997]) ).

tcf(c_54016,plain,
    app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_53971,c_35790]) ).

tcf(c_54017,plain,
    app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_53971,c_35787]) ).

tcf(c_54018,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),nil)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_4463]) ).

tcf(c_54019,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3155]) ).

tcf(c_54020,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_33403]) ).

tcf(c_54021,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_33402]) ).

tcf(c_54022,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_33401]) ).

tcf(c_54023,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_32111]) ).

tcf(c_54024,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_32098]) ).

tcf(c_54025,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_15410]) ).

tcf(c_54026,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_15408]) ).

tcf(c_54027,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_15407]) ).

tcf(c_54028,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3153]) ).

tcf(c_54029,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_4038]) ).

tcf(c_54030,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_17993]) ).

tcf(c_54031,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_17992]) ).

tcf(c_54032,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_17991]) ).

tcf(c_54033,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_4036]) ).

tcf(c_54034,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3953]) ).

tcf(c_54035,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_15403]) ).

tcf(c_54036,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_15402]) ).

tcf(c_54037,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_15401]) ).

tcf(c_54038,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3951]) ).

tcf(c_54039,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3423]) ).

tcf(c_54040,plain,
    app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_53971,c_13452]) ).

tcf(c_54041,plain,
    app(app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_53971,c_12354]) ).

tcf(c_54042,plain,
    app(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_53971,c_12353]) ).

tcf(c_54043,plain,
    app(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_53971,c_12352]) ).

tcf(c_54044,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_53971,c_3199]) ).

tcf(c_54045,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3066]) ).

tcf(c_54046,plain,
    app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_53971,c_8061]) ).

tcf(c_54047,plain,
    app(app(sk4,sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_53971,c_8048]) ).

tcf(c_54048,plain,
    app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_53971,c_5745]) ).

tcf(c_54049,plain,
    app(app(sk3,sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_53971,c_8047]) ).

tcf(c_54050,plain,
    app(app(sk4,sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_53971,c_5738]) ).

tcf(c_54051,plain,
    app(app(sk3,sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_53971,c_5737]) ).

tcf(c_54052,plain,
    app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = tl(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_53971,c_4136]) ).

tcf(c_54053,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),sk4)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_4462]) ).

tcf(c_54054,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),sk3)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_4461]) ).

tcf(c_54055,plain,
    app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = tl(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))),
    inference(superposition,[status(thm)],[c_53971,c_4284]) ).

tcf(c_54056,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_4027]) ).

tcf(c_54058,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3019]) ).

tcf(c_54059,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3452]) ).

tcf(c_54060,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3444]) ).

tcf(c_54061,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3065]) ).

tcf(c_54062,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3215]) ).

tcf(c_54063,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3207]) ).

tcf(c_54064,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_253]) ).

tcf(c_54065,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_275]) ).

tcf(c_54066,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3018]) ).

tcf(c_54067,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_53971,c_3191]) ).

tcf(c_54068,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_53971,c_3183]) ).

tcf(c_54069,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_284]) ).

tcf(c_54070,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_276]) ).

tcf(c_54071,plain,
    app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),nil) = app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_53971,c_258]) ).

tcf(c_54072,plain,
    app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),
    inference(superposition,[status(thm)],[c_53971,c_257]) ).

tcf(c_54173,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_53988,c_15976]) ).

tcf(c_54182,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) ) ),
    inference(light_normalisation,[status(thm)],[c_54065,c_15976]) ).

tcf(c_54562,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(sk3,X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_18497]) ).

tcf(c_54563,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(sk4,X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_18497]) ).

tcf(c_54564,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(nil,X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_18497]) ).

tcf(c_54565,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk4,app(tl(X0),X1)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18497]) ).

tcf(c_54566,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(X1,X0),X2)))) = hd(sk3) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18497]) ).

tcf(c_54567,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(X2,X0),X1)))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18497]) ).

tcf(c_54568,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk3),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_18497]) ).

tcf(c_54569,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk4),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_18497]) ).

tcf(c_54570,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk3),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_18497]) ).

tcf(c_54571,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk4),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_18497]) ).

tcf(c_54572,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk3,app(sk4,app(app(tl(sk3),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18497]) ).

tcf(c_54573,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk3,app(sk4,app(app(tl(sk3),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18497]) ).

tcf(c_54574,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk3,app(sk4,app(app(tl(sk4),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18497]) ).

tcf(c_54575,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk3,app(sk4,app(app(tl(sk4),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_18497]) ).

tcf(c_54576,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk4),app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_18497]) ).

tcf(c_54577,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18497]) ).

tcf(c_54578,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18497]) ).

tcf(c_54579,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18497]) ).

tcf(c_54580,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk4),app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_18497]) ).

tcf(c_54581,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18497]) ).

tcf(c_54582,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18497]) ).

tcf(c_54583,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18497]) ).

tcf(c_54584,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18497]) ).

tcf(c_54585,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18497]) ).

tcf(c_54586,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk4),app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_18497]) ).

tcf(c_54587,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk4),app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_18497]) ).

tcf(c_54588,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18497]) ).

tcf(c_54589,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18497]) ).

tcf(c_54590,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18497]) ).

tcf(c_54591,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk3),app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_18497]) ).

tcf(c_54592,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk3),app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_18497]) ).

tcf(c_54593,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk3),app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_18497]) ).

tcf(c_54594,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk3),app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_18497]) ).

tcf(c_54595,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18497]) ).

tcf(c_54596,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18497]) ).

tcf(c_54597,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_18497]) ).

tcf(c_54598,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_18497]) ).

tcf(c_54599,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_18497]) ).

tcf(c_54600,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_18497]) ).

tcf(c_54601,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18497]) ).

tcf(c_54602,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18497]) ).

tcf(c_54603,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_18497]) ).

tcf(c_54604,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_18497]) ).

tcf(c_54605,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18497]) ).

tcf(c_54606,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_18497]) ).

tcf(c_54607,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_18497]) ).

tcf(c_54855,plain,
    hd(app(sk3,app(sk4,app(sk3,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_54562]) ).

tcf(c_54856,plain,
    hd(app(sk3,app(sk4,app(sk3,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_54562]) ).

tcf(c_54857,plain,
    hd(app(sk3,app(sk4,app(sk3,nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_54562]) ).

tcf(c_54858,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk4,app(sk3,tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_54562]) ).

tcf(c_54859,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk4,app(sk3,app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_54562]) ).

tcf(c_54860,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk4,app(sk3,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_54562]) ).

tcf(c_54861,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_54562]) ).

tcf(c_54862,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_54562]) ).

tcf(c_54863,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_54562]) ).

tcf(c_54864,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_54562]) ).

tcf(c_54865,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(sk4,app(sk3,app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_54562]) ).

tcf(c_54866,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(sk4,app(sk3,app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_54562]) ).

tcf(c_54867,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(sk4,app(sk3,app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_54562]) ).

tcf(c_54868,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(sk4,app(sk3,app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_54562]) ).

tcf(c_54869,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_54562]) ).

tcf(c_54870,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_54562]) ).

tcf(c_54871,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_54562]) ).

tcf(c_54872,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_54562]) ).

tcf(c_54873,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_54562]) ).

tcf(c_54874,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_54562]) ).

tcf(c_54875,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_54562]) ).

tcf(c_54876,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_54562]) ).

tcf(c_54877,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_54562]) ).

tcf(c_54878,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_54562]) ).

tcf(c_54879,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_54562]) ).

tcf(c_54880,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_54562]) ).

tcf(c_54881,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_54562]) ).

tcf(c_54882,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_54562]) ).

tcf(c_54883,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_54562]) ).

tcf(c_54884,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_54562]) ).

tcf(c_54885,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_54562]) ).

tcf(c_54886,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_54562]) ).

tcf(c_54887,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_54562]) ).

tcf(c_54888,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_54562]) ).

tcf(c_54889,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_54562]) ).

tcf(c_54890,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_54562]) ).

tcf(c_54891,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_54562]) ).

tcf(c_54892,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_54562]) ).

tcf(c_54893,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_54562]) ).

tcf(c_54894,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_54562]) ).

tcf(c_54895,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_54562]) ).

tcf(c_54896,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_54562]) ).

tcf(c_54897,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_54562]) ).

tcf(c_54898,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_54562]) ).

tcf(c_54899,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_54562]) ).

tcf(c_54900,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_54562]) ).

tcf(c_55093,plain,
    ( ssList(app(sk4,sk3))
    | ~ ssList(sk4)
    | ~ ssList(sk3) ),
    inference(instantiation,[status(thm)],[c_6137]) ).

tcf(c_55105,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,sk3)))))
      | ( app(sk3,app(sk4,app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,sk3))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_54855,c_280]) ).

tcf(c_55106,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,sk3)))))
      | ( app(sk3,app(sk4,app(sk3,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,sk3))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_54855,c_279]) ).

tcf(c_55146,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,sk4)))))
      | ( app(sk3,app(sk4,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,sk4))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_54856,c_280]) ).

tcf(c_55147,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,sk4)))))
      | ( app(sk3,app(sk4,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,sk4))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_54856,c_279]) ).

tcf(c_55166,plain,
    hd(app(sk3,app(sk4,app(sk4,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_54563]) ).

tcf(c_55167,plain,
    hd(app(sk3,app(sk4,app(sk4,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_54563]) ).

tcf(c_55168,plain,
    hd(app(sk3,app(sk4,app(sk4,nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_54563]) ).

tcf(c_55169,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk4,app(sk4,tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_54563]) ).

tcf(c_55170,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk4,app(sk4,app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_54563]) ).

tcf(c_55171,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk4,app(sk4,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_54563]) ).

tcf(c_55172,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_54563]) ).

tcf(c_55174,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_54563]) ).

tcf(c_55176,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(sk4,app(sk4,app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_54563]) ).

tcf(c_55177,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(sk4,app(sk4,app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_54563]) ).

tcf(c_55178,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(sk4,app(sk4,app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_54563]) ).

tcf(c_55179,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(sk4,app(sk4,app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_54563]) ).

tcf(c_55181,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_54563]) ).

tcf(c_55182,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_54563]) ).

tcf(c_55183,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_54563]) ).

tcf(c_55185,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_54563]) ).

tcf(c_55186,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_54563]) ).

tcf(c_55187,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_54563]) ).

tcf(c_55188,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_54563]) ).

tcf(c_55189,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_54563]) ).

tcf(c_55190,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_54563]) ).

tcf(c_55191,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_54563]) ).

tcf(c_55192,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_54563]) ).

tcf(c_55193,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_54563]) ).

tcf(c_55194,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_54563]) ).

tcf(c_55195,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_54563]) ).

tcf(c_55196,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_54563]) ).

tcf(c_55197,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_54563]) ).

tcf(c_55198,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_54563]) ).

tcf(c_55199,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_54563]) ).

tcf(c_55200,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_54563]) ).

tcf(c_55201,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_54563]) ).

tcf(c_55202,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_54563]) ).

tcf(c_55203,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_54563]) ).

tcf(c_55204,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_54563]) ).

tcf(c_55205,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_54563]) ).

tcf(c_55206,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_54563]) ).

tcf(c_55207,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_54563]) ).

tcf(c_55208,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_54563]) ).

tcf(c_55209,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_54563]) ).

tcf(c_55210,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_54563]) ).

tcf(c_55211,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_54563]) ).

tcf(c_55364,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,sk3)))))
      | ( app(sk3,app(sk4,app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,sk3))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_55166,c_280]) ).

tcf(c_55365,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,sk3)))))
      | ( app(sk3,app(sk4,app(sk4,sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,sk3))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_55166,c_279]) ).

tcf(c_55381,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,sk4)))))
      | ( app(sk3,app(sk4,app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,sk4))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_55167,c_280]) ).

tcf(c_55382,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,sk4)))))
      | ( app(sk3,app(sk4,app(sk4,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,sk4))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_55167,c_279]) ).

tcf(c_55398,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_54861,c_280]) ).

tcf(c_55399,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_54861,c_279]) ).

tcf(c_55415,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_54862,c_280]) ).

tcf(c_55416,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_54862,c_279]) ).

tcf(c_55432,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_54863,c_280]) ).

tcf(c_55433,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_54863,c_279]) ).

tcf(c_55449,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_54864,c_280]) ).

tcf(c_55450,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_54864,c_279]) ).

tcf(c_55484,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_55172,c_280]) ).

tcf(c_55485,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_55172,c_279]) ).

tcf(c_55501,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_55174,c_280]) ).

tcf(c_55502,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_55174,c_279]) ).

tcf(c_55529,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3))))
      | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_9878,c_270]) ).

tcf(c_55530,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3))))
      | ( app(X0,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_9878,c_269]) ).

tcf(c_55531,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3))))
      | ( app(X0,app(sk4,cons(hd(sk4),app(sk3,sk3)))) != app(sk4,cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_55530,c_259]) ).

tcf(c_55536,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3))))
      | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_55529,c_259]) ).

tcf(c_55546,plain,
    hd(app(sk3,app(sk4,app(nil,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_54564]) ).

tcf(c_55547,plain,
    hd(app(sk3,app(sk4,app(nil,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_54564]) ).

tcf(c_55548,plain,
    hd(app(sk3,app(sk4,app(nil,nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_54564]) ).

tcf(c_55549,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk4,app(nil,tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_54564]) ).

tcf(c_55550,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk4,app(nil,app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_54564]) ).

tcf(c_55551,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(sk4,app(nil,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_54564]) ).

tcf(c_55552,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk3),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_54564]) ).

tcf(c_55553,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_54564]) ).

tcf(c_55554,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk3),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_54564]) ).

tcf(c_55555,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_54564]) ).

tcf(c_55556,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(sk4,app(nil,app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_54564]) ).

tcf(c_55557,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(sk4,app(nil,app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_54564]) ).

tcf(c_55558,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(sk4,app(nil,app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_54564]) ).

tcf(c_55559,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(sk4,app(nil,app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_54564]) ).

tcf(c_55560,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_54564]) ).

tcf(c_55561,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_54564]) ).

tcf(c_55562,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_54564]) ).

tcf(c_55563,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_54564]) ).

tcf(c_55564,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_54564]) ).

tcf(c_55565,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_54564]) ).

tcf(c_55566,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_54564]) ).

tcf(c_55567,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_54564]) ).

tcf(c_55568,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_54564]) ).

tcf(c_55569,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_54564]) ).

tcf(c_55570,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_54564]) ).

tcf(c_55571,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_54564]) ).

tcf(c_55572,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_54564]) ).

tcf(c_55573,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_54564]) ).

tcf(c_55574,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_54564]) ).

tcf(c_55575,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_54564]) ).

tcf(c_55576,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_54564]) ).

tcf(c_55577,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_54564]) ).

tcf(c_55578,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_54564]) ).

tcf(c_55579,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_54564]) ).

tcf(c_55580,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_54564]) ).

tcf(c_55581,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_54564]) ).

tcf(c_55582,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_54564]) ).

tcf(c_55583,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_54564]) ).

tcf(c_55584,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_54564]) ).

tcf(c_55585,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_54564]) ).

tcf(c_55586,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_54564]) ).

tcf(c_55587,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_54564]) ).

tcf(c_55588,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_54564]) ).

tcf(c_55589,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_54564]) ).

tcf(c_55590,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_54564]) ).

tcf(c_55591,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_54564]) ).

tcf(c_55740,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,sk3)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_18498]) ).

tcf(c_55741,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,sk4)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_18498]) ).

tcf(c_55742,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,nil)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_18498]) ).

tcf(c_55743,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk4,cons(X1,tl(X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18498]) ).

tcf(c_55744,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X2,app(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18498]) ).

tcf(c_55745,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X2,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18498]) ).

tcf(c_55746,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk3),sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_18498]) ).

tcf(c_55747,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk4),sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_18498]) ).

tcf(c_55748,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk3),sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_18498]) ).

tcf(c_55749,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk4),sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_18498]) ).

tcf(c_55750,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk3,app(sk4,cons(X0,app(tl(sk3),sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18498]) ).

tcf(c_55751,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk3,app(sk4,cons(X0,app(tl(sk3),sk4))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18498]) ).

tcf(c_55752,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk3,app(sk4,cons(X0,app(tl(sk4),sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18498]) ).

tcf(c_55753,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk3,app(sk4,cons(X0,app(tl(sk4),sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_18498]) ).

tcf(c_55754,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_18498]) ).

tcf(c_55755,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18498]) ).

tcf(c_55756,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18498]) ).

tcf(c_55757,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18498]) ).

tcf(c_55758,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_18498]) ).

tcf(c_55759,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18498]) ).

tcf(c_55760,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18498]) ).

tcf(c_55761,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18498]) ).

tcf(c_55762,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18498]) ).

tcf(c_55763,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18498]) ).

tcf(c_55764,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_18498]) ).

tcf(c_55765,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_18498]) ).

tcf(c_55766,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18498]) ).

tcf(c_55767,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18498]) ).

tcf(c_55768,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18498]) ).

tcf(c_55769,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_18498]) ).

tcf(c_55770,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_18498]) ).

tcf(c_55771,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_18498]) ).

tcf(c_55772,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_18498]) ).

tcf(c_55773,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18498]) ).

tcf(c_55774,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18498]) ).

tcf(c_55775,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_18498]) ).

tcf(c_55776,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_18498]) ).

tcf(c_55777,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_18498]) ).

tcf(c_55778,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_18498]) ).

tcf(c_55779,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18498]) ).

tcf(c_55780,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18498]) ).

tcf(c_55781,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_18498]) ).

tcf(c_55782,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_18498]) ).

tcf(c_55783,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18498]) ).

tcf(c_55784,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_18498]) ).

tcf(c_55785,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_18498]) ).

tcf(c_56219,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk4,cons(hd(X0),sk3)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_55740]) ).

tcf(c_56229,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk4,cons(hd(X0),sk4)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_55741]) ).

tcf(c_56251,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(sk4,cons(hd(X0),nil)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_55742]) ).

tcf(c_56252,plain,
    hd(app(sk3,app(sk4,cons(hd(sk4),nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4059,c_55742]) ).

tcf(c_56253,plain,
    hd(app(sk3,app(sk4,cons(hd(sk3),nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_55742]) ).

tcf(c_56351,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),nil)))))
      | ( app(sk3,app(sk4,cons(hd(sk4),nil))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),nil))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_56252,c_280]) ).

tcf(c_56352,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk4),nil)))))
      | ( app(sk3,app(sk4,cons(hd(sk4),nil))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk4),nil))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_56252,c_279]) ).

tcf(c_56368,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),nil)))))
      | ( app(sk3,app(sk4,cons(hd(sk3),nil))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),nil))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_56253,c_280]) ).

tcf(c_56369,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),nil)))))
      | ( app(sk3,app(sk4,cons(hd(sk3),nil))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk3),nil))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_56253,c_279]) ).

tcf(c_56388,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_15409]) ).

tcf(c_56389,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_15409]) ).

tcf(c_56390,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_15409]) ).

tcf(c_56391,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(cons(hd(sk3),sk4),tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_15409]) ).

tcf(c_56392,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_15409]) ).

tcf(c_56393,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),sk4),cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_15409]) ).

tcf(c_56394,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_15409]) ).

tcf(c_56395,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_15409]) ).

tcf(c_56396,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_15409]) ).

tcf(c_56397,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_15409]) ).

tcf(c_56398,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(cons(hd(sk3),sk4),app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_15409]) ).

tcf(c_56399,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(cons(hd(sk3),sk4),app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_15409]) ).

tcf(c_56400,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(cons(hd(sk3),sk4),app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_15409]) ).

tcf(c_56401,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(cons(hd(sk3),sk4),app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_15409]) ).

tcf(c_56402,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_15409]) ).

tcf(c_56403,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_15409]) ).

tcf(c_56404,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_15409]) ).

tcf(c_56405,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_15409]) ).

tcf(c_56406,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_15409]) ).

tcf(c_56407,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_15409]) ).

tcf(c_56408,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_15409]) ).

tcf(c_56409,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_15409]) ).

tcf(c_56410,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_15409]) ).

tcf(c_56411,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_15409]) ).

tcf(c_56412,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_15409]) ).

tcf(c_56413,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_15409]) ).

tcf(c_56414,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_15409]) ).

tcf(c_56415,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_15409]) ).

tcf(c_56416,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_15409]) ).

tcf(c_56417,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_15409]) ).

tcf(c_56418,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_15409]) ).

tcf(c_56419,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_15409]) ).

tcf(c_56420,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_15409]) ).

tcf(c_56421,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_15409]) ).

tcf(c_56422,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_15409]) ).

tcf(c_56423,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_15409]) ).

tcf(c_56424,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_15409]) ).

tcf(c_56425,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_15409]) ).

tcf(c_56426,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_15409]) ).

tcf(c_56427,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_15409]) ).

tcf(c_56428,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_15409]) ).

tcf(c_56429,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_15409]) ).

tcf(c_56430,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_15409]) ).

tcf(c_56431,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_15409]) ).

tcf(c_56432,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_15409]) ).

tcf(c_56433,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_15409]) ).

tcf(c_56613,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_56394,c_280]) ).

tcf(c_56614,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_56394,c_279]) ).

tcf(c_56630,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_56395,c_280]) ).

tcf(c_56631,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_56395,c_279]) ).

tcf(c_56647,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_56397,c_280]) ).

tcf(c_56648,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_56397,c_279]) ).

tcf(c_56681,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3))))
      | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_9882,c_270]) ).

tcf(c_56682,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3))))
      | ( app(X0,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_9882,c_269]) ).

tcf(c_56683,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3))))
      | ( app(X0,app(sk4,cons(hd(sk4),app(sk4,sk3)))) != app(sk4,cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_56682,c_259]) ).

tcf(c_56688,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3))))
      | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_56681,c_259]) ).

tcf(c_56700,plain,
    ( ( sk3 = nil )
    | ( hd(app(sk3,app(nil,tl(sk3)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_246,c_18772]) ).

tcf(c_56701,plain,
    ( ( sk4 = nil )
    | ( hd(app(sk3,app(nil,tl(sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_247,c_18772]) ).

tcf(c_56703,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk3,app(nil,tl(tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18772]) ).

tcf(c_56704,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk3,app(nil,tl(app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18772]) ).

tcf(c_56705,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk3,app(nil,tl(cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18772]) ).

tcf(c_56706,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk3),sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_18772]) ).

tcf(c_56707,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk4),sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_18772]) ).

tcf(c_56708,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk3),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_18772]) ).

tcf(c_56709,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_18772]) ).

tcf(c_56710,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk3,app(nil,tl(app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18772]) ).

tcf(c_56711,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk3,app(nil,tl(app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18772]) ).

tcf(c_56712,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk3,app(nil,tl(app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18772]) ).

tcf(c_56713,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk3,app(nil,tl(app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_18772]) ).

tcf(c_56714,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_18772]) ).

tcf(c_56715,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18772]) ).

tcf(c_56716,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18772]) ).

tcf(c_56717,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18772]) ).

tcf(c_56718,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_18772]) ).

tcf(c_56719,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18772]) ).

tcf(c_56720,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18772]) ).

tcf(c_56721,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18772]) ).

tcf(c_56722,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18772]) ).

tcf(c_56723,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18772]) ).

tcf(c_56724,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_18772]) ).

tcf(c_56725,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_18772]) ).

tcf(c_56726,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18772]) ).

tcf(c_56727,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18772]) ).

tcf(c_56728,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18772]) ).

tcf(c_56729,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_18772]) ).

tcf(c_56730,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_18772]) ).

tcf(c_56731,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_18772]) ).

tcf(c_56732,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_18772]) ).

tcf(c_56733,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18772]) ).

tcf(c_56734,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18772]) ).

tcf(c_56735,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_18772]) ).

tcf(c_56736,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_18772]) ).

tcf(c_56737,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_18772]) ).

tcf(c_56738,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_18772]) ).

tcf(c_56739,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18772]) ).

tcf(c_56740,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18772]) ).

tcf(c_56741,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_18772]) ).

tcf(c_56742,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_18772]) ).

tcf(c_56743,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18772]) ).

tcf(c_56744,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_18772]) ).

tcf(c_56745,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_18772]) ).

tcf(c_56756,plain,
    hd(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_56732,c_20706]) ).

tcf(c_56757,plain,
    hd(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_56731,c_17701]) ).

tcf(c_56758,plain,
    hd(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_56730,c_19513]) ).

tcf(c_56759,plain,
    hd(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_56729,c_16926]) ).

tcf(c_56799,plain,
    hd(app(sk3,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_56738,c_44126]) ).

tcf(c_56800,plain,
    hd(app(sk3,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_56737,c_43038]) ).

tcf(c_56801,plain,
    hd(app(sk3,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_56736,c_51895]) ).

tcf(c_56802,plain,
    hd(app(sk3,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(forward_subsumption_resolution,[status(thm)],[c_56735,c_50642]) ).

tcf(c_57008,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(sk3,X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_246,c_18773]) ).

tcf(c_57009,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(sk4,X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_247,c_18773]) ).

tcf(c_57010,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(nil,X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_259,c_18773]) ).

tcf(c_57011,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(nil,app(tl(X0),X1)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18773]) ).

tcf(c_57012,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(nil,app(app(X1,X0),X2)))) = hd(sk3) )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18773]) ).

tcf(c_57013,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(X2,X0),X1)))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18773]) ).

tcf(c_57014,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk3),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_18773]) ).

tcf(c_57015,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk4),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_18773]) ).

tcf(c_57016,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk3),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_18773]) ).

tcf(c_57017,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk4),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_18773]) ).

tcf(c_57018,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk3,app(nil,app(app(tl(sk3),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18773]) ).

tcf(c_57019,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk3,app(nil,app(app(tl(sk3),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18773]) ).

tcf(c_57020,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk3,app(nil,app(app(tl(sk4),sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18773]) ).

tcf(c_57021,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk3,app(nil,app(app(tl(sk4),sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_18773]) ).

tcf(c_57022,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk4),app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_18773]) ).

tcf(c_57023,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18773]) ).

tcf(c_57024,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18773]) ).

tcf(c_57025,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18773]) ).

tcf(c_57026,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk4),app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_18773]) ).

tcf(c_57027,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18773]) ).

tcf(c_57028,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18773]) ).

tcf(c_57029,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18773]) ).

tcf(c_57030,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18773]) ).

tcf(c_57031,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18773]) ).

tcf(c_57032,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk4),app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_18773]) ).

tcf(c_57033,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk4),app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_18773]) ).

tcf(c_57034,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18773]) ).

tcf(c_57035,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18773]) ).

tcf(c_57036,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18773]) ).

tcf(c_57037,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk3),app(sk4,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_18773]) ).

tcf(c_57038,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk3),app(sk4,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_18773]) ).

tcf(c_57039,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk3),app(sk3,sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_18773]) ).

tcf(c_57040,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk3),app(sk3,sk3)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_18773]) ).

tcf(c_57041,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18773]) ).

tcf(c_57042,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18773]) ).

tcf(c_57043,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_18773]) ).

tcf(c_57044,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_18773]) ).

tcf(c_57045,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_18773]) ).

tcf(c_57046,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_18773]) ).

tcf(c_57047,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18773]) ).

tcf(c_57048,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18773]) ).

tcf(c_57049,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_18773]) ).

tcf(c_57050,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_18773]) ).

tcf(c_57051,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18773]) ).

tcf(c_57052,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_18773]) ).

tcf(c_57053,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_18773]) ).

tcf(c_57520,plain,
    hd(app(sk3,app(nil,app(sk3,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_57008]) ).

tcf(c_57521,plain,
    hd(app(sk3,app(nil,app(sk3,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_57008]) ).

tcf(c_57522,plain,
    hd(app(sk3,app(nil,app(sk3,nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_57008]) ).

tcf(c_57523,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(nil,app(sk3,tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_57008]) ).

tcf(c_57524,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(nil,app(sk3,app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_57008]) ).

tcf(c_57525,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(nil,app(sk3,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_57008]) ).

tcf(c_57526,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk3),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_57008]) ).

tcf(c_57527,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_57008]) ).

tcf(c_57528,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk3),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_57008]) ).

tcf(c_57529,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_57008]) ).

tcf(c_57530,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(nil,app(sk3,app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_57008]) ).

tcf(c_57531,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(nil,app(sk3,app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_57008]) ).

tcf(c_57532,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(nil,app(sk3,app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_57008]) ).

tcf(c_57533,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(nil,app(sk3,app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_57008]) ).

tcf(c_57534,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_57008]) ).

tcf(c_57535,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_57008]) ).

tcf(c_57536,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_57008]) ).

tcf(c_57537,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_57008]) ).

tcf(c_57538,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_57008]) ).

tcf(c_57539,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_57008]) ).

tcf(c_57540,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_57008]) ).

tcf(c_57541,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_57008]) ).

tcf(c_57542,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_57008]) ).

tcf(c_57543,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_57008]) ).

tcf(c_57544,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_57008]) ).

tcf(c_57545,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_57008]) ).

tcf(c_57546,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_57008]) ).

tcf(c_57547,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_57008]) ).

tcf(c_57548,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_57008]) ).

tcf(c_57549,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_57008]) ).

tcf(c_57550,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_57008]) ).

tcf(c_57551,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_57008]) ).

tcf(c_57552,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_57008]) ).

tcf(c_57553,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_57008]) ).

tcf(c_57554,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_57008]) ).

tcf(c_57555,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_57008]) ).

tcf(c_57556,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_57008]) ).

tcf(c_57557,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_57008]) ).

tcf(c_57558,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_57008]) ).

tcf(c_57559,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_57008]) ).

tcf(c_57560,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_57008]) ).

tcf(c_57561,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_57008]) ).

tcf(c_57562,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_57008]) ).

tcf(c_57563,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_57008]) ).

tcf(c_57564,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_57008]) ).

tcf(c_57565,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_57008]) ).

tcf(c_57683,plain,
    hd(app(sk3,app(nil,app(sk4,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_57009]) ).

tcf(c_57684,plain,
    hd(app(sk3,app(nil,app(sk4,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_57009]) ).

tcf(c_57685,plain,
    hd(app(sk3,app(nil,app(sk4,nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_57009]) ).

tcf(c_57686,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(nil,app(sk4,tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_57009]) ).

tcf(c_57687,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(nil,app(sk4,app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_57009]) ).

tcf(c_57688,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(nil,app(sk4,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_57009]) ).

tcf(c_57689,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk3),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_57009]) ).

tcf(c_57690,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_57009]) ).

tcf(c_57691,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk3),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_57009]) ).

tcf(c_57692,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_57009]) ).

tcf(c_57693,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(nil,app(sk4,app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_57009]) ).

tcf(c_57694,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(nil,app(sk4,app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_57009]) ).

tcf(c_57695,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(nil,app(sk4,app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_57009]) ).

tcf(c_57696,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(nil,app(sk4,app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_57009]) ).

tcf(c_57697,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_57009]) ).

tcf(c_57698,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_57009]) ).

tcf(c_57699,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_57009]) ).

tcf(c_57700,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_57009]) ).

tcf(c_57701,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_57009]) ).

tcf(c_57702,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_57009]) ).

tcf(c_57703,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_57009]) ).

tcf(c_57704,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_57009]) ).

tcf(c_57705,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_57009]) ).

tcf(c_57706,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_57009]) ).

tcf(c_57707,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_57009]) ).

tcf(c_57708,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_57009]) ).

tcf(c_57709,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_57009]) ).

tcf(c_57710,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_57009]) ).

tcf(c_57711,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_57009]) ).

tcf(c_57712,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_57009]) ).

tcf(c_57713,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_57009]) ).

tcf(c_57714,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_57009]) ).

tcf(c_57715,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_57009]) ).

tcf(c_57716,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_57009]) ).

tcf(c_57717,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_57009]) ).

tcf(c_57718,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_57009]) ).

tcf(c_57719,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_57009]) ).

tcf(c_57720,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_57009]) ).

tcf(c_57721,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_57009]) ).

tcf(c_57722,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_57009]) ).

tcf(c_57723,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_57009]) ).

tcf(c_57724,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_57009]) ).

tcf(c_57725,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_57009]) ).

tcf(c_57726,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_57009]) ).

tcf(c_57727,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_57009]) ).

tcf(c_57728,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_57009]) ).

tcf(c_57828,plain,
    hd(app(sk3,app(nil,app(nil,sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_57010]) ).

tcf(c_57829,plain,
    hd(app(sk3,app(nil,app(nil,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_57010]) ).

tcf(c_57830,plain,
    hd(app(sk3,app(nil,app(nil,nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_57010]) ).

tcf(c_57831,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(nil,app(nil,tl(X0))))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_57010]) ).

tcf(c_57832,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(nil,app(nil,app(X1,X0))))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_57010]) ).

tcf(c_57833,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(nil,app(nil,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_57010]) ).

tcf(c_57834,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk3),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_57010]) ).

tcf(c_57835,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk4),sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_57010]) ).

tcf(c_57836,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk3),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_57010]) ).

tcf(c_57837,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk4),sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_57010]) ).

tcf(c_57838,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(nil,app(nil,app(tl(sk3),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_57010]) ).

tcf(c_57839,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(nil,app(nil,app(tl(sk3),sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_57010]) ).

tcf(c_57840,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(nil,app(nil,app(tl(sk4),sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_57010]) ).

tcf(c_57841,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(nil,app(nil,app(tl(sk4),sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_57010]) ).

tcf(c_57842,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_57010]) ).

tcf(c_57843,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_57010]) ).

tcf(c_57844,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_57010]) ).

tcf(c_57845,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_57010]) ).

tcf(c_57846,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_57010]) ).

tcf(c_57847,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_57010]) ).

tcf(c_57848,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_57010]) ).

tcf(c_57849,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_57010]) ).

tcf(c_57850,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_57010]) ).

tcf(c_57851,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_57010]) ).

tcf(c_57852,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_57010]) ).

tcf(c_57853,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_57010]) ).

tcf(c_57854,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_57010]) ).

tcf(c_57855,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_57010]) ).

tcf(c_57856,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_57010]) ).

tcf(c_57857,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_57010]) ).

tcf(c_57858,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_57010]) ).

tcf(c_57859,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_57010]) ).

tcf(c_57860,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_57010]) ).

tcf(c_57861,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_57010]) ).

tcf(c_57862,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_57010]) ).

tcf(c_57863,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_57010]) ).

tcf(c_57864,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_57010]) ).

tcf(c_57865,plain,
    hd(app(sk3,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_57010]) ).

tcf(c_57866,plain,
    hd(app(sk3,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_57010]) ).

tcf(c_57867,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_57010]) ).

tcf(c_57868,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_57010]) ).

tcf(c_57869,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_57010]) ).

tcf(c_57870,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_57010]) ).

tcf(c_57871,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_57010]) ).

tcf(c_57872,plain,
    hd(app(sk3,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_57010]) ).

tcf(c_57873,plain,
    hd(app(sk3,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_57010]) ).

tcf(c_57991,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,cons(hd(X0),cons(hd(sk3),sk4)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_16555]) ).

tcf(c_57992,plain,
    hd(app(sk4,cons(hd(sk4),cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_16555]) ).

tcf(c_57993,plain,
    hd(app(sk4,cons(hd(sk3),cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10117,c_16555]) ).

tcf(c_57998,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk4),cons(hd(sk3),sk4)))))
      | ( app(sk4,cons(hd(sk4),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk4),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_57992,c_280]) ).

tcf(c_57999,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk4),cons(hd(sk3),sk4)))))
      | ( app(sk4,cons(hd(sk4),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk4),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_57992,c_279]) ).

tcf(c_58015,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),cons(hd(sk3),sk4)))))
      | ( app(sk4,cons(hd(sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_57993,c_280]) ).

tcf(c_58016,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),cons(hd(sk3),sk4)))))
      | ( app(sk4,cons(hd(sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_57993,c_279]) ).

tcf(c_58032,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_56756,c_280]) ).

tcf(c_58033,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_56756,c_279]) ).

tcf(c_58083,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_56757,c_280]) ).

tcf(c_58084,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_56757,c_279]) ).

tcf(c_58100,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_56758,c_280]) ).

tcf(c_58101,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_56758,c_279]) ).

tcf(c_58117,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_56759,c_280]) ).

tcf(c_58118,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_56759,c_279]) ).

tcf(c_58151,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,sk3)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_18774]) ).

tcf(c_58152,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,sk4)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_18774]) ).

tcf(c_58153,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,nil)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_259,c_18774]) ).

tcf(c_58154,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(nil,cons(X1,tl(X0))))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_18774]) ).

tcf(c_58155,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(nil,cons(X2,app(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_18774]) ).

tcf(c_58156,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( hd(app(sk3,app(nil,cons(X2,cons(X1,X0))))) = hd(sk3) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_18774]) ).

tcf(c_58157,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk3),sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_18774]) ).

tcf(c_58158,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk4),sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_18774]) ).

tcf(c_58159,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk3),sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_18774]) ).

tcf(c_58160,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk4),sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_18774]) ).

tcf(c_58161,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( hd(app(sk3,app(nil,cons(X0,app(tl(sk3),sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_18774]) ).

tcf(c_58162,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( hd(app(sk3,app(nil,cons(X0,app(tl(sk3),sk4))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_18774]) ).

tcf(c_58163,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( hd(app(sk3,app(nil,cons(X0,app(tl(sk4),sk3))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_18774]) ).

tcf(c_58164,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( hd(app(sk3,app(nil,cons(X0,app(tl(sk4),sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_18774]) ).

tcf(c_58165,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk4),app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_18774]) ).

tcf(c_58166,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_18774]) ).

tcf(c_58167,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_18774]) ).

tcf(c_58168,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_18774]) ).

tcf(c_58169,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk4),app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_18774]) ).

tcf(c_58170,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_18774]) ).

tcf(c_58171,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_18774]) ).

tcf(c_58172,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_18774]) ).

tcf(c_58173,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_18774]) ).

tcf(c_58174,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_18774]) ).

tcf(c_58175,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk4),app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_18774]) ).

tcf(c_58176,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk4),app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_18774]) ).

tcf(c_58177,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_18774]) ).

tcf(c_58178,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_18774]) ).

tcf(c_58179,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_18774]) ).

tcf(c_58180,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk3),app(sk4,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_18774]) ).

tcf(c_58181,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk3),app(sk4,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_18774]) ).

tcf(c_58182,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk3),app(sk3,sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_18774]) ).

tcf(c_58183,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk3),app(sk3,sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_18774]) ).

tcf(c_58184,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_18774]) ).

tcf(c_58185,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_18774]) ).

tcf(c_58186,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_18774]) ).

tcf(c_58187,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_18774]) ).

tcf(c_58188,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_18774]) ).

tcf(c_58189,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_18774]) ).

tcf(c_58190,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_18774]) ).

tcf(c_58191,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_18774]) ).

tcf(c_58192,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_18774]) ).

tcf(c_58193,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_18774]) ).

tcf(c_58194,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_18774]) ).

tcf(c_58195,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_18774]) ).

tcf(c_58196,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_18774]) ).

tcf(c_58421,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(nil,cons(hd(X0),sk3)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_58151]) ).

tcf(c_58449,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(nil,cons(hd(X0),sk4)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_58152]) ).

tcf(c_58459,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(nil,cons(hd(X0),nil)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_58153]) ).

tcf(c_58460,plain,
    hd(app(sk3,app(nil,cons(hd(sk4),nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4059,c_58153]) ).

tcf(c_58461,plain,
    hd(app(sk3,app(nil,cons(hd(sk3),nil)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_58153]) ).

tcf(c_58471,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_17999]) ).

tcf(c_58472,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_17999]) ).

tcf(c_58473,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_17999]) ).

tcf(c_58474,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(cons(hd(sk3),sk4),tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_17999]) ).

tcf(c_58475,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_17999]) ).

tcf(c_58476,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),sk4),cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_17999]) ).

tcf(c_58477,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_17999]) ).

tcf(c_58478,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_17999]) ).

tcf(c_58479,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_17999]) ).

tcf(c_58480,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_17999]) ).

tcf(c_58481,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(cons(hd(sk3),sk4),app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_17999]) ).

tcf(c_58482,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(cons(hd(sk3),sk4),app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_17999]) ).

tcf(c_58483,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(cons(hd(sk3),sk4),app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_17999]) ).

tcf(c_58484,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(cons(hd(sk3),sk4),app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_17999]) ).

tcf(c_58485,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_17999]) ).

tcf(c_58486,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_17999]) ).

tcf(c_58487,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_17999]) ).

tcf(c_58488,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_17999]) ).

tcf(c_58489,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_17999]) ).

tcf(c_58490,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_17999]) ).

tcf(c_58491,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_17999]) ).

tcf(c_58492,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_17999]) ).

tcf(c_58493,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_17999]) ).

tcf(c_58494,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_17999]) ).

tcf(c_58495,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_17999]) ).

tcf(c_58496,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_17999]) ).

tcf(c_58497,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_17999]) ).

tcf(c_58498,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_17999]) ).

tcf(c_58499,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_17999]) ).

tcf(c_58500,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_17999]) ).

tcf(c_58501,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_17999]) ).

tcf(c_58502,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_17999]) ).

tcf(c_58503,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_17999]) ).

tcf(c_58504,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_17999]) ).

tcf(c_58505,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_17999]) ).

tcf(c_58506,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_17999]) ).

tcf(c_58507,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_17999]) ).

tcf(c_58508,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_17999]) ).

tcf(c_58509,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_17999]) ).

tcf(c_58510,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_17999]) ).

tcf(c_58511,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_17999]) ).

tcf(c_58512,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_17999]) ).

tcf(c_58513,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_17999]) ).

tcf(c_58514,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_17999]) ).

tcf(c_58515,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_17999]) ).

tcf(c_58516,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_17999]) ).

tcf(c_58632,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,cons(hd(X0),cons(hd(sk3),sk4)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_18853]) ).

tcf(c_58633,plain,
    hd(app(sk3,cons(hd(sk4),cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4059,c_18853]) ).

tcf(c_58634,plain,
    hd(app(sk3,cons(hd(sk3),cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_18853]) ).

tcf(c_58639,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk4),cons(hd(sk3),sk4)))))
      | ( app(sk3,cons(hd(sk4),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk4),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_58633,c_280]) ).

tcf(c_58640,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk4),cons(hd(sk3),sk4)))))
      | ( app(sk3,cons(hd(sk4),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk4),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_58633,c_279]) ).

tcf(c_58656,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),cons(hd(sk3),sk4)))))
      | ( app(sk3,cons(hd(sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_58634,c_280]) ).

tcf(c_58657,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),cons(hd(sk3),sk4)))))
      | ( app(sk3,cons(hd(sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_58634,c_279]) ).

tcf(c_58673,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_58477,c_280]) ).

tcf(c_58674,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_58477,c_279]) ).

tcf(c_58708,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_58478,c_280]) ).

tcf(c_58709,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_58478,c_279]) ).

tcf(c_58725,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_58480,c_280]) ).

tcf(c_58726,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_58480,c_279]) ).

tcf(c_58743,plain,
    cons(hd(sk3),sk4) != cons(hd(sk3),nil),
    inference(global_subsumption_just,[status(thm)],[c_14649,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7561,c_14649,c_20375]) ).

tcf(c_58745,plain,
    ~ strictorderedP(cons(hd(sk4),app(sk3,sk4))),
    inference(global_subsumption_just,[status(thm)],[c_14720,c_247,c_1242,c_3427,c_3439,c_3700,c_14720]) ).

tcf(c_58747,plain,
    ~ strictorderedP(cons(hd(sk4),app(sk4,sk4))),
    inference(global_subsumption_just,[status(thm)],[c_14751,c_247,c_1242,c_3427,c_3439,c_3700,c_14751]) ).

tcf(c_58749,plain,
    leq(hd(sk4),hd(sk4)),
    inference(global_subsumption_just,[status(thm)],[c_15056,c_247,c_1242,c_3439,c_3699]) ).

tcf(c_58755,plain,
    ( totalorderedP(cons(hd(sk4),sk4))
    | ( sk4 = nil )
    | ~ totalorderedP(sk4)
    | ~ ssList(sk4)
    | ~ ssItem(hd(sk4)) ),
    inference(superposition,[status(thm)],[c_58749,c_280]) ).

tcf(c_58756,plain,
    ( totalorderedP(cons(hd(sk4),sk4))
    | ~ totalorderedP(sk4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_58755,c_1243,c_247,c_4059]) ).

tcf(c_58767,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4))))
      | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_10207,c_270]) ).

tcf(c_58768,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4))))
      | ( app(X0,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10207,c_269]) ).

tcf(c_58769,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4))))
      | ( app(X0,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_58768,c_259]) ).

tcf(c_58774,plain,
    ! [X0: $i] :
      ( ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4))))
      | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_58767,c_259]) ).

tcf(c_58795,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk3,cons(hd(tl(X0)),sk3))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_19014]) ).

tcf(c_58796,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk3,cons(hd(app(X1,X0)),sk3))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_19014]) ).

tcf(c_58797,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk3,cons(hd(cons(X1,X0)),sk3))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_19014]) ).

tcf(c_58798,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),sk3)),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_19014]) ).

tcf(c_58799,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),sk3)),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_19014]) ).

tcf(c_58800,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),sk4)),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_19014]) ).

tcf(c_58801,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),sk4)),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_19014]) ).

tcf(c_58802,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk3),sk3)),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_19014]) ).

tcf(c_58803,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk3),sk4)),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_19014]) ).

tcf(c_58804,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk4),sk3)),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_19014]) ).

tcf(c_58805,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk4),sk4)),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_19014]) ).

tcf(c_58806,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_19014]) ).

tcf(c_58807,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,sk3))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_19014]) ).

tcf(c_58808,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,sk4))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_19014]) ).

tcf(c_58809,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,sk3))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_19014]) ).

tcf(c_58810,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_19014]) ).

tcf(c_58811,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,sk4))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_19014]) ).

tcf(c_58812,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,sk3))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_19014]) ).

tcf(c_58813,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,sk4))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_19014]) ).

tcf(c_58814,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,sk3))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_19014]) ).

tcf(c_58815,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,sk4))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_19014]) ).

tcf(c_58816,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_19014]) ).

tcf(c_58817,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk4,sk4))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_19014]) ).

tcf(c_58818,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_19014]) ).

tcf(c_58819,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_19014]) ).

tcf(c_58820,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_19014]) ).

tcf(c_58821,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk4,sk4))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_19014]) ).

tcf(c_58822,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk4,sk3))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_19014]) ).

tcf(c_58823,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk3,sk4))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_19014]) ).

tcf(c_58824,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk3,sk3))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_19014]) ).

tcf(c_58825,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_19014]) ).

tcf(c_58826,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_19014]) ).

tcf(c_58827,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_19014]) ).

tcf(c_58828,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_19014]) ).

tcf(c_58829,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_19014]) ).

tcf(c_58830,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_19014]) ).

tcf(c_58831,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_19014]) ).

tcf(c_58832,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_19014]) ).

tcf(c_58833,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_19014]) ).

tcf(c_58834,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_19014]) ).

tcf(c_58835,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_19014]) ).

tcf(c_58836,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_19014]) ).

tcf(c_58837,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_19014]) ).

tcf(c_58911,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk3,cons(hd(tl(X0)),sk4))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_19024]) ).

tcf(c_58912,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk3,cons(hd(app(X1,X0)),sk4))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_19024]) ).

tcf(c_58913,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk3,cons(hd(cons(X1,X0)),sk4))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_19024]) ).

tcf(c_58914,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),sk3)),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_19024]) ).

tcf(c_58915,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),sk3)),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_19024]) ).

tcf(c_58916,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),sk4)),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_19024]) ).

tcf(c_58917,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),sk4)),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_19024]) ).

tcf(c_58918,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk3),sk3)),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_19024]) ).

tcf(c_58919,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk3),sk4)),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_19024]) ).

tcf(c_58920,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk4),sk3)),sk4))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_19024]) ).

tcf(c_58921,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk4),sk4)),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_19024]) ).

tcf(c_58922,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_19024]) ).

tcf(c_58923,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,sk3))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_19024]) ).

tcf(c_58924,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,sk4))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_19024]) ).

tcf(c_58925,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,sk3))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_19024]) ).

tcf(c_58926,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_19024]) ).

tcf(c_58927,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,sk4))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_19024]) ).

tcf(c_58928,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,sk3))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_19024]) ).

tcf(c_58929,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,sk4))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_19024]) ).

tcf(c_58930,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,sk3))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_19024]) ).

tcf(c_58931,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,sk4))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_19024]) ).

tcf(c_58932,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_19024]) ).

tcf(c_58933,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk4,sk4))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_19024]) ).

tcf(c_58934,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_19024]) ).

tcf(c_58935,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_19024]) ).

tcf(c_58936,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_19024]) ).

tcf(c_58937,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk4,sk4))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_19024]) ).

tcf(c_58938,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk4,sk3))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_19024]) ).

tcf(c_58939,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk3,sk4))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_19024]) ).

tcf(c_58940,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk3,sk3))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_19024]) ).

tcf(c_58941,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_19024]) ).

tcf(c_58942,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_19024]) ).

tcf(c_58943,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_19024]) ).

tcf(c_58944,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_19024]) ).

tcf(c_58945,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_19024]) ).

tcf(c_58946,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_19024]) ).

tcf(c_58947,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_19024]) ).

tcf(c_58948,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_19024]) ).

tcf(c_58949,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_19024]) ).

tcf(c_58950,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_19024]) ).

tcf(c_58951,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_19024]) ).

tcf(c_58952,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_19024]) ).

tcf(c_58953,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_19024]) ).

tcf(c_59045,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(app(sk3,cons(hd(tl(X0)),nil))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_19899]) ).

tcf(c_59046,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(app(sk3,cons(hd(app(X1,X0)),nil))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_19899]) ).

tcf(c_59047,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(app(sk3,cons(hd(cons(X1,X0)),nil))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_19899]) ).

tcf(c_59048,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),sk3)),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_19899]) ).

tcf(c_59049,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),sk3)),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_19899]) ).

tcf(c_59050,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),sk4)),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_19899]) ).

tcf(c_59051,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),sk4)),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_19899]) ).

tcf(c_59052,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk3),sk3)),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_19899]) ).

tcf(c_59053,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk3),sk4)),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_19899]) ).

tcf(c_59054,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk4),sk3)),nil))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_19899]) ).

tcf(c_59055,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(app(sk3,cons(hd(app(tl(sk4),sk4)),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_19899]) ).

tcf(c_59056,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk3,sk3))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_19899]) ).

tcf(c_59057,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,sk3))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_19899]) ).

tcf(c_59058,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,sk4))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_19899]) ).

tcf(c_59059,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,sk3))),nil))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_19899]) ).

tcf(c_59060,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk4,sk3))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_19899]) ).

tcf(c_59061,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,sk4))),nil))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_19899]) ).

tcf(c_59062,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,sk3))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_19899]) ).

tcf(c_59063,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,sk4))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_19899]) ).

tcf(c_59064,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,sk3))),nil))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_19899]) ).

tcf(c_59065,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,sk4))),nil))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_19899]) ).

tcf(c_59066,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk3,sk4))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_19899]) ).

tcf(c_59067,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk4),app(sk4,sk4))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_19899]) ).

tcf(c_59068,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_19899]) ).

tcf(c_59069,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_19899]) ).

tcf(c_59070,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_19899]) ).

tcf(c_59071,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk4,sk4))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_19899]) ).

tcf(c_59072,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk4,sk3))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_19899]) ).

tcf(c_59073,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk3,sk4))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_19899]) ).

tcf(c_59074,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),app(sk3,sk3))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_19899]) ).

tcf(c_59075,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_19899]) ).

tcf(c_59076,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_19899]) ).

tcf(c_59077,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_19899]) ).

tcf(c_59078,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_19899]) ).

tcf(c_59079,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_19899]) ).

tcf(c_59080,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_19899]) ).

tcf(c_59081,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_19899]) ).

tcf(c_59082,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_19899]) ).

tcf(c_59083,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_19899]) ).

tcf(c_59084,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_19899]) ).

tcf(c_59085,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_19899]) ).

tcf(c_59086,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_19899]) ).

tcf(c_59087,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_19899]) ).

tcf(c_59166,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_32315,c_280]) ).

tcf(c_59167,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_32315,c_279]) ).

tcf(c_59183,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_32563,c_280]) ).

tcf(c_59184,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_32563,c_279]) ).

tcf(c_59200,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_32972,c_280]) ).

tcf(c_59201,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_32972,c_279]) ).

tcf(c_59217,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_36642,c_280]) ).

tcf(c_59218,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_36642,c_279]) ).

tcf(c_59248,plain,
    cons(hd(sk3),app(sk3,sk4)) != sk4,
    inference(global_subsumption_just,[status(thm)],[c_17698,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7561,c_9218,c_17698,c_20375]) ).

tcf(c_59250,plain,
    cons(hd(sk3),app(sk3,sk3)) != sk3,
    inference(global_subsumption_just,[status(thm)],[c_20487,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7561,c_9218,c_20375,c_20487]) ).

tcf(c_59252,plain,
    hd(app(sk3,app(tl(sk4),sk4))) = hd(sk3),
    inference(global_subsumption_just,[status(thm)],[c_22134,c_247,c_1242,c_22134,c_44932]) ).

tcf(c_59255,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),sk4))))
      | ( app(sk3,app(tl(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),sk4)))
      | ~ ssList(app(sk3,app(tl(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_59252,c_280]) ).

tcf(c_59256,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),sk4))))
      | ( app(sk3,app(tl(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),sk4)))
      | ~ ssList(app(sk3,app(tl(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_59252,c_279]) ).

tcf(c_59275,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk4),app(sk3,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33753]) ).

tcf(c_59276,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33753]) ).

tcf(c_59277,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33753]) ).

tcf(c_59319,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk4),app(sk4,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33757]) ).

tcf(c_59320,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33757]) ).

tcf(c_59321,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33757]) ).

tcf(c_59329,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk4),app(sk3,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33763]) ).

tcf(c_59330,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33763]) ).

tcf(c_59331,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33763]) ).

tcf(c_59339,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk4),app(sk4,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33764]) ).

tcf(c_59340,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33764]) ).

tcf(c_59341,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33764]) ).

tcf(c_59347,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(superposition,[status(thm)],[c_10208,c_255]) ).

tcf(c_59348,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(superposition,[status(thm)],[c_10208,c_254]) ).

tcf(c_59349,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_10208,c_272]) ).

tcf(c_59350,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(app(sk4,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_10208,c_270]) ).

tcf(c_59351,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(X0,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10208,c_269]) ).

tcf(c_59352,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(app(sk4,sk4),cons(hd(sk4),app(sk3,sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10208,c_300]) ).

tcf(c_59353,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(app(sk4,sk4),cons(hd(sk4),app(sk3,sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10208,c_287]) ).

tcf(c_59354,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10208,c_9527]) ).

tcf(c_59355,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk3 )
    | ~ ssList(app(sk4,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10208,c_9248]) ).

tcf(c_59356,plain,
    ( ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk4,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59349,c_10188]) ).

tcf(c_59363,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59348,c_10190,c_10188]) ).

tcf(c_59366,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk3 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59355,c_10188]) ).

tcf(c_59370,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59354,c_10189,c_10188]) ).

tcf(c_59373,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(X0,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59351,c_10188]) ).

tcf(c_59378,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(app(sk4,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59350,c_10188]) ).

tcf(c_59383,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_59353,c_10208]) ).

tcf(c_59384,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59383,c_4059]) ).

tcf(c_59392,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_59352,c_10208]) ).

tcf(c_59393,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59392,c_4059]) ).

tcf(c_59405,plain,
    ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(global_subsumption_just,[status(thm)],[c_59356,c_247,c_20236,c_59356]) ).

tcf(c_59407,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_18773]) ).

tcf(c_59408,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_18497]) ).

tcf(c_59409,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_18185]) ).

tcf(c_59410,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_16330]) ).

tcf(c_59411,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_15966]) ).

tcf(c_59412,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_15593]) ).

tcf(c_59413,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),nil),X0) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_4541]) ).

tcf(c_59414,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3154]) ).

tcf(c_59415,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_4037]) ).

tcf(c_59416,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3952]) ).

tcf(c_59417,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3050]) ).

tcf(c_59418,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0),nil) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3049]) ).

tcf(c_59419,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),sk4),X0) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_4540]) ).

tcf(c_59420,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),sk3),X0) = app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_4539]) ).

tcf(c_59421,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),X0) = app(X1,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_271]) ).

tcf(c_59422,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(cons(X1,X0),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_266]) ).

tcf(c_59423,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),X0) = tl(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_274]) ).

tcf(c_59424,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_283]) ).

tcf(c_59425,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_19899]) ).

tcf(c_59426,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_19024]) ).

tcf(c_59427,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_19014]) ).

tcf(c_59428,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_17999]) ).

tcf(c_59429,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_18774]) ).

tcf(c_59430,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_57010]) ).

tcf(c_59431,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_57009]) ).

tcf(c_59432,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_57008]) ).

tcf(c_59433,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_18772]) ).

tcf(c_59434,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_15409]) ).

tcf(c_59435,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_18498]) ).

tcf(c_59436,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_54564]) ).

tcf(c_59437,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_54563]) ).

tcf(c_59438,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_54562]) ).

tcf(c_59439,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_18496]) ).

tcf(c_59440,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_18186]) ).

tcf(c_59441,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_48819]) ).

tcf(c_59442,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_48818]) ).

tcf(c_59443,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_48817]) ).

tcf(c_59444,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_18184]) ).

tcf(c_59445,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_17287]) ).

tcf(c_59446,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_16680]) ).

tcf(c_59447,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_16670]) ).

tcf(c_59448,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_16331]) ).

tcf(c_59449,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_45260]) ).

tcf(c_59450,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_45259]) ).

tcf(c_59451,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_45258]) ).

tcf(c_59452,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_16329]) ).

tcf(c_59453,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_15967]) ).

tcf(c_59454,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_40467]) ).

tcf(c_59455,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_40466]) ).

tcf(c_59456,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_40465]) ).

tcf(c_59457,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_15965]) ).

tcf(c_59458,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_15594]) ).

tcf(c_59459,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_37606]) ).

tcf(c_59460,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_37605]) ).

tcf(c_59461,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_37604]) ).

tcf(c_59462,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_15592]) ).

tcf(c_59463,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_18000]) ).

tcf(c_59464,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_17998]) ).

tcf(c_59465,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_17997]) ).

tcf(c_59466,plain,
    app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_59405,c_35790]) ).

tcf(c_59467,plain,
    app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_59405,c_35787]) ).

tcf(c_59468,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),nil)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_4463]) ).

tcf(c_59469,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3155]) ).

tcf(c_59470,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_33403]) ).

tcf(c_59471,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_33402]) ).

tcf(c_59472,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_33401]) ).

tcf(c_59473,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_32111]) ).

tcf(c_59474,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_32098]) ).

tcf(c_59475,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_15410]) ).

tcf(c_59476,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_15408]) ).

tcf(c_59477,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_15407]) ).

tcf(c_59478,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3153]) ).

tcf(c_59479,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_4038]) ).

tcf(c_59480,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_17993]) ).

tcf(c_59481,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_17992]) ).

tcf(c_59482,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_17991]) ).

tcf(c_59483,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_4036]) ).

tcf(c_59484,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3953]) ).

tcf(c_59485,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_15403]) ).

tcf(c_59486,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_15402]) ).

tcf(c_59487,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_15401]) ).

tcf(c_59488,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3951]) ).

tcf(c_59489,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3423]) ).

tcf(c_59490,plain,
    app(nil,app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_59405,c_13452]) ).

tcf(c_59491,plain,
    app(app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_59405,c_12354]) ).

tcf(c_59492,plain,
    app(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_59405,c_12353]) ).

tcf(c_59493,plain,
    app(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_59405,c_12352]) ).

tcf(c_59494,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_59405,c_3199]) ).

tcf(c_59495,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3066]) ).

tcf(c_59496,plain,
    app(nil,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_59405,c_8061]) ).

tcf(c_59497,plain,
    app(app(sk4,sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_59405,c_8048]) ).

tcf(c_59498,plain,
    app(nil,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_59405,c_5745]) ).

tcf(c_59499,plain,
    app(app(sk3,sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_59405,c_8047]) ).

tcf(c_59500,plain,
    app(app(sk4,sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_59405,c_5738]) ).

tcf(c_59501,plain,
    app(app(sk3,sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_59405,c_5737]) ).

tcf(c_59502,plain,
    app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = tl(app(sk4,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_59405,c_4136]) ).

tcf(c_59503,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),sk4)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_4462]) ).

tcf(c_59504,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),sk3)) = app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_4461]) ).

tcf(c_59505,plain,
    app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = tl(app(sk3,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_59405,c_4284]) ).

tcf(c_59508,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3019]) ).

tcf(c_59509,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3452]) ).

tcf(c_59510,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3444]) ).

tcf(c_59511,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3065]) ).

tcf(c_59512,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3215]) ).

tcf(c_59513,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3)) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3207]) ).

tcf(c_59514,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_253]) ).

tcf(c_59515,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_275]) ).

tcf(c_59516,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3018]) ).

tcf(c_59517,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_59405,c_3191]) ).

tcf(c_59518,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_59405,c_3183]) ).

tcf(c_59519,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_284]) ).

tcf(c_59520,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_276]) ).

tcf(c_59521,plain,
    app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),nil) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_59405,c_258]) ).

tcf(c_59522,plain,
    app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_59405,c_257]) ).

tcf(c_59636,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(app(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_59424,c_15982]) ).

tcf(c_59645,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) ) ),
    inference(light_normalisation,[status(thm)],[c_59515,c_15982]) ).

tcf(c_59796,plain,
    ssItem(hd(sk3)),
    inference(global_subsumption_just,[status(thm)],[c_49465,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7561]) ).

tcf(c_59952,plain,
    app(app(tl(sk4),sk4),nil) = app(tl(sk4),sk4),
    inference(global_subsumption_just,[status(thm)],[c_22149,c_247,c_1242,c_22149,c_44932]) ).

tcf(c_59962,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(tl(sk4),sk4))
      | ( app(app(tl(sk4),sk4),X0) != app(tl(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_59952,c_270]) ).

tcf(c_59963,plain,
    ! [X0: $i] :
      ( ( app(tl(sk4),sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(tl(sk4),sk4))
      | ( app(tl(sk4),sk4) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_59952,c_269]) ).

tcf(c_59964,plain,
    ! [X0: $i] :
      ( ( app(tl(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(tl(sk4),sk4))
      | ( app(tl(sk4),sk4) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59963,c_259]) ).

tcf(c_59969,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(tl(sk4),sk4))
      | ( app(app(tl(sk4),sk4),X0) != app(tl(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59962,c_259]) ).

tcf(c_59975,plain,
    app(nil,app(tl(sk4),sk4)) = app(tl(sk4),sk4),
    inference(global_subsumption_just,[status(thm)],[c_22150,c_247,c_1242,c_22150,c_44932]) ).

tcf(c_59985,plain,
    ! [X0: $i] :
      ( ( app(tl(sk4),sk4) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(tl(sk4),sk4))
      | ( app(tl(sk4),sk4) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_59975,c_270]) ).

tcf(c_59986,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(tl(sk4),sk4))
      | ( app(X0,app(tl(sk4),sk4)) != app(tl(sk4),sk4) ) ),
    inference(superposition,[status(thm)],[c_59975,c_269]) ).

tcf(c_59987,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(tl(sk4),sk4))
      | ( app(X0,app(tl(sk4),sk4)) != app(tl(sk4),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59986,c_259]) ).

tcf(c_59992,plain,
    ! [X0: $i] :
      ( ( app(tl(sk4),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(tl(sk4),sk4))
      | ( app(tl(sk4),sk4) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_59985,c_259]) ).

tcf(c_60006,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),app(sk3,sk3))) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_34101]) ).

tcf(c_60007,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),app(sk3,sk3))) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_34101]) ).

tcf(c_60008,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),app(sk3,sk3))) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_34101]) ).

tcf(c_60009,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),app(sk3,sk3))) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_34101]) ).

tcf(c_60010,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),app(sk3,sk3))) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_34101]) ).

tcf(c_60011,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),app(sk3,sk3))) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_34101]) ).

tcf(c_60012,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),app(sk3,sk3))) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_34101]) ).

tcf(c_60013,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),app(sk3,sk3))) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_34101]) ).

tcf(c_60014,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),app(sk3,sk3))) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_34101]) ).

tcf(c_60015,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),app(sk3,sk3))) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_34101]) ).

tcf(c_60016,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),app(sk3,sk3))) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_34101]) ).

tcf(c_60017,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),app(sk3,sk3))) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_34101]) ).

tcf(c_60018,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),app(sk3,sk3))) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_34101]) ).

tcf(c_60019,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),app(sk3,sk3))) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_34101]) ).

tcf(c_60020,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),app(sk3,sk3))) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_34101]) ).

tcf(c_60021,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),app(sk3,sk3))) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_34101]) ).

tcf(c_60022,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),app(sk3,sk3))) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_34101]) ).

tcf(c_60023,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),app(sk3,sk3))) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_34101]) ).

tcf(c_60024,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),app(sk3,sk3))) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_34101]) ).

tcf(c_60025,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),app(sk3,sk3))) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_34101]) ).

tcf(c_60026,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),app(sk3,sk3))) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_34101]) ).

tcf(c_60027,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),app(sk3,sk3))) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_34101]) ).

tcf(c_60028,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),app(sk3,sk3))) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_34101]) ).

tcf(c_60029,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),app(sk3,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_34101]) ).

tcf(c_60030,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),app(sk3,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_34101]) ).

tcf(c_60031,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),app(sk3,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_34101]) ).

tcf(c_60032,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),app(sk3,sk3))) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_34101]) ).

tcf(c_60033,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),app(sk3,sk3))) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_34101]) ).

tcf(c_60034,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),app(sk3,sk3))) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_34101]) ).

tcf(c_60035,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),app(sk3,sk3))) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_34101]) ).

tcf(c_60036,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),app(sk3,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_34101]) ).

tcf(c_60037,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),app(sk3,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_34101]) ).

tcf(c_60038,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),app(sk3,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_34101]) ).

tcf(c_60039,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),app(sk3,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_34101]) ).

tcf(c_60040,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),app(sk3,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_34101]) ).

tcf(c_60041,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),app(sk3,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_34101]) ).

tcf(c_60042,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),app(sk3,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_34101]) ).

tcf(c_60043,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),app(sk3,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_34101]) ).

tcf(c_60044,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),app(sk3,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_34101]) ).

tcf(c_60045,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),app(sk3,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_34101]) ).

tcf(c_60046,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),app(sk3,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_34101]) ).

tcf(c_60047,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),app(sk3,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_34101]) ).

tcf(c_60048,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),app(sk3,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_34101]) ).

tcf(c_60049,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),app(sk3,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_34101]) ).

tcf(c_60134,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_36863,c_280]) ).

tcf(c_60135,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_36863,c_279]) ).

tcf(c_60151,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_37186,c_280]) ).

tcf(c_60152,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_37186,c_279]) ).

tcf(c_60168,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3))))))
      | ( cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_43045,c_280]) ).

tcf(c_60169,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3))))))
      | ( cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_43045,c_279]) ).

tcf(c_60185,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3))))))
      | ( cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_43046,c_280]) ).

tcf(c_60186,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3))))))
      | ( cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))
      | ~ ssList(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_43046,c_279]) ).

tcf(c_60205,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk3),app(sk4,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33768]) ).

tcf(c_60206,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33768]) ).

tcf(c_60207,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33768]) ).

tcf(c_60233,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk3),app(sk4,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33769]) ).

tcf(c_60234,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33769]) ).

tcf(c_60235,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33769]) ).

tcf(c_60243,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk3),app(sk3,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33770]) ).

tcf(c_60244,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33770]) ).

tcf(c_60245,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33770]) ).

tcf(c_60253,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,cons(hd(sk3),app(sk3,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_33771]) ).

tcf(c_60254,plain,
    hd(cons(hd(sk4),app(sk3,cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_33771]) ).

tcf(c_60255,plain,
    hd(cons(hd(sk3),app(sk3,cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_33771]) ).

tcf(c_60263,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk4),app(sk3,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34176]) ).

tcf(c_60264,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34176]) ).

tcf(c_60265,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34176]) ).

tcf(c_60301,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk4),app(sk4,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34180]) ).

tcf(c_60302,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34180]) ).

tcf(c_60303,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34180]) ).

tcf(c_60311,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk4),app(sk3,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34186]) ).

tcf(c_60312,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34186]) ).

tcf(c_60313,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34186]) ).

tcf(c_60321,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk4),app(sk4,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34187]) ).

tcf(c_60322,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34187]) ).

tcf(c_60323,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34187]) ).

tcf(c_60335,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4))))
      | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_10209,c_270]) ).

tcf(c_60336,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4))))
      | ( app(X0,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10209,c_269]) ).

tcf(c_60337,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4))))
      | ( app(X0,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60336,c_259]) ).

tcf(c_60342,plain,
    ! [X0: $i] :
      ( ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4))))
      | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60335,c_259]) ).

tcf(c_60357,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),app(sk3,sk4))) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_34149]) ).

tcf(c_60358,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),app(sk3,sk4))) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_34149]) ).

tcf(c_60359,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),app(sk3,sk4))) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_34149]) ).

tcf(c_60360,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),app(sk3,sk4))) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_34149]) ).

tcf(c_60361,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),app(sk3,sk4))) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_34149]) ).

tcf(c_60362,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),app(sk3,sk4))) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_34149]) ).

tcf(c_60363,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),app(sk3,sk4))) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_34149]) ).

tcf(c_60364,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),app(sk3,sk4))) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_34149]) ).

tcf(c_60365,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),app(sk3,sk4))) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_34149]) ).

tcf(c_60366,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),app(sk3,sk4))) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_34149]) ).

tcf(c_60367,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),app(sk3,sk4))) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_34149]) ).

tcf(c_60368,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),app(sk3,sk4))) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_34149]) ).

tcf(c_60369,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),app(sk3,sk4))) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_34149]) ).

tcf(c_60370,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),app(sk3,sk4))) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_34149]) ).

tcf(c_60371,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),app(sk3,sk4))) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_34149]) ).

tcf(c_60372,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),app(sk3,sk4))) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_34149]) ).

tcf(c_60373,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),app(sk3,sk4))) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_34149]) ).

tcf(c_60374,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),app(sk3,sk4))) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_34149]) ).

tcf(c_60375,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),app(sk3,sk4))) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_34149]) ).

tcf(c_60376,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),app(sk3,sk4))) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_34149]) ).

tcf(c_60377,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),app(sk3,sk4))) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_34149]) ).

tcf(c_60378,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),app(sk3,sk4))) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_34149]) ).

tcf(c_60379,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),app(sk3,sk4))) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_34149]) ).

tcf(c_60380,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),app(sk3,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_34149]) ).

tcf(c_60381,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),app(sk3,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_34149]) ).

tcf(c_60382,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),app(sk3,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_34149]) ).

tcf(c_60383,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),app(sk3,sk4))) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_34149]) ).

tcf(c_60384,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),app(sk3,sk4))) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_34149]) ).

tcf(c_60385,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),app(sk3,sk4))) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_34149]) ).

tcf(c_60386,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),app(sk3,sk4))) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_34149]) ).

tcf(c_60387,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),app(sk3,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_34149]) ).

tcf(c_60388,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),app(sk3,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_34149]) ).

tcf(c_60389,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),app(sk3,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_34149]) ).

tcf(c_60390,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),app(sk3,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_34149]) ).

tcf(c_60391,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),app(sk3,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_34149]) ).

tcf(c_60392,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),app(sk3,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_34149]) ).

tcf(c_60393,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),app(sk3,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_34149]) ).

tcf(c_60394,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),app(sk3,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_34149]) ).

tcf(c_60395,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),app(sk3,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_34149]) ).

tcf(c_60396,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),app(sk3,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_34149]) ).

tcf(c_60397,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),app(sk3,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_34149]) ).

tcf(c_60398,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),app(sk3,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_34149]) ).

tcf(c_60399,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),app(sk3,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_34149]) ).

tcf(c_60400,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),app(sk3,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_34149]) ).

tcf(c_60506,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),app(sk4,sk3))) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_34490]) ).

tcf(c_60507,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),app(sk4,sk3))) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_34490]) ).

tcf(c_60508,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),app(sk4,sk3))) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_34490]) ).

tcf(c_60509,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),app(sk4,sk3))) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_34490]) ).

tcf(c_60510,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),app(sk4,sk3))) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_34490]) ).

tcf(c_60511,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),app(sk4,sk3))) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_34490]) ).

tcf(c_60512,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),app(sk4,sk3))) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_34490]) ).

tcf(c_60513,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),app(sk4,sk3))) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_34490]) ).

tcf(c_60514,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),app(sk4,sk3))) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_34490]) ).

tcf(c_60515,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),app(sk4,sk3))) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_34490]) ).

tcf(c_60516,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),app(sk4,sk3))) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_34490]) ).

tcf(c_60517,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),app(sk4,sk3))) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_34490]) ).

tcf(c_60518,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),app(sk4,sk3))) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_34490]) ).

tcf(c_60519,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),app(sk4,sk3))) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_34490]) ).

tcf(c_60520,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),app(sk4,sk3))) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_34490]) ).

tcf(c_60521,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),app(sk4,sk3))) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_34490]) ).

tcf(c_60522,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),app(sk4,sk3))) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_34490]) ).

tcf(c_60523,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),app(sk4,sk3))) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_34490]) ).

tcf(c_60524,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),app(sk4,sk3))) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_34490]) ).

tcf(c_60525,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),app(sk4,sk3))) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_34490]) ).

tcf(c_60526,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),app(sk4,sk3))) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_34490]) ).

tcf(c_60527,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),app(sk4,sk3))) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_34490]) ).

tcf(c_60528,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),app(sk4,sk3))) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_34490]) ).

tcf(c_60529,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),app(sk4,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_34490]) ).

tcf(c_60530,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),app(sk4,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_34490]) ).

tcf(c_60531,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),app(sk4,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_34490]) ).

tcf(c_60532,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),app(sk4,sk3))) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_34490]) ).

tcf(c_60533,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),app(sk4,sk3))) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_34490]) ).

tcf(c_60534,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),app(sk4,sk3))) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_34490]) ).

tcf(c_60535,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),app(sk4,sk3))) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_34490]) ).

tcf(c_60536,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),app(sk4,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_34490]) ).

tcf(c_60537,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),app(sk4,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_34490]) ).

tcf(c_60538,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),app(sk4,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_34490]) ).

tcf(c_60539,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),app(sk4,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_34490]) ).

tcf(c_60540,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),app(sk4,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_34490]) ).

tcf(c_60541,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),app(sk4,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_34490]) ).

tcf(c_60542,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),app(sk4,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_34490]) ).

tcf(c_60543,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),app(sk4,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_34490]) ).

tcf(c_60544,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),app(sk4,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_34490]) ).

tcf(c_60545,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),app(sk4,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_34490]) ).

tcf(c_60546,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),app(sk4,sk3))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_34490]) ).

tcf(c_60547,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),app(sk4,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_34490]) ).

tcf(c_60548,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),app(sk4,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_34490]) ).

tcf(c_60549,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),app(sk4,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_34490]) ).

tcf(c_60644,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),app(sk4,sk4))) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_34548]) ).

tcf(c_60645,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),app(sk4,sk4))) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_34548]) ).

tcf(c_60646,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),app(sk4,sk4))) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_34548]) ).

tcf(c_60647,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),app(sk4,sk4))) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_34548]) ).

tcf(c_60648,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),app(sk4,sk4))) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_34548]) ).

tcf(c_60649,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),app(sk4,sk4))) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_34548]) ).

tcf(c_60650,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),app(sk4,sk4))) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_34548]) ).

tcf(c_60651,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),app(sk4,sk4))) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_34548]) ).

tcf(c_60652,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),app(sk4,sk4))) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_34548]) ).

tcf(c_60653,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),app(sk4,sk4))) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_34548]) ).

tcf(c_60654,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),app(sk4,sk4))) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_34548]) ).

tcf(c_60655,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),app(sk4,sk4))) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_34548]) ).

tcf(c_60656,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),app(sk4,sk4))) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_34548]) ).

tcf(c_60657,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),app(sk4,sk4))) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_34548]) ).

tcf(c_60658,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),app(sk4,sk4))) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_34548]) ).

tcf(c_60659,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),app(sk4,sk4))) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_34548]) ).

tcf(c_60660,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),app(sk4,sk4))) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_34548]) ).

tcf(c_60661,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),app(sk4,sk4))) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_34548]) ).

tcf(c_60662,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),app(sk4,sk4))) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_34548]) ).

tcf(c_60663,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),app(sk4,sk4))) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_34548]) ).

tcf(c_60664,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),app(sk4,sk4))) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_34548]) ).

tcf(c_60665,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),app(sk4,sk4))) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_34548]) ).

tcf(c_60666,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),app(sk4,sk4))) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_34548]) ).

tcf(c_60667,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),app(sk4,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_34548]) ).

tcf(c_60668,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),app(sk4,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_34548]) ).

tcf(c_60669,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),app(sk4,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_34548]) ).

tcf(c_60670,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),app(sk4,sk4))) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_34548]) ).

tcf(c_60671,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),app(sk4,sk4))) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_34548]) ).

tcf(c_60672,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),app(sk4,sk4))) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_34548]) ).

tcf(c_60673,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),app(sk4,sk4))) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_34548]) ).

tcf(c_60674,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),app(sk4,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_34548]) ).

tcf(c_60675,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),app(sk4,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_34548]) ).

tcf(c_60676,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),app(sk4,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_34548]) ).

tcf(c_60677,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),app(sk4,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_34548]) ).

tcf(c_60678,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),app(sk4,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_34548]) ).

tcf(c_60679,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),app(sk4,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_34548]) ).

tcf(c_60680,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),app(sk4,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_34548]) ).

tcf(c_60681,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),app(sk4,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_34548]) ).

tcf(c_60682,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),app(sk4,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_34548]) ).

tcf(c_60683,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),app(sk4,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_34548]) ).

tcf(c_60684,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),app(sk4,sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_34548]) ).

tcf(c_60685,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),app(sk4,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_34548]) ).

tcf(c_60686,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),app(sk4,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_34548]) ).

tcf(c_60687,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),app(sk4,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_34548]) ).

tcf(c_60774,plain,
    ! [X0: $i] :
      ( ( sk3 = nil )
      | ( tl(cons(X0,tl(sk3))) = tl(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_246,c_3118]) ).

tcf(c_60775,plain,
    ! [X0: $i] :
      ( ( sk4 = nil )
      | ( tl(cons(X0,tl(sk4))) = tl(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_247,c_3118]) ).

tcf(c_60777,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( tl(cons(X1,tl(tl(X0)))) = tl(tl(X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3118]) ).

tcf(c_60778,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( app(X1,X0) = nil )
      | ( tl(cons(X2,tl(app(X1,X0)))) = tl(app(X1,X0)) )
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3118]) ).

tcf(c_60779,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( cons(X1,X0) = nil )
      | ( tl(cons(X2,tl(cons(X1,X0)))) = tl(cons(X1,X0)) )
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3118]) ).

tcf(c_60780,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk3) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk3),sk3)))) = tl(cons(hd(sk3),sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_13784,c_3118]) ).

tcf(c_60781,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk4),sk3)))) = tl(cons(hd(sk4),sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4358,c_3118]) ).

tcf(c_60782,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),sk4) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk3),sk4)))) = tl(cons(hd(sk3),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_12796,c_3118]) ).

tcf(c_60783,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk4),sk4)))) = tl(cons(hd(sk4),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_4223,c_3118]) ).

tcf(c_60784,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = nil )
      | ( app(tl(sk3),sk3) = nil )
      | ( tl(cons(X0,tl(app(tl(sk3),sk3)))) = tl(app(tl(sk3),sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3118]) ).

tcf(c_60785,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = nil )
      | ( app(tl(sk3),sk4) = nil )
      | ( tl(cons(X0,tl(app(tl(sk3),sk4)))) = tl(app(tl(sk3),sk4)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3118]) ).

tcf(c_60786,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = nil )
      | ( app(tl(sk4),sk3) = nil )
      | ( tl(cons(X0,tl(app(tl(sk4),sk3)))) = tl(app(tl(sk4),sk3)) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3118]) ).

tcf(c_60787,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = nil )
      | ( app(tl(sk4),sk4) = nil )
      | ( tl(cons(X0,tl(app(tl(sk4),sk4)))) = tl(app(tl(sk4),sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_22091,c_3118]) ).

tcf(c_60788,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk4),app(sk3,sk3))))) = tl(cons(hd(sk4),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_5886,c_3118]) ).

tcf(c_60789,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,sk3)) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk3,sk3))))) = tl(app(sk3,app(sk3,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3118]) ).

tcf(c_60790,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,sk4)) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk3,sk4))))) = tl(app(sk3,app(sk3,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3118]) ).

tcf(c_60791,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,sk3)) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk3,sk3))))) = tl(app(sk4,app(sk3,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3118]) ).

tcf(c_60792,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk4),app(sk4,sk3))))) = tl(cons(hd(sk4),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_7540,c_3118]) ).

tcf(c_60793,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,sk4)) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk3,sk4))))) = tl(app(sk4,app(sk3,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3118]) ).

tcf(c_60794,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,sk3)) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk4,sk3))))) = tl(app(sk3,app(sk4,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3118]) ).

tcf(c_60795,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,sk4)) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk4,sk4))))) = tl(app(sk3,app(sk4,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3118]) ).

tcf(c_60796,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,sk3)) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk4,sk3))))) = tl(app(sk4,app(sk4,sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3118]) ).

tcf(c_60797,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,sk4)) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk4,sk4))))) = tl(app(sk4,app(sk4,sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3118]) ).

tcf(c_60798,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk4),app(sk3,sk4))))) = tl(cons(hd(sk4),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10188,c_3118]) ).

tcf(c_60799,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk4),app(sk4,sk4))))) = tl(cons(hd(sk4),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_10606,c_3118]) ).

tcf(c_60800,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3118]) ).

tcf(c_60801,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3118]) ).

tcf(c_60802,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3118]) ).

tcf(c_60803,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk3),app(sk4,sk4))))) = tl(cons(hd(sk3),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_16922,c_3118]) ).

tcf(c_60804,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk3),app(sk4,sk3))))) = tl(cons(hd(sk3),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_19123,c_3118]) ).

tcf(c_60805,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk3),app(sk3,sk4))))) = tl(cons(hd(sk3),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_17697,c_3118]) ).

tcf(c_60806,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk3),app(sk3,sk3))))) = tl(cons(hd(sk3),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_20483,c_3118]) ).

tcf(c_60807,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3118]) ).

tcf(c_60808,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3118]) ).

tcf(c_60809,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_50099,c_3118]) ).

tcf(c_60810,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_51167,c_3118]) ).

tcf(c_60811,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_42609,c_3118]) ).

tcf(c_60812,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_43441,c_3118]) ).

tcf(c_60813,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3118]) ).

tcf(c_60814,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3118]) ).

tcf(c_60815,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_52696,c_3118]) ).

tcf(c_60816,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_53971,c_3118]) ).

tcf(c_60817,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_59405,c_3118]) ).

tcf(c_60818,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3118]) ).

tcf(c_60819,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_44714,c_3118]) ).

tcf(c_60820,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_46613,c_3118]) ).

tcf(c_60821,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(sk4))) = tl(sk4) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60775,c_1243]) ).

tcf(c_60827,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk4) = nil )
      | ( tl(cons(X0,sk4)) = sk4 )
      | ~ ssItem(X0) ),
    inference(light_normalisation,[status(thm)],[c_60783,c_3280]) ).

tcf(c_60830,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),sk3) = nil )
      | ( tl(cons(X0,sk3)) = sk3 )
      | ~ ssItem(X0) ),
    inference(light_normalisation,[status(thm)],[c_60781,c_3246]) ).

tcf(c_60848,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(cons(hd(sk3),app(sk3,sk3))))) = tl(cons(hd(sk3),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60806,c_20706]) ).

tcf(c_60851,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(cons(hd(sk3),app(sk3,sk4))))) = tl(cons(hd(sk3),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60805,c_17701]) ).

tcf(c_60854,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(cons(hd(sk3),app(sk4,sk3))))) = tl(cons(hd(sk3),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60804,c_19513]) ).

tcf(c_60857,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(cons(hd(sk3),app(sk4,sk4))))) = tl(cons(hd(sk3),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60803,c_16926]) ).

tcf(c_60860,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(cons(hd(sk4),app(sk4,sk4))))) = tl(cons(hd(sk4),app(sk4,sk4))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60799,c_10611]) ).

tcf(c_60863,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(cons(hd(sk4),app(sk3,sk4))))) = tl(cons(hd(sk4),app(sk3,sk4))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60798,c_10190]) ).

tcf(c_60866,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(cons(hd(sk4),app(sk4,sk3))))) = tl(cons(hd(sk4),app(sk4,sk3))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60792,c_7545]) ).

tcf(c_60869,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(cons(hd(sk4),app(sk3,sk3))))) = tl(cons(hd(sk4),app(sk3,sk3))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60788,c_5891]) ).

tcf(c_60923,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60812,c_44126]) ).

tcf(c_60926,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60811,c_43038]) ).

tcf(c_60929,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60810,c_51895]) ).

tcf(c_60932,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))) )
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60809,c_50642]) ).

tcf(c_61324,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),tl(sk4))) = tl(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_60821]) ).

tcf(c_61325,plain,
    tl(cons(hd(sk4),tl(sk4))) = tl(sk4),
    inference(superposition,[status(thm)],[c_4059,c_60821]) ).

tcf(c_61326,plain,
    tl(cons(hd(sk3),tl(sk4))) = tl(sk4),
    inference(superposition,[status(thm)],[c_10117,c_60821]) ).

tcf(c_61332,plain,
    ( ssList(tl(sk4))
    | ( cons(hd(sk3),tl(sk4)) = nil )
    | ~ ssList(cons(hd(sk3),tl(sk4))) ),
    inference(superposition,[status(thm)],[c_61326,c_278]) ).

tcf(c_61333,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),tl(sk4)) = nil )
      | ( cons(hd(sk3),tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),tl(sk4)))
      | ( tl(X0) != tl(sk4) )
      | ( hd(cons(hd(sk3),tl(sk4))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_61326,c_273]) ).

tcf(c_61337,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),tl(sk4)) = nil )
      | ( cons(hd(sk3),tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),tl(sk4)))
      | ( hd(X0) != hd(sk3) )
      | ( tl(X0) != tl(sk4) ) ),
    inference(light_normalisation,[status(thm)],[c_61333,c_32100]) ).

tcf(c_61346,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4))))))
      | ( cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_44133,c_280]) ).

tcf(c_61347,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4))))))
      | ( cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_44133,c_279]) ).

tcf(c_61380,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4))))))
      | ( cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_44134,c_280]) ).

tcf(c_61381,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4))))))
      | ( cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))
      | ~ ssList(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_44134,c_279]) ).

tcf(c_61396,plain,
    ! [X0: $i] :
      ( ~ ssItem(X0)
      | ( tl(cons(X0,tl(sk3))) = tl(sk3) ) ),
    inference(global_subsumption_just,[status(thm)],[c_60774,c_24765]) ).

tcf(c_61397,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,tl(sk3))) = tl(sk3) )
      | ~ ssItem(X0) ),
    inference(renaming,[status(thm)],[c_61396]) ).

tcf(c_61402,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),tl(sk3))) = tl(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_61397]) ).

tcf(c_61403,plain,
    tl(cons(hd(sk4),tl(sk3))) = tl(sk3),
    inference(superposition,[status(thm)],[c_4059,c_61397]) ).

tcf(c_61404,plain,
    tl(cons(hd(sk3),tl(sk3))) = tl(sk3),
    inference(superposition,[status(thm)],[c_10117,c_61397]) ).

tcf(c_61409,plain,
    ( ssList(tl(sk3))
    | ( cons(hd(sk4),tl(sk3)) = nil )
    | ~ ssList(cons(hd(sk4),tl(sk3))) ),
    inference(superposition,[status(thm)],[c_61403,c_278]) ).

tcf(c_61410,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),tl(sk3)) = nil )
      | ( cons(hd(sk4),tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),tl(sk3)))
      | ( tl(X0) != tl(sk3) )
      | ( hd(cons(hd(sk4),tl(sk3))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_61403,c_273]) ).

tcf(c_61414,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk4),tl(sk3)) = nil )
      | ( cons(hd(sk4),tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),tl(sk3)))
      | ( hd(X0) != hd(sk4) )
      | ( tl(X0) != tl(sk3) ) ),
    inference(light_normalisation,[status(thm)],[c_61410,c_32112]) ).

tcf(c_61423,plain,
    ( ssList(tl(sk3))
    | ( cons(hd(sk3),tl(sk3)) = nil )
    | ~ ssList(cons(hd(sk3),tl(sk3))) ),
    inference(superposition,[status(thm)],[c_61404,c_278]) ).

tcf(c_61424,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),tl(sk3)) = nil )
      | ( cons(hd(sk3),tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),tl(sk3)))
      | ( tl(X0) != tl(sk3) )
      | ( hd(cons(hd(sk3),tl(sk3))) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_61404,c_273]) ).

tcf(c_61428,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(sk3),tl(sk3)) = nil )
      | ( cons(hd(sk3),tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),tl(sk3)))
      | ( hd(X0) != hd(sk3) )
      | ( tl(X0) != tl(sk3) ) ),
    inference(light_normalisation,[status(thm)],[c_61424,c_32113]) ).

tcf(c_61549,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk3),app(sk4,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34191]) ).

tcf(c_61550,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34191]) ).

tcf(c_61551,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34191]) ).

tcf(c_61567,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk3),app(sk4,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34192]) ).

tcf(c_61568,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34192]) ).

tcf(c_61569,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34192]) ).

tcf(c_61610,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk3),app(sk3,sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34193]) ).

tcf(c_61611,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34193]) ).

tcf(c_61612,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34193]) ).

tcf(c_61620,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,cons(hd(sk3),app(sk3,sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_34194]) ).

tcf(c_61621,plain,
    hd(cons(hd(sk4),app(sk4,cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_34194]) ).

tcf(c_61622,plain,
    hd(cons(hd(sk3),app(sk4,cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_34194]) ).

tcf(c_61627,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38016,c_280]) ).

tcf(c_61628,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38016,c_279]) ).

tcf(c_61645,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(superposition,[status(thm)],[c_10210,c_255]) ).

tcf(c_61646,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(superposition,[status(thm)],[c_10210,c_254]) ).

tcf(c_61647,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_10210,c_272]) ).

tcf(c_61648,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(app(sk3,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_10210,c_270]) ).

tcf(c_61649,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(X0,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10210,c_269]) ).

tcf(c_61650,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(app(sk3,sk4),cons(hd(sk4),app(sk3,sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10210,c_300]) ).

tcf(c_61651,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(app(sk3,sk4),cons(hd(sk4),app(sk3,sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10210,c_287]) ).

tcf(c_61652,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10210,c_8552]) ).

tcf(c_61653,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk3 )
    | ~ ssList(app(sk3,sk4))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10210,c_8271]) ).

tcf(c_61654,plain,
    ( ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk3,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61647,c_10188]) ).

tcf(c_61661,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61646,c_10190,c_10188]) ).

tcf(c_61664,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk3 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61653,c_10188]) ).

tcf(c_61668,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61652,c_10189,c_10188]) ).

tcf(c_61671,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(X0,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61649,c_10188]) ).

tcf(c_61676,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) != app(app(sk3,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61648,c_10188]) ).

tcf(c_61681,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_61651,c_10210]) ).

tcf(c_61682,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61681,c_4059]) ).

tcf(c_61689,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_61650,c_10210]) ).

tcf(c_61690,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61689,c_4059]) ).

tcf(c_61722,plain,
    ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(global_subsumption_just,[status(thm)],[c_61654,c_247,c_246,c_42153,c_61654]) ).

tcf(c_61724,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_18773]) ).

tcf(c_61725,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_18497]) ).

tcf(c_61726,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_18185]) ).

tcf(c_61727,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_16330]) ).

tcf(c_61728,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_15966]) ).

tcf(c_61729,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_15593]) ).

tcf(c_61730,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),nil),X0) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_4541]) ).

tcf(c_61731,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3154]) ).

tcf(c_61732,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_4037]) ).

tcf(c_61733,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3952]) ).

tcf(c_61734,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3050]) ).

tcf(c_61735,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0),nil) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3049]) ).

tcf(c_61736,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),sk4),X0) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_4540]) ).

tcf(c_61737,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),sk3),X0) = app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_4539]) ).

tcf(c_61738,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),X0) = app(X1,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_271]) ).

tcf(c_61739,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(cons(X1,X0),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_266]) ).

tcf(c_61740,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),X0) = tl(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_274]) ).

tcf(c_61741,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_283]) ).

tcf(c_61742,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3118]) ).

tcf(c_61743,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),app(sk4,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_34548]) ).

tcf(c_61744,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),app(sk4,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_34490]) ).

tcf(c_61745,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),app(sk3,sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_34149]) ).

tcf(c_61746,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),app(sk3,sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_34101]) ).

tcf(c_61747,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_19899]) ).

tcf(c_61748,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_19024]) ).

tcf(c_61749,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_19014]) ).

tcf(c_61750,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_17999]) ).

tcf(c_61751,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_18774]) ).

tcf(c_61752,plain,
    hd(app(sk3,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_57010]) ).

tcf(c_61753,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_57009]) ).

tcf(c_61754,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_57008]) ).

tcf(c_61755,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_18772]) ).

tcf(c_61756,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_15409]) ).

tcf(c_61757,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_18498]) ).

tcf(c_61758,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_54564]) ).

tcf(c_61759,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_54563]) ).

tcf(c_61760,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_54562]) ).

tcf(c_61761,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_18496]) ).

tcf(c_61762,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_18186]) ).

tcf(c_61763,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_48819]) ).

tcf(c_61764,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_48818]) ).

tcf(c_61765,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_48817]) ).

tcf(c_61766,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_18184]) ).

tcf(c_61767,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_17287]) ).

tcf(c_61768,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_16680]) ).

tcf(c_61769,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_16670]) ).

tcf(c_61770,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_16331]) ).

tcf(c_61771,plain,
    hd(app(sk4,app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_45260]) ).

tcf(c_61772,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_45259]) ).

tcf(c_61773,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_45258]) ).

tcf(c_61774,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_16329]) ).

tcf(c_61775,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_15967]) ).

tcf(c_61776,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_40467]) ).

tcf(c_61777,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_40466]) ).

tcf(c_61778,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_40465]) ).

tcf(c_61779,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_15965]) ).

tcf(c_61780,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_15594]) ).

tcf(c_61781,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_37606]) ).

tcf(c_61782,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_37605]) ).

tcf(c_61783,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_37604]) ).

tcf(c_61784,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_15592]) ).

tcf(c_61785,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_18000]) ).

tcf(c_61786,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_17998]) ).

tcf(c_61787,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_17997]) ).

tcf(c_61788,plain,
    app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_61722,c_35790]) ).

tcf(c_61789,plain,
    app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_61722,c_35787]) ).

tcf(c_61790,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),nil)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_4463]) ).

tcf(c_61791,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3155]) ).

tcf(c_61792,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_33403]) ).

tcf(c_61793,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_33402]) ).

tcf(c_61794,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_33401]) ).

tcf(c_61795,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(sk3))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_32111]) ).

tcf(c_61796,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_32098]) ).

tcf(c_61797,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_15410]) ).

tcf(c_61798,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_15408]) ).

tcf(c_61799,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_15407]) ).

tcf(c_61800,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3153]) ).

tcf(c_61801,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_4038]) ).

tcf(c_61802,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_17993]) ).

tcf(c_61803,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_17992]) ).

tcf(c_61804,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_17991]) ).

tcf(c_61805,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_4036]) ).

tcf(c_61806,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3953]) ).

tcf(c_61807,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_15403]) ).

tcf(c_61808,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_15402]) ).

tcf(c_61809,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_15401]) ).

tcf(c_61810,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3951]) ).

tcf(c_61811,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3423]) ).

tcf(c_61812,plain,
    app(nil,app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_61722,c_13452]) ).

tcf(c_61813,plain,
    app(app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_61722,c_12354]) ).

tcf(c_61814,plain,
    app(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_61722,c_12353]) ).

tcf(c_61815,plain,
    app(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_61722,c_12352]) ).

tcf(c_61816,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_61722,c_3199]) ).

tcf(c_61817,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3066]) ).

tcf(c_61818,plain,
    app(nil,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_61722,c_8061]) ).

tcf(c_61819,plain,
    app(app(sk4,sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_61722,c_8048]) ).

tcf(c_61820,plain,
    app(nil,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_61722,c_5745]) ).

tcf(c_61821,plain,
    app(app(sk3,sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_61722,c_8047]) ).

tcf(c_61822,plain,
    app(app(sk4,sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_61722,c_5738]) ).

tcf(c_61823,plain,
    app(app(sk3,sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_61722,c_5737]) ).

tcf(c_61824,plain,
    app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = tl(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_61722,c_4136]) ).

tcf(c_61825,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),sk4)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_4462]) ).

tcf(c_61826,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),sk3)) = app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_4461]) ).

tcf(c_61827,plain,
    app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = tl(app(sk3,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_61722,c_4284]) ).

tcf(c_61830,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3019]) ).

tcf(c_61831,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3452]) ).

tcf(c_61832,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3444]) ).

tcf(c_61833,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3065]) ).

tcf(c_61834,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3215]) ).

tcf(c_61835,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3)) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3207]) ).

tcf(c_61836,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_253]) ).

tcf(c_61837,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_275]) ).

tcf(c_61838,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) = cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_3018]) ).

tcf(c_61839,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_61722,c_3191]) ).

tcf(c_61840,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_61722,c_3183]) ).

tcf(c_61841,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_284]) ).

tcf(c_61842,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_61722,c_276]) ).

tcf(c_61843,plain,
    app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),nil) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_61722,c_258]) ).

tcf(c_61844,plain,
    app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_61722,c_257]) ).

tcf(c_61962,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(app(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_61741,c_18513]) ).

tcf(c_61974,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) ) ),
    inference(light_normalisation,[status(thm)],[c_61837,c_18513]) ).

tcf(c_62471,plain,
    ( ( sk4 = nil )
    | ( tl(cons(hd(sk4),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_247,c_61324]) ).

tcf(c_62473,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( tl(cons(hd(tl(X0)),tl(sk4))) = tl(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_61324]) ).

tcf(c_62474,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( tl(cons(hd(app(X1,X0)),tl(sk4))) = tl(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_61324]) ).

tcf(c_62475,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( tl(cons(hd(cons(X1,X0)),tl(sk4))) = tl(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_61324]) ).

tcf(c_62476,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk3)),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_61324]) ).

tcf(c_62477,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk3)),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_61324]) ).

tcf(c_62478,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk4)),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_61324]) ).

tcf(c_62479,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk4)),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_61324]) ).

tcf(c_62480,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk3)),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_61324]) ).

tcf(c_62481,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk4)),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_61324]) ).

tcf(c_62482,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk3)),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_61324]) ).

tcf(c_62483,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk4)),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_61324]) ).

tcf(c_62484,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_61324]) ).

tcf(c_62485,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk3))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_61324]) ).

tcf(c_62486,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk4))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_61324]) ).

tcf(c_62487,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk3))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_61324]) ).

tcf(c_62488,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk3))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_61324]) ).

tcf(c_62489,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk4))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_61324]) ).

tcf(c_62490,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk3))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_61324]) ).

tcf(c_62491,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk4))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_61324]) ).

tcf(c_62492,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk3))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_61324]) ).

tcf(c_62493,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk4))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_61324]) ).

tcf(c_62494,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk4))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_61324]) ).

tcf(c_62495,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk4))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_61324]) ).

tcf(c_62496,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_61324]) ).

tcf(c_62497,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_61324]) ).

tcf(c_62498,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_61324]) ).

tcf(c_62499,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk4))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_61324]) ).

tcf(c_62500,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk3))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_61324]) ).

tcf(c_62501,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk4))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_61324]) ).

tcf(c_62502,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk3))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_61324]) ).

tcf(c_62503,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_61324]) ).

tcf(c_62504,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_61324]) ).

tcf(c_62505,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_61324]) ).

tcf(c_62506,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_61324]) ).

tcf(c_62507,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_61324]) ).

tcf(c_62508,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_61324]) ).

tcf(c_62509,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_61324]) ).

tcf(c_62510,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_61324]) ).

tcf(c_62511,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_61324]) ).

tcf(c_62512,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_61324]) ).

tcf(c_62513,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_61324]) ).

tcf(c_62514,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_61324]) ).

tcf(c_62515,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_61324]) ).

tcf(c_62516,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_61324]) ).

tcf(c_62517,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_61324]) ).

tcf(c_62639,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( tl(cons(hd(tl(X0)),tl(sk3))) = tl(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_61402]) ).

tcf(c_62640,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( tl(cons(hd(app(X1,X0)),tl(sk3))) = tl(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_61402]) ).

tcf(c_62641,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( tl(cons(hd(cons(X1,X0)),tl(sk3))) = tl(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_61402]) ).

tcf(c_62642,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk3)),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_61402]) ).

tcf(c_62643,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk3)),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_61402]) ).

tcf(c_62644,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk3),sk4)),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_61402]) ).

tcf(c_62645,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( tl(cons(hd(cons(hd(sk4),sk4)),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_61402]) ).

tcf(c_62646,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk3)),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_61402]) ).

tcf(c_62647,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk3),sk4)),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_61402]) ).

tcf(c_62648,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk3)),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_61402]) ).

tcf(c_62649,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( tl(cons(hd(app(tl(sk4),sk4)),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_61402]) ).

tcf(c_62650,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk3))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_61402]) ).

tcf(c_62651,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk3))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_61402]) ).

tcf(c_62652,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,sk4))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_61402]) ).

tcf(c_62653,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk3))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_61402]) ).

tcf(c_62654,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk3))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_61402]) ).

tcf(c_62655,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,sk4))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_61402]) ).

tcf(c_62656,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk3))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_61402]) ).

tcf(c_62657,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,sk4))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_61402]) ).

tcf(c_62658,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk3))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_61402]) ).

tcf(c_62659,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,sk4))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_61402]) ).

tcf(c_62660,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk3,sk4))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_61402]) ).

tcf(c_62661,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk4),app(sk4,sk4))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_61402]) ).

tcf(c_62662,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_61402]) ).

tcf(c_62663,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_61402]) ).

tcf(c_62664,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_61402]) ).

tcf(c_62665,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk4))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_61402]) ).

tcf(c_62666,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk4,sk3))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_61402]) ).

tcf(c_62667,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk4))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_61402]) ).

tcf(c_62668,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),app(sk3,sk3))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_61402]) ).

tcf(c_62669,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_61402]) ).

tcf(c_62670,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_61402]) ).

tcf(c_62671,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_61402]) ).

tcf(c_62672,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_61402]) ).

tcf(c_62673,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_61402]) ).

tcf(c_62674,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_61402]) ).

tcf(c_62675,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_61402]) ).

tcf(c_62676,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_61402]) ).

tcf(c_62677,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_61402]) ).

tcf(c_62678,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_61402]) ).

tcf(c_62679,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_61402]) ).

tcf(c_62680,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_61402]) ).

tcf(c_62681,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_61402]) ).

tcf(c_62682,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_61402]) ).

tcf(c_62683,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_61402]) ).

tcf(c_62750,plain,
    ssList(tl(sk4)),
    inference(global_subsumption_just,[status(thm)],[c_61332,c_247,c_1242,c_3427]) ).

tcf(c_62752,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(tl(sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_18773]) ).

tcf(c_62753,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(tl(sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_18497]) ).

tcf(c_62754,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(tl(sk4),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_18185]) ).

tcf(c_62755,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(tl(sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_16330]) ).

tcf(c_62756,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(tl(sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_15966]) ).

tcf(c_62757,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(tl(sk4),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_15593]) ).

tcf(c_62758,plain,
    ! [X0: $i] :
      ( ( app(app(tl(sk4),nil),X0) = app(tl(sk4),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_4541]) ).

tcf(c_62759,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(tl(sk4),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3154]) ).

tcf(c_62760,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(tl(sk4),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_4037]) ).

tcf(c_62761,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(tl(sk4),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3952]) ).

tcf(c_62762,plain,
    ! [X0: $i] :
      ( ( app(nil,app(tl(sk4),X0)) = app(tl(sk4),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3050]) ).

tcf(c_62763,plain,
    ! [X0: $i] :
      ( ( app(app(tl(sk4),X0),nil) = app(tl(sk4),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3049]) ).

tcf(c_62764,plain,
    ! [X0: $i] :
      ( ( app(app(tl(sk4),sk4),X0) = app(tl(sk4),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_4540]) ).

tcf(c_62765,plain,
    ! [X0: $i] :
      ( ( app(app(tl(sk4),sk3),X0) = app(tl(sk4),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_4539]) ).

tcf(c_62766,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,tl(sk4)),X0) = app(X1,app(tl(sk4),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_271]) ).

tcf(c_62767,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,tl(sk4))) = app(cons(X1,X0),tl(sk4)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_266]) ).

tcf(c_62768,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = nil )
      | ( app(tl(tl(sk4)),X0) = tl(app(tl(sk4),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_274]) ).

tcf(c_62769,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = nil )
      | ( hd(app(tl(sk4),X0)) = hd(tl(sk4)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_283]) ).

tcf(c_62770,plain,
    ( ( tl(sk4) = nil )
    | ( tl(cons(hd(tl(sk4)),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_61402]) ).

tcf(c_62771,plain,
    ( ( tl(sk4) = nil )
    | ( tl(cons(hd(tl(sk4)),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_61324]) ).

tcf(c_62772,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = nil )
      | ( tl(cons(X0,tl(tl(sk4)))) = tl(tl(sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3118]) ).

tcf(c_62773,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),app(sk4,sk4))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_34548]) ).

tcf(c_62774,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),app(sk4,sk3))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_34490]) ).

tcf(c_62775,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),app(sk3,sk4))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_34149]) ).

tcf(c_62776,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),app(sk3,sk3))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_34101]) ).

tcf(c_62777,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk3,cons(hd(tl(sk4)),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_19899]) ).

tcf(c_62778,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk3,cons(hd(tl(sk4)),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_19024]) ).

tcf(c_62779,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk3,cons(hd(tl(sk4)),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_19014]) ).

tcf(c_62780,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_17999]) ).

tcf(c_62781,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,tl(sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_18774]) ).

tcf(c_62782,plain,
    hd(app(sk3,app(nil,app(nil,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_57010]) ).

tcf(c_62783,plain,
    hd(app(sk3,app(nil,app(sk4,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_57009]) ).

tcf(c_62784,plain,
    hd(app(sk3,app(nil,app(sk3,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_57008]) ).

tcf(c_62785,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk3,app(nil,tl(tl(sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_18772]) ).

tcf(c_62786,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_15409]) ).

tcf(c_62787,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,tl(sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_18498]) ).

tcf(c_62788,plain,
    hd(app(sk3,app(sk4,app(nil,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_54564]) ).

tcf(c_62789,plain,
    hd(app(sk3,app(sk4,app(sk4,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_54563]) ).

tcf(c_62790,plain,
    hd(app(sk3,app(sk4,app(sk3,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_54562]) ).

tcf(c_62791,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk3,app(sk4,tl(tl(sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_18496]) ).

tcf(c_62792,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,tl(sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_18186]) ).

tcf(c_62793,plain,
    hd(app(sk3,app(sk3,app(nil,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_48819]) ).

tcf(c_62794,plain,
    hd(app(sk3,app(sk3,app(sk4,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_48818]) ).

tcf(c_62795,plain,
    hd(app(sk3,app(sk3,app(sk3,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_48817]) ).

tcf(c_62796,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk3,app(sk3,tl(tl(sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_18184]) ).

tcf(c_62797,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk4,cons(hd(tl(sk4)),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_17287]) ).

tcf(c_62798,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk4,cons(hd(tl(sk4)),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_16680]) ).

tcf(c_62799,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk4,cons(hd(tl(sk4)),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_16670]) ).

tcf(c_62800,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,tl(sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_16331]) ).

tcf(c_62801,plain,
    hd(app(sk4,app(nil,app(nil,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_45260]) ).

tcf(c_62802,plain,
    hd(app(sk4,app(nil,app(sk4,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_45259]) ).

tcf(c_62803,plain,
    hd(app(sk4,app(nil,app(sk3,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_45258]) ).

tcf(c_62804,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk4,app(nil,tl(tl(sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_16329]) ).

tcf(c_62805,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,tl(sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_15967]) ).

tcf(c_62806,plain,
    hd(app(sk4,app(sk4,app(nil,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_40467]) ).

tcf(c_62807,plain,
    hd(app(sk4,app(sk4,app(sk4,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_40466]) ).

tcf(c_62808,plain,
    hd(app(sk4,app(sk4,app(sk3,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_40465]) ).

tcf(c_62809,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk4,app(sk4,tl(tl(sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_15965]) ).

tcf(c_62810,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,tl(sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_15594]) ).

tcf(c_62811,plain,
    hd(app(sk4,app(sk3,app(nil,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_37606]) ).

tcf(c_62812,plain,
    hd(app(sk4,app(sk3,app(sk4,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_37605]) ).

tcf(c_62813,plain,
    hd(app(sk4,app(sk3,app(sk3,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_37604]) ).

tcf(c_62814,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk4,app(sk3,tl(tl(sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_15592]) ).

tcf(c_62815,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_18000]) ).

tcf(c_62816,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_17998]) ).

tcf(c_62817,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_17997]) ).

tcf(c_62818,plain,
    app(sk3,app(nil,tl(sk4))) = app(sk3,tl(sk4)),
    inference(superposition,[status(thm)],[c_62750,c_35790]) ).

tcf(c_62819,plain,
    app(sk4,app(nil,tl(sk4))) = app(sk4,tl(sk4)),
    inference(superposition,[status(thm)],[c_62750,c_35787]) ).

tcf(c_62820,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(tl(sk4),nil)) = app(cons(X0,tl(sk4)),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_4463]) ).

tcf(c_62821,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,tl(sk4)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3155]) ).

tcf(c_62822,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,tl(sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_33403]) ).

tcf(c_62823,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,tl(sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_33402]) ).

tcf(c_62824,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,tl(sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_33401]) ).

tcf(c_62825,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),tl(sk3))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_32111]) ).

tcf(c_62826,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),tl(sk4))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_32098]) ).

tcf(c_62827,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_15410]) ).

tcf(c_62828,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_15408]) ).

tcf(c_62829,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_15407]) ).

tcf(c_62830,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = nil )
      | ( hd(cons(X0,tl(tl(sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3153]) ).

tcf(c_62831,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,tl(sk4)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_4038]) ).

tcf(c_62832,plain,
    hd(app(sk3,app(nil,tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_17993]) ).

tcf(c_62835,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk3,tl(tl(sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_4036]) ).

tcf(c_62836,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,tl(sk4)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3953]) ).

tcf(c_62837,plain,
    hd(app(sk4,app(nil,tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_15403]) ).

tcf(c_62840,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(sk4,tl(tl(sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3951]) ).

tcf(c_62841,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),nil)) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3423]) ).

tcf(c_62842,plain,
    app(nil,app(nil,tl(sk4))) = app(nil,tl(sk4)),
    inference(superposition,[status(thm)],[c_62750,c_13452]) ).

tcf(c_62843,plain,
    app(app(nil,tl(sk4)),nil) = app(nil,tl(sk4)),
    inference(superposition,[status(thm)],[c_62750,c_12354]) ).

tcf(c_62844,plain,
    app(app(sk4,tl(sk4)),nil) = app(sk4,tl(sk4)),
    inference(superposition,[status(thm)],[c_62750,c_12353]) ).

tcf(c_62845,plain,
    app(app(sk3,tl(sk4)),nil) = app(sk3,tl(sk4)),
    inference(superposition,[status(thm)],[c_62750,c_12352]) ).

tcf(c_62846,plain,
    ( ( tl(sk4) = nil )
    | ( tl(cons(hd(tl(sk4)),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_62750,c_3199]) ).

tcf(c_62847,plain,
    ( ( tl(sk4) = nil )
    | ( app(nil,tl(tl(sk4))) = tl(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3066]) ).

tcf(c_62848,plain,
    app(nil,app(sk4,tl(sk4))) = app(sk4,tl(sk4)),
    inference(superposition,[status(thm)],[c_62750,c_8061]) ).

tcf(c_62849,plain,
    app(app(sk4,sk4),tl(sk4)) = app(sk4,app(sk4,tl(sk4))),
    inference(superposition,[status(thm)],[c_62750,c_8048]) ).

tcf(c_62850,plain,
    app(nil,app(sk3,tl(sk4))) = app(sk3,tl(sk4)),
    inference(superposition,[status(thm)],[c_62750,c_5745]) ).

tcf(c_62851,plain,
    app(app(sk3,sk4),tl(sk4)) = app(sk3,app(sk4,tl(sk4))),
    inference(superposition,[status(thm)],[c_62750,c_8047]) ).

tcf(c_62852,plain,
    app(app(sk4,sk3),tl(sk4)) = app(sk4,app(sk3,tl(sk4))),
    inference(superposition,[status(thm)],[c_62750,c_5738]) ).

tcf(c_62853,plain,
    app(app(sk3,sk3),tl(sk4)) = app(sk3,app(sk3,tl(sk4))),
    inference(superposition,[status(thm)],[c_62750,c_5737]) ).

tcf(c_62854,plain,
    app(tl(sk4),tl(sk4)) = tl(app(sk4,tl(sk4))),
    inference(superposition,[status(thm)],[c_62750,c_4136]) ).

tcf(c_62855,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(tl(sk4),sk4)) = app(cons(X0,tl(sk4)),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_4462]) ).

tcf(c_62856,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(tl(sk4),sk3)) = app(cons(X0,tl(sk4)),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_4461]) ).

tcf(c_62857,plain,
    app(tl(sk3),tl(sk4)) = tl(app(sk3,tl(sk4))),
    inference(superposition,[status(thm)],[c_62750,c_4284]) ).

tcf(c_62860,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,tl(sk4))) = cons(X0,tl(sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3019]) ).

tcf(c_62861,plain,
    ( ( tl(sk4) = nil )
    | ( app(cons(hd(tl(sk4)),sk4),nil) = cons(hd(tl(sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3452]) ).

tcf(c_62862,plain,
    ( ( tl(sk4) = nil )
    | ( app(cons(hd(tl(sk4)),sk3),nil) = cons(hd(tl(sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3444]) ).

tcf(c_62863,plain,
    ( ( tl(sk4) = nil )
    | ( app(tl(tl(sk4)),nil) = tl(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3065]) ).

tcf(c_62864,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),sk4)) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3215]) ).

tcf(c_62865,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),sk3)) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3207]) ).

tcf(c_62866,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),tl(sk4)) = cons(X0,tl(sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_253]) ).

tcf(c_62867,plain,
    ( ( tl(sk4) = nil )
    | ( cons(hd(tl(sk4)),tl(tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_275]) ).

tcf(c_62868,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,tl(sk4)),nil) = cons(X0,tl(sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_62750,c_3018]) ).

tcf(c_62869,plain,
    ( ( tl(sk4) = nil )
    | ( tl(cons(hd(tl(sk4)),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_62750,c_3191]) ).

tcf(c_62870,plain,
    ( ( tl(sk4) = nil )
    | ( tl(cons(hd(tl(sk4)),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_62750,c_3183]) ).

tcf(c_63006,plain,
    ! [X0: $i] :
      ( ( app(tl(sk4),app(nil,X0)) = app(tl(sk4),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_62758,c_3673]) ).

tcf(c_63243,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ( cons(hd(app(sk3,X0)),tl(app(sk3,X0))) = app(sk3,X0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_25166,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7560,c_25166]) ).

tcf(c_63244,plain,
    ! [X0: $i] :
      ( ( cons(hd(app(sk3,X0)),tl(app(sk3,X0))) = app(sk3,X0) )
      | ~ ssList(X0) ),
    inference(renaming,[status(thm)],[c_63243]) ).

tcf(c_63251,plain,
    cons(hd(app(sk3,sk4)),tl(app(sk3,sk4))) = app(sk3,sk4),
    inference(superposition,[status(thm)],[c_247,c_63244]) ).

tcf(c_63271,plain,
    cons(hd(sk3),tl(app(sk3,sk4))) = app(sk3,sk4),
    inference(light_normalisation,[status(thm)],[c_63251,c_47393]) ).

tcf(c_63428,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( app(app(sk4,tl(sk4)),X0) != app(sk4,tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62844,c_270]) ).

tcf(c_63429,plain,
    ! [X0: $i] :
      ( ( app(sk4,tl(sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( app(sk4,tl(sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_62844,c_269]) ).

tcf(c_63430,plain,
    ! [X0: $i] :
      ( ( app(sk4,tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( app(sk4,tl(sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63429,c_259]) ).

tcf(c_63435,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( app(app(sk4,tl(sk4)),X0) != app(sk4,tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63428,c_259]) ).

tcf(c_63449,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( app(app(sk3,tl(sk4)),X0) != app(sk3,tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62845,c_270]) ).

tcf(c_63450,plain,
    ! [X0: $i] :
      ( ( app(sk3,tl(sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( app(sk3,tl(sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_62845,c_269]) ).

tcf(c_63451,plain,
    ! [X0: $i] :
      ( ( app(sk3,tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( app(sk3,tl(sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63450,c_259]) ).

tcf(c_63456,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( app(app(sk3,tl(sk4)),X0) != app(sk3,tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63449,c_259]) ).

tcf(c_63557,plain,
    ! [X0: $i] :
      ( ( app(sk4,tl(sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( app(sk4,tl(sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_62848,c_270]) ).

tcf(c_63558,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( app(X0,app(sk4,tl(sk4))) != app(sk4,tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62848,c_269]) ).

tcf(c_63559,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( app(X0,app(sk4,tl(sk4))) != app(sk4,tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63558,c_259]) ).

tcf(c_63564,plain,
    ! [X0: $i] :
      ( ( app(sk4,tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( app(sk4,tl(sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63557,c_259]) ).

tcf(c_63610,plain,
    ! [X0: $i] :
      ( ( app(sk3,tl(sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( app(sk3,tl(sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_62850,c_270]) ).

tcf(c_63611,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( app(X0,app(sk3,tl(sk4))) != app(sk3,tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62850,c_269]) ).

tcf(c_63612,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( app(X0,app(sk3,tl(sk4))) != app(sk3,tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63611,c_259]) ).

tcf(c_63617,plain,
    ! [X0: $i] :
      ( ( app(sk3,tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( app(sk3,tl(sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63610,c_259]) ).

tcf(c_63623,plain,
    ( ssList(app(tl(sk3),tl(sk4)))
    | ( app(sk3,tl(sk4)) = nil )
    | ~ ssList(app(sk3,tl(sk4))) ),
    inference(superposition,[status(thm)],[c_62857,c_278]) ).

tcf(c_63624,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,tl(sk4)) = nil )
      | ( app(sk3,tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( hd(app(sk3,tl(sk4))) != hd(X0) )
      | ( app(tl(sk3),tl(sk4)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_62857,c_273]) ).

tcf(c_63628,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,tl(sk4)) = nil )
      | ( app(sk3,tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk4)))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),tl(sk4)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_63624,c_17373]) ).

tcf(c_63639,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,tl(sk4))))))
      | ( app(sk3,app(sk4,app(sk4,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,tl(sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62789,c_280]) ).

tcf(c_63640,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,tl(sk4))))))
      | ( app(sk3,app(sk4,app(sk4,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,tl(sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62789,c_279]) ).

tcf(c_63656,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,tl(sk4))))))
      | ( app(sk3,app(sk4,app(sk3,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,tl(sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62790,c_280]) ).

tcf(c_63657,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,tl(sk4))))))
      | ( app(sk3,app(sk4,app(sk3,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,tl(sk4)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62790,c_279]) ).

tcf(c_63734,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,tl(sk4))))))
      | ( app(sk3,app(sk3,app(sk4,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,tl(sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62794,c_280]) ).

tcf(c_63735,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,tl(sk4))))))
      | ( app(sk3,app(sk3,app(sk4,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,tl(sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62794,c_279]) ).

tcf(c_63751,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,tl(sk4))))))
      | ( app(sk3,app(sk3,app(sk3,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,tl(sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62795,c_280]) ).

tcf(c_63752,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,tl(sk4))))))
      | ( app(sk3,app(sk3,app(sk3,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,tl(sk4)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62795,c_279]) ).

tcf(c_63770,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(superposition,[status(thm)],[c_10211,c_255]) ).

tcf(c_63771,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(superposition,[status(thm)],[c_10211,c_254]) ).

tcf(c_63772,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_10211,c_272]) ).

tcf(c_63773,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(app(sk4,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_10211,c_270]) ).

tcf(c_63774,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(X0,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10211,c_269]) ).

tcf(c_63775,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(app(sk4,sk3),cons(hd(sk4),app(sk3,sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10211,c_300]) ).

tcf(c_63776,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(app(sk4,sk3),cons(hd(sk4),app(sk3,sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10211,c_287]) ).

tcf(c_63777,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10211,c_7768]) ).

tcf(c_63778,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk3 )
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10211,c_7262]) ).

tcf(c_63779,plain,
    ( ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk4,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63772,c_10188]) ).

tcf(c_63786,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63771,c_10190,c_10188]) ).

tcf(c_63789,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk3 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63778,c_10188]) ).

tcf(c_63793,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63777,c_10189,c_10188]) ).

tcf(c_63796,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(X0,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63774,c_10188]) ).

tcf(c_63801,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(app(sk4,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63773,c_10188]) ).

tcf(c_63806,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_63776,c_10211]) ).

tcf(c_63807,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63806,c_4059]) ).

tcf(c_63815,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_63775,c_10211]) ).

tcf(c_63816,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk4,sk3))
      | ~ ssList(app(sk3,sk4))
      | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63815,c_4059]) ).

tcf(c_63850,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),nil),tl(sk4)) = cons(hd(X0),tl(sk4)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_62866]) ).

tcf(c_63851,plain,
    app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)),
    inference(superposition,[status(thm)],[c_4059,c_62866]) ).

tcf(c_63852,plain,
    app(cons(hd(sk3),nil),tl(sk4)) = cons(hd(sk3),tl(sk4)),
    inference(superposition,[status(thm)],[c_10117,c_62866]) ).

tcf(c_63853,plain,
    app(cons(hd(sk4),nil),tl(sk4)) = sk4,
    inference(light_normalisation,[status(thm)],[c_63851,c_3365]) ).

tcf(c_63862,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),tl(sk4)))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_52451]) ).

tcf(c_63863,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),tl(sk4)))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_52397]) ).

tcf(c_63864,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),tl(sk4)))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_50869]) ).

tcf(c_63865,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),tl(sk4)))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_50771]) ).

tcf(c_63866,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),tl(sk4)))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_44478]) ).

tcf(c_63867,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),tl(sk4)))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_44436]) ).

tcf(c_63868,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),tl(sk4)))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_43161]) ).

tcf(c_63869,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),tl(sk4)))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_43119]) ).

tcf(c_63870,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),tl(sk4)))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_23857]) ).

tcf(c_63871,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),tl(sk4)))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_23849]) ).

tcf(c_63872,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),tl(sk4)))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_23004]) ).

tcf(c_63873,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),tl(sk4)))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_22996]) ).

tcf(c_63874,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),tl(sk4)))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_12052]) ).

tcf(c_63875,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),tl(sk4)))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_12044]) ).

tcf(c_63876,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),tl(sk4)))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_11285]) ).

tcf(c_63877,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),tl(sk4)))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_11277]) ).

tcf(c_63878,plain,
    ( leq(hd(sk3),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(cons(hd(sk3),sk3),tl(sk4)))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_12667]) ).

tcf(c_63879,plain,
    ( lt(hd(sk3),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(cons(hd(sk3),sk3),tl(sk4)))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_12660]) ).

tcf(c_63880,plain,
    ( leq(hd(sk3),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(cons(hd(sk3),sk4),tl(sk4)))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_12629]) ).

tcf(c_63881,plain,
    ( lt(hd(sk3),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(cons(hd(sk3),sk4),tl(sk4)))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_12622]) ).

tcf(c_63882,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(cons(hd(sk4),sk4),tl(sk4)))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_6332]) ).

tcf(c_63883,plain,
    ( leq(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(cons(hd(sk4),sk3),tl(sk4)))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_6325]) ).

tcf(c_63884,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(cons(hd(sk4),sk4),tl(sk4)))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_6196]) ).

tcf(c_63885,plain,
    ( lt(hd(sk4),hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ~ ssList(app(cons(hd(sk4),sk3),tl(sk4)))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_6189]) ).

tcf(c_63888,plain,
    ( lt(hd(tl(sk4)),hd(tl(tl(sk4))))
    | ( tl(sk4) = nil )
    | ( tl(tl(sk4)) = nil )
    | ~ strictorderedP(tl(sk4))
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4))) ),
    inference(superposition,[status(thm)],[c_62867,c_282]) ).

tcf(c_63889,plain,
    ( leq(hd(tl(sk4)),hd(tl(tl(sk4))))
    | ( tl(sk4) = nil )
    | ( tl(tl(sk4)) = nil )
    | ~ totalorderedP(tl(sk4))
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4))) ),
    inference(superposition,[status(thm)],[c_62867,c_281]) ).

tcf(c_63890,plain,
    ( totalorderedP(tl(tl(sk4)))
    | ( tl(sk4) = nil )
    | ( tl(tl(sk4)) = nil )
    | ~ totalorderedP(tl(sk4))
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4))) ),
    inference(superposition,[status(thm)],[c_62867,c_301]) ).

tcf(c_63891,plain,
    ( strictorderedP(tl(tl(sk4)))
    | ( tl(sk4) = nil )
    | ( tl(tl(sk4)) = nil )
    | ~ strictorderedP(tl(sk4))
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4))) ),
    inference(superposition,[status(thm)],[c_62867,c_288]) ).

tcf(c_63892,plain,
    ( ( tl(sk4) = nil )
    | ~ ssItem(hd(tl(sk4)))
    | ~ ssList(tl(tl(sk4)))
    | ( tl(tl(sk4)) != tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_62867,c_267]) ).

tcf(c_63894,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(tl(sk4)),X1)
      | ( tl(sk4) = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(tl(sk4)))
      | ~ ssList(tl(tl(sk4)))
      | ~ ssList(app(app(X0,tl(sk4)),cons(X1,X2)))
      | ~ totalorderedP(app(app(X0,cons(hd(tl(sk4)),tl(tl(sk4)))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_62867,c_300]) ).

tcf(c_63895,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(tl(sk4)),X1)
      | ( tl(sk4) = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(tl(sk4)))
      | ~ ssList(tl(tl(sk4)))
      | ~ ssList(app(app(X0,tl(sk4)),cons(X1,X2)))
      | ~ strictorderedP(app(app(X0,cons(hd(tl(sk4)),tl(tl(sk4)))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_62867,c_287]) ).

tcf(c_63896,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk4) = nil )
      | ( hd(tl(sk4)) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(tl(sk4)))
      | ~ ssList(tl(tl(sk4)))
      | ( cons(X0,X1) != tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_62867,c_265]) ).

tcf(c_63897,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk4) = nil )
      | ( tl(tl(sk4)) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(tl(sk4)))
      | ~ ssList(tl(tl(sk4)))
      | ( cons(X0,X1) != tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_62867,c_264]) ).

tcf(c_63898,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(tl(sk4)))
      | ( tl(sk4) = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(tl(sk4)))
      | ~ ssList(tl(tl(sk4)))
      | ~ ssList(app(app(X0,cons(X1,X2)),tl(sk4)))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_300]) ).

tcf(c_63899,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(tl(sk4)))
      | ( tl(sk4) = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(tl(sk4)))
      | ~ ssList(tl(tl(sk4)))
      | ~ ssList(app(app(X0,cons(X1,X2)),tl(sk4)))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(tl(sk4)),tl(tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62867,c_287]) ).

tcf(c_64396,plain,
    ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(global_subsumption_just,[status(thm)],[c_63779,c_247,c_246,c_55093,c_63779]) ).

tcf(c_64398,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_18773]) ).

tcf(c_64399,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_18497]) ).

tcf(c_64400,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_18185]) ).

tcf(c_64401,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_16330]) ).

tcf(c_64402,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_15966]) ).

tcf(c_64403,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_15593]) ).

tcf(c_64404,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),nil),X0) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_4541]) ).

tcf(c_64405,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3154]) ).

tcf(c_64406,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_4037]) ).

tcf(c_64407,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3952]) ).

tcf(c_64408,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3050]) ).

tcf(c_64409,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0),nil) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3049]) ).

tcf(c_64410,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),sk4),X0) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_4540]) ).

tcf(c_64411,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),sk3),X0) = app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_4539]) ).

tcf(c_64412,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),X0) = app(X1,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_271]) ).

tcf(c_64413,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(cons(X1,X0),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_266]) ).

tcf(c_64414,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),X0) = tl(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_274]) ).

tcf(c_64415,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_283]) ).

tcf(c_64416,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_61402]) ).

tcf(c_64417,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_61324]) ).

tcf(c_64418,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3118]) ).

tcf(c_64419,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),app(sk4,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_34548]) ).

tcf(c_64420,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),app(sk4,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_34490]) ).

tcf(c_64421,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),app(sk3,sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_34149]) ).

tcf(c_64422,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),app(sk3,sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_34101]) ).

tcf(c_64423,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_19899]) ).

tcf(c_64424,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_19024]) ).

tcf(c_64425,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_19014]) ).

tcf(c_64426,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_17999]) ).

tcf(c_64427,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_18774]) ).

tcf(c_64428,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_57010]) ).

tcf(c_64429,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_57009]) ).

tcf(c_64430,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_57008]) ).

tcf(c_64431,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_18772]) ).

tcf(c_64432,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_15409]) ).

tcf(c_64433,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_18498]) ).

tcf(c_64434,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_54564]) ).

tcf(c_64435,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_54563]) ).

tcf(c_64436,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_54562]) ).

tcf(c_64437,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_18496]) ).

tcf(c_64438,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_18186]) ).

tcf(c_64439,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_48819]) ).

tcf(c_64440,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_48818]) ).

tcf(c_64441,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_48817]) ).

tcf(c_64442,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_18184]) ).

tcf(c_64443,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_17287]) ).

tcf(c_64444,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_16680]) ).

tcf(c_64445,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_16670]) ).

tcf(c_64446,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_16331]) ).

tcf(c_64447,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_45260]) ).

tcf(c_64448,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_45259]) ).

tcf(c_64449,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_45258]) ).

tcf(c_64450,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_16329]) ).

tcf(c_64451,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_15967]) ).

tcf(c_64452,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_40467]) ).

tcf(c_64453,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_40466]) ).

tcf(c_64454,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_40465]) ).

tcf(c_64455,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_15965]) ).

tcf(c_64456,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_15594]) ).

tcf(c_64457,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_37606]) ).

tcf(c_64458,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_37605]) ).

tcf(c_64459,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_37604]) ).

tcf(c_64460,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_15592]) ).

tcf(c_64461,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_18000]) ).

tcf(c_64462,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_17998]) ).

tcf(c_64463,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_17997]) ).

tcf(c_64464,plain,
    app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_64396,c_35790]) ).

tcf(c_64465,plain,
    app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_64396,c_35787]) ).

tcf(c_64466,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),nil)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_4463]) ).

tcf(c_64467,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3155]) ).

tcf(c_64468,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_33403]) ).

tcf(c_64469,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_33402]) ).

tcf(c_64470,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_33401]) ).

tcf(c_64471,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(sk3))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_32111]) ).

tcf(c_64472,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_32098]) ).

tcf(c_64473,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_15410]) ).

tcf(c_64474,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_15408]) ).

tcf(c_64475,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_15407]) ).

tcf(c_64476,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3153]) ).

tcf(c_64477,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_4038]) ).

tcf(c_64478,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_17993]) ).

tcf(c_64479,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_17992]) ).

tcf(c_64480,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_17991]) ).

tcf(c_64481,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_4036]) ).

tcf(c_64482,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3953]) ).

tcf(c_64483,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_15403]) ).

tcf(c_64484,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_15402]) ).

tcf(c_64485,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_15401]) ).

tcf(c_64486,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3951]) ).

tcf(c_64487,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3423]) ).

tcf(c_64488,plain,
    app(nil,app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_64396,c_13452]) ).

tcf(c_64489,plain,
    app(app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_64396,c_12354]) ).

tcf(c_64490,plain,
    app(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_64396,c_12353]) ).

tcf(c_64491,plain,
    app(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_64396,c_12352]) ).

tcf(c_64492,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_64396,c_3199]) ).

tcf(c_64493,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3066]) ).

tcf(c_64494,plain,
    app(nil,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_64396,c_8061]) ).

tcf(c_64495,plain,
    app(app(sk4,sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_64396,c_8048]) ).

tcf(c_64496,plain,
    app(nil,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_64396,c_5745]) ).

tcf(c_64497,plain,
    app(app(sk3,sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_64396,c_8047]) ).

tcf(c_64498,plain,
    app(app(sk4,sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_64396,c_5738]) ).

tcf(c_64499,plain,
    app(app(sk3,sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_64396,c_5737]) ).

tcf(c_64500,plain,
    app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = tl(app(sk4,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_64396,c_4136]) ).

tcf(c_64501,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),sk4)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_4462]) ).

tcf(c_64502,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),sk3)) = app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_4461]) ).

tcf(c_64503,plain,
    app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = tl(app(sk3,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))),
    inference(superposition,[status(thm)],[c_64396,c_4284]) ).

tcf(c_64506,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3019]) ).

tcf(c_64507,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3452]) ).

tcf(c_64508,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3444]) ).

tcf(c_64509,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3065]) ).

tcf(c_64510,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3215]) ).

tcf(c_64511,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3)) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3207]) ).

tcf(c_64512,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_253]) ).

tcf(c_64513,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_275]) ).

tcf(c_64514,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_3018]) ).

tcf(c_64515,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_64396,c_3191]) ).

tcf(c_64516,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_64396,c_3183]) ).

tcf(c_64517,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_284]) ).

tcf(c_64518,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_64396,c_276]) ).

tcf(c_64519,plain,
    app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),nil) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_64396,c_258]) ).

tcf(c_64520,plain,
    app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),
    inference(superposition,[status(thm)],[c_64396,c_257]) ).

tcf(c_64640,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(app(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_64415,c_15609]) ).

tcf(c_64652,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) ) ),
    inference(light_normalisation,[status(thm)],[c_64513,c_15609]) ).

tcf(c_64910,plain,
    ( ssList(app(sk3,sk4))
    | ~ ssItem(hd(sk3))
    | ~ ssList(tl(app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_63271,c_268]) ).

tcf(c_64925,plain,
    ( ssList(app(sk3,sk4))
    | ~ ssList(tl(app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_64910,c_59796]) ).

tcf(c_65060,plain,
    ssList(tl(sk3)),
    inference(global_subsumption_just,[status(thm)],[c_61409,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7562]) ).

tcf(c_65062,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(tl(sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_18773]) ).

tcf(c_65063,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(tl(sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_18497]) ).

tcf(c_65064,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(tl(sk3),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_18185]) ).

tcf(c_65065,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(tl(sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_16330]) ).

tcf(c_65066,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(tl(sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_15966]) ).

tcf(c_65067,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(tl(sk3),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_15593]) ).

tcf(c_65068,plain,
    ! [X0: $i] :
      ( ( app(app(tl(sk3),nil),X0) = app(tl(sk3),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_4541]) ).

tcf(c_65069,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(tl(sk3),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3154]) ).

tcf(c_65070,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(tl(sk3),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_4037]) ).

tcf(c_65071,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(tl(sk3),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3952]) ).

tcf(c_65072,plain,
    ! [X0: $i] :
      ( ( app(nil,app(tl(sk3),X0)) = app(tl(sk3),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3050]) ).

tcf(c_65073,plain,
    ! [X0: $i] :
      ( ( app(app(tl(sk3),X0),nil) = app(tl(sk3),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3049]) ).

tcf(c_65074,plain,
    ! [X0: $i] :
      ( ( app(app(tl(sk3),sk4),X0) = app(tl(sk3),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_4540]) ).

tcf(c_65075,plain,
    ! [X0: $i] :
      ( ( app(app(tl(sk3),sk3),X0) = app(tl(sk3),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_4539]) ).

tcf(c_65076,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,tl(sk3)),X0) = app(X1,app(tl(sk3),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_271]) ).

tcf(c_65077,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,tl(sk3))) = app(cons(X1,X0),tl(sk3)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_266]) ).

tcf(c_65078,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = nil )
      | ( app(tl(tl(sk3)),X0) = tl(app(tl(sk3),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_274]) ).

tcf(c_65079,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = nil )
      | ( hd(app(tl(sk3),X0)) = hd(tl(sk3)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_283]) ).

tcf(c_65080,plain,
    ( ( tl(sk3) = nil )
    | ( tl(cons(hd(tl(sk3)),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_61402]) ).

tcf(c_65081,plain,
    ( ( tl(sk3) = nil )
    | ( tl(cons(hd(tl(sk3)),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_61324]) ).

tcf(c_65082,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = nil )
      | ( tl(cons(X0,tl(tl(sk3)))) = tl(tl(sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3118]) ).

tcf(c_65083,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),app(sk4,sk4))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_34548]) ).

tcf(c_65084,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),app(sk4,sk3))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_34490]) ).

tcf(c_65085,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),app(sk3,sk4))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_34149]) ).

tcf(c_65086,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),app(sk3,sk3))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_34101]) ).

tcf(c_65087,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk3,cons(hd(tl(sk3)),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_19899]) ).

tcf(c_65088,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk3,cons(hd(tl(sk3)),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_19024]) ).

tcf(c_65089,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk3,cons(hd(tl(sk3)),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_19014]) ).

tcf(c_65090,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),tl(sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_17999]) ).

tcf(c_65091,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,tl(sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_18774]) ).

tcf(c_65092,plain,
    hd(app(sk3,app(nil,app(nil,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_57010]) ).

tcf(c_65093,plain,
    hd(app(sk3,app(nil,app(sk4,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_57009]) ).

tcf(c_65094,plain,
    hd(app(sk3,app(nil,app(sk3,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_57008]) ).

tcf(c_65095,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk3,app(nil,tl(tl(sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_18772]) ).

tcf(c_65096,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),tl(sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_15409]) ).

tcf(c_65097,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,tl(sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_18498]) ).

tcf(c_65098,plain,
    hd(app(sk3,app(sk4,app(nil,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_54564]) ).

tcf(c_65099,plain,
    hd(app(sk3,app(sk4,app(sk4,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_54563]) ).

tcf(c_65100,plain,
    hd(app(sk3,app(sk4,app(sk3,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_54562]) ).

tcf(c_65101,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk3,app(sk4,tl(tl(sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_18496]) ).

tcf(c_65102,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,tl(sk3))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_18186]) ).

tcf(c_65103,plain,
    hd(app(sk3,app(sk3,app(nil,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_48819]) ).

tcf(c_65104,plain,
    hd(app(sk3,app(sk3,app(sk4,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_48818]) ).

tcf(c_65105,plain,
    hd(app(sk3,app(sk3,app(sk3,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_48817]) ).

tcf(c_65106,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk3,app(sk3,tl(tl(sk3))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_18184]) ).

tcf(c_65107,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk4,cons(hd(tl(sk3)),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_17287]) ).

tcf(c_65108,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk4,cons(hd(tl(sk3)),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_16680]) ).

tcf(c_65109,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk4,cons(hd(tl(sk3)),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_16670]) ).

tcf(c_65110,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,tl(sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_16331]) ).

tcf(c_65111,plain,
    hd(app(sk4,app(nil,app(nil,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_45260]) ).

tcf(c_65112,plain,
    hd(app(sk4,app(nil,app(sk4,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_45259]) ).

tcf(c_65113,plain,
    hd(app(sk4,app(nil,app(sk3,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_45258]) ).

tcf(c_65114,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk4,app(nil,tl(tl(sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_16329]) ).

tcf(c_65115,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,tl(sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_15967]) ).

tcf(c_65116,plain,
    hd(app(sk4,app(sk4,app(nil,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_40467]) ).

tcf(c_65117,plain,
    hd(app(sk4,app(sk4,app(sk4,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_40466]) ).

tcf(c_65118,plain,
    hd(app(sk4,app(sk4,app(sk3,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_40465]) ).

tcf(c_65119,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk4,app(sk4,tl(tl(sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_15965]) ).

tcf(c_65120,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,tl(sk3))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_15594]) ).

tcf(c_65121,plain,
    hd(app(sk4,app(sk3,app(nil,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_37606]) ).

tcf(c_65122,plain,
    hd(app(sk4,app(sk3,app(sk4,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_37605]) ).

tcf(c_65123,plain,
    hd(app(sk4,app(sk3,app(sk3,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_37604]) ).

tcf(c_65124,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk4,app(sk3,tl(tl(sk3))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_15592]) ).

tcf(c_65125,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),tl(sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_18000]) ).

tcf(c_65126,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),tl(sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_17998]) ).

tcf(c_65127,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),tl(sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_17997]) ).

tcf(c_65128,plain,
    app(sk3,app(nil,tl(sk3))) = app(sk3,tl(sk3)),
    inference(superposition,[status(thm)],[c_65060,c_35790]) ).

tcf(c_65129,plain,
    app(sk4,app(nil,tl(sk3))) = app(sk4,tl(sk3)),
    inference(superposition,[status(thm)],[c_65060,c_35787]) ).

tcf(c_65130,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(tl(sk3),nil)) = app(cons(X0,tl(sk3)),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_4463]) ).

tcf(c_65131,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,tl(sk3)))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3155]) ).

tcf(c_65132,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,tl(sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_33403]) ).

tcf(c_65133,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,tl(sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_33402]) ).

tcf(c_65134,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,tl(sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_33401]) ).

tcf(c_65135,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),tl(sk3))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_32111]) ).

tcf(c_65136,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),tl(sk4))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_32098]) ).

tcf(c_65137,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),tl(sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_15410]) ).

tcf(c_65138,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),tl(sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_15408]) ).

tcf(c_65139,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),tl(sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_15407]) ).

tcf(c_65140,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = nil )
      | ( hd(cons(X0,tl(tl(sk3)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3153]) ).

tcf(c_65141,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,tl(sk3)))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_4038]) ).

tcf(c_65142,plain,
    hd(app(sk3,app(nil,tl(sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_17993]) ).

tcf(c_65145,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk3,tl(tl(sk3)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_4036]) ).

tcf(c_65146,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,tl(sk3)))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3953]) ).

tcf(c_65147,plain,
    hd(app(sk4,app(nil,tl(sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_15403]) ).

tcf(c_65150,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(sk4,tl(tl(sk3)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3951]) ).

tcf(c_65151,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),nil)) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3423]) ).

tcf(c_65152,plain,
    app(nil,app(nil,tl(sk3))) = app(nil,tl(sk3)),
    inference(superposition,[status(thm)],[c_65060,c_13452]) ).

tcf(c_65153,plain,
    app(app(nil,tl(sk3)),nil) = app(nil,tl(sk3)),
    inference(superposition,[status(thm)],[c_65060,c_12354]) ).

tcf(c_65154,plain,
    app(app(sk4,tl(sk3)),nil) = app(sk4,tl(sk3)),
    inference(superposition,[status(thm)],[c_65060,c_12353]) ).

tcf(c_65155,plain,
    app(app(sk3,tl(sk3)),nil) = app(sk3,tl(sk3)),
    inference(superposition,[status(thm)],[c_65060,c_12352]) ).

tcf(c_65156,plain,
    ( ( tl(sk3) = nil )
    | ( tl(cons(hd(tl(sk3)),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_65060,c_3199]) ).

tcf(c_65157,plain,
    ( ( tl(sk3) = nil )
    | ( app(nil,tl(tl(sk3))) = tl(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3066]) ).

tcf(c_65158,plain,
    app(nil,app(sk4,tl(sk3))) = app(sk4,tl(sk3)),
    inference(superposition,[status(thm)],[c_65060,c_8061]) ).

tcf(c_65159,plain,
    app(app(sk4,sk4),tl(sk3)) = app(sk4,app(sk4,tl(sk3))),
    inference(superposition,[status(thm)],[c_65060,c_8048]) ).

tcf(c_65160,plain,
    app(nil,app(sk3,tl(sk3))) = app(sk3,tl(sk3)),
    inference(superposition,[status(thm)],[c_65060,c_5745]) ).

tcf(c_65161,plain,
    app(app(sk3,sk4),tl(sk3)) = app(sk3,app(sk4,tl(sk3))),
    inference(superposition,[status(thm)],[c_65060,c_8047]) ).

tcf(c_65162,plain,
    app(app(sk4,sk3),tl(sk3)) = app(sk4,app(sk3,tl(sk3))),
    inference(superposition,[status(thm)],[c_65060,c_5738]) ).

tcf(c_65163,plain,
    app(app(sk3,sk3),tl(sk3)) = app(sk3,app(sk3,tl(sk3))),
    inference(superposition,[status(thm)],[c_65060,c_5737]) ).

tcf(c_65164,plain,
    app(tl(sk4),tl(sk3)) = tl(app(sk4,tl(sk3))),
    inference(superposition,[status(thm)],[c_65060,c_4136]) ).

tcf(c_65165,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(tl(sk3),sk4)) = app(cons(X0,tl(sk3)),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_4462]) ).

tcf(c_65166,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(tl(sk3),sk3)) = app(cons(X0,tl(sk3)),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_4461]) ).

tcf(c_65167,plain,
    app(tl(sk3),tl(sk3)) = tl(app(sk3,tl(sk3))),
    inference(superposition,[status(thm)],[c_65060,c_4284]) ).

tcf(c_65170,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,tl(sk3))) = cons(X0,tl(sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3019]) ).

tcf(c_65171,plain,
    ( ( tl(sk3) = nil )
    | ( app(cons(hd(tl(sk3)),sk4),nil) = cons(hd(tl(sk3)),sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3452]) ).

tcf(c_65172,plain,
    ( ( tl(sk3) = nil )
    | ( app(cons(hd(tl(sk3)),sk3),nil) = cons(hd(tl(sk3)),sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3444]) ).

tcf(c_65173,plain,
    ( ( tl(sk3) = nil )
    | ( app(tl(tl(sk3)),nil) = tl(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3065]) ).

tcf(c_65174,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),sk4)) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3215]) ).

tcf(c_65175,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),sk3)) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3207]) ).

tcf(c_65176,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),tl(sk3)) = cons(X0,tl(sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_253]) ).

tcf(c_65177,plain,
    ( ( tl(sk3) = nil )
    | ( cons(hd(tl(sk3)),tl(tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_275]) ).

tcf(c_65178,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,tl(sk3)),nil) = cons(X0,tl(sk3)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65060,c_3018]) ).

tcf(c_65179,plain,
    ( ( tl(sk3) = nil )
    | ( tl(cons(hd(tl(sk3)),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_65060,c_3191]) ).

tcf(c_65180,plain,
    ( ( tl(sk3) = nil )
    | ( tl(cons(hd(tl(sk3)),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_65060,c_3183]) ).

tcf(c_65316,plain,
    ! [X0: $i] :
      ( ( app(tl(sk3),app(nil,X0)) = app(tl(sk3),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_65068,c_3727]) ).

tcf(c_65513,plain,
    ssList(app(sk3,sk4)),
    inference(global_subsumption_just,[status(thm)],[c_64925,c_247,c_246,c_42153]) ).

tcf(c_65569,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_65513,c_24635]) ).

tcf(c_65955,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(cons(hd(sk4),nil),X0) != sk4 ) ),
    inference(superposition,[status(thm)],[c_63853,c_270]) ).

tcf(c_65956,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(X0,tl(sk4)) != sk4 ) ),
    inference(superposition,[status(thm)],[c_63853,c_269]) ).

tcf(c_65957,plain,
    ( ( tl(sk4) = sk4 )
    | ~ ssList(tl(sk4))
    | ( cons(hd(sk4),sk4) != sk4 ) ),
    inference(superposition,[status(thm)],[c_63853,c_14602]) ).

tcf(c_65958,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(tl(sk4))
    | ( cons(hd(sk4),sk3) != sk4 ) ),
    inference(superposition,[status(thm)],[c_63853,c_14143]) ).

tcf(c_65959,plain,
    ( ( tl(sk4) = sk3 )
    | ( cons(hd(sk4),sk3) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_65958,c_62750]) ).

tcf(c_65962,plain,
    cons(hd(sk4),sk4) != sk4,
    inference(forward_subsumption_resolution,[status(thm)],[c_65957,c_3659,c_62750]) ).

tcf(c_65963,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(X0,tl(sk4)) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_65956,c_62750]) ).

tcf(c_65968,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk4),nil))
      | ( app(cons(hd(sk4),nil),X0) != sk4 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_65955,c_62750]) ).

tcf(c_65976,plain,
    ( ssList(app(tl(sk4),tl(sk4)))
    | ( app(sk4,tl(sk4)) = nil )
    | ~ ssList(app(sk4,tl(sk4))) ),
    inference(superposition,[status(thm)],[c_62854,c_278]) ).

tcf(c_65977,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,tl(sk4)) = nil )
      | ( app(sk4,tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( hd(app(sk4,tl(sk4))) != hd(X0) )
      | ( app(tl(sk4),tl(sk4)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_62854,c_273]) ).

tcf(c_65981,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,tl(sk4)) = nil )
      | ( app(sk4,tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk4)))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),tl(sk4)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_65977,c_14808]) ).

tcf(c_65997,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( app(app(sk4,tl(sk3)),X0) != app(sk4,tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65154,c_270]) ).

tcf(c_65998,plain,
    ! [X0: $i] :
      ( ( app(sk4,tl(sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( app(sk4,tl(sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_65154,c_269]) ).

tcf(c_65999,plain,
    ! [X0: $i] :
      ( ( app(sk4,tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( app(sk4,tl(sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_65998,c_259]) ).

tcf(c_66004,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( app(app(sk4,tl(sk3)),X0) != app(sk4,tl(sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_65997,c_259]) ).

tcf(c_66018,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( app(app(sk3,tl(sk3)),X0) != app(sk3,tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65155,c_270]) ).

tcf(c_66019,plain,
    ! [X0: $i] :
      ( ( app(sk3,tl(sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( app(sk3,tl(sk3)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_65155,c_269]) ).

tcf(c_66020,plain,
    ! [X0: $i] :
      ( ( app(sk3,tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( app(sk3,tl(sk3)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66019,c_259]) ).

tcf(c_66025,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( app(app(sk3,tl(sk3)),X0) != app(sk3,tl(sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66018,c_259]) ).

tcf(c_66032,plain,
    ( ssList(app(tl(sk3),tl(sk3)))
    | ( app(sk3,tl(sk3)) = nil )
    | ~ ssList(app(sk3,tl(sk3))) ),
    inference(superposition,[status(thm)],[c_65167,c_278]) ).

tcf(c_66033,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,tl(sk3)) = nil )
      | ( app(sk3,tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( hd(app(sk3,tl(sk3))) != hd(X0) )
      | ( app(tl(sk3),tl(sk3)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_65167,c_273]) ).

tcf(c_66037,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,tl(sk3)) = nil )
      | ( app(sk3,tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),tl(sk3)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_66033,c_17619]) ).

tcf(c_66047,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,tl(sk4))))))
      | ( app(sk4,app(sk4,app(sk4,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,tl(sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62807,c_280]) ).

tcf(c_66048,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,tl(sk4))))))
      | ( app(sk4,app(sk4,app(sk4,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,tl(sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62807,c_279]) ).

tcf(c_66064,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,tl(sk4))))))
      | ( app(sk4,app(sk4,app(sk3,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,tl(sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62808,c_280]) ).

tcf(c_66065,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,tl(sk4))))))
      | ( app(sk4,app(sk4,app(sk3,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,tl(sk4)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62808,c_279]) ).

tcf(c_66081,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,tl(sk4))))))
      | ( app(sk4,app(sk3,app(sk4,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,tl(sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62812,c_280]) ).

tcf(c_66082,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,tl(sk4))))))
      | ( app(sk4,app(sk3,app(sk4,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,tl(sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62812,c_279]) ).

tcf(c_66098,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,tl(sk4))))))
      | ( app(sk4,app(sk3,app(sk3,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,tl(sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62813,c_280]) ).

tcf(c_66099,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,tl(sk4))))))
      | ( app(sk4,app(sk3,app(sk3,tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,tl(sk4)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62813,c_279]) ).

tcf(c_66118,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,tl(sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_62823]) ).

tcf(c_66119,plain,
    hd(cons(hd(sk4),app(sk4,tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_62823]) ).

tcf(c_66120,plain,
    hd(cons(hd(sk3),app(sk4,tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_62823]) ).

tcf(c_66126,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(superposition,[status(thm)],[c_10212,c_255]) ).

tcf(c_66127,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(superposition,[status(thm)],[c_10212,c_254]) ).

tcf(c_66128,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_10212,c_272]) ).

tcf(c_66129,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(app(sk3,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_10212,c_270]) ).

tcf(c_66130,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(X0,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10212,c_269]) ).

tcf(c_66131,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(app(sk3,sk3),cons(hd(sk4),app(sk3,sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10212,c_300]) ).

tcf(c_66132,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(app(sk3,sk3),cons(hd(sk4),app(sk3,sk4))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_10212,c_287]) ).

tcf(c_66133,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_10212,c_6948]) ).

tcf(c_66134,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk3 )
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4)))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_10212,c_6605]) ).

tcf(c_66135,plain,
    ( ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk3,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66128,c_10188]) ).

tcf(c_66142,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66127,c_10190,c_10188]) ).

tcf(c_66145,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = sk3 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66134,c_10188]) ).

tcf(c_66149,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66133,c_10189,c_10188]) ).

tcf(c_66152,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(X0,cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66130,c_10188]) ).

tcf(c_66157,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk4),app(sk3,sk4)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) != app(app(sk3,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66129,c_10188]) ).

tcf(c_66162,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_66132,c_10212]) ).

tcf(c_66163,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66162,c_4059]) ).

tcf(c_66171,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_66131,c_10212]) ).

tcf(c_66172,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk4),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(app(sk3,sk4))
      | ~ ssList(app(sk3,sk3))
      | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1)))
      | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66171,c_4059]) ).

tcf(c_66231,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),nil),tl(sk3)) = cons(hd(X0),tl(sk3)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_65176]) ).

tcf(c_66232,plain,
    app(cons(hd(sk4),nil),tl(sk3)) = cons(hd(sk4),tl(sk3)),
    inference(superposition,[status(thm)],[c_4059,c_65176]) ).

tcf(c_66233,plain,
    app(cons(hd(sk3),nil),tl(sk3)) = cons(hd(sk3),tl(sk3)),
    inference(superposition,[status(thm)],[c_10117,c_65176]) ).

tcf(c_66242,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),tl(sk3)))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_52451]) ).

tcf(c_66243,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),tl(sk3)))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_52397]) ).

tcf(c_66244,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),tl(sk3)))
    | ~ totalorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_50869]) ).

tcf(c_66245,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),tl(sk3)))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_50771]) ).

tcf(c_66246,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),tl(sk3)))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_44478]) ).

tcf(c_66247,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),tl(sk3)))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_44436]) ).

tcf(c_66248,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),tl(sk3)))
    | ~ totalorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_43161]) ).

tcf(c_66249,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),tl(sk3)))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_43119]) ).

tcf(c_66250,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),tl(sk3)))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_23857]) ).

tcf(c_66251,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),tl(sk3)))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_23849]) ).

tcf(c_66252,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),tl(sk3)))
    | ~ totalorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_23004]) ).

tcf(c_66253,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),tl(sk3)))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_22996]) ).

tcf(c_66254,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),tl(sk3)))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_12052]) ).

tcf(c_66255,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),tl(sk3)))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_12044]) ).

tcf(c_66256,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),tl(sk3)))
    | ~ totalorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_11285]) ).

tcf(c_66257,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),tl(sk3)))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_11277]) ).

tcf(c_66258,plain,
    ( leq(hd(sk3),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(cons(hd(sk3),sk3),tl(sk3)))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_12667]) ).

tcf(c_66259,plain,
    ( lt(hd(sk3),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(cons(hd(sk3),sk3),tl(sk3)))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_12660]) ).

tcf(c_66260,plain,
    ( leq(hd(sk3),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(cons(hd(sk3),sk4),tl(sk3)))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_12629]) ).

tcf(c_66261,plain,
    ( lt(hd(sk3),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(cons(hd(sk3),sk4),tl(sk3)))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_12622]) ).

tcf(c_66262,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(cons(hd(sk4),sk4),tl(sk3)))
    | ~ totalorderedP(app(cons(hd(sk4),sk4),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_6332]) ).

tcf(c_66263,plain,
    ( leq(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(cons(hd(sk4),sk3),tl(sk3)))
    | ~ totalorderedP(app(cons(hd(sk4),sk3),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_6325]) ).

tcf(c_66264,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(cons(hd(sk4),sk4),tl(sk3)))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_6196]) ).

tcf(c_66265,plain,
    ( lt(hd(sk4),hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ~ ssList(app(cons(hd(sk4),sk3),tl(sk3)))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_6189]) ).

tcf(c_66268,plain,
    ( lt(hd(tl(sk3)),hd(tl(tl(sk3))))
    | ( tl(sk3) = nil )
    | ( tl(tl(sk3)) = nil )
    | ~ strictorderedP(tl(sk3))
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3))) ),
    inference(superposition,[status(thm)],[c_65177,c_282]) ).

tcf(c_66269,plain,
    ( leq(hd(tl(sk3)),hd(tl(tl(sk3))))
    | ( tl(sk3) = nil )
    | ( tl(tl(sk3)) = nil )
    | ~ totalorderedP(tl(sk3))
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3))) ),
    inference(superposition,[status(thm)],[c_65177,c_281]) ).

tcf(c_66270,plain,
    ( totalorderedP(tl(tl(sk3)))
    | ( tl(sk3) = nil )
    | ( tl(tl(sk3)) = nil )
    | ~ totalorderedP(tl(sk3))
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3))) ),
    inference(superposition,[status(thm)],[c_65177,c_301]) ).

tcf(c_66271,plain,
    ( strictorderedP(tl(tl(sk3)))
    | ( tl(sk3) = nil )
    | ( tl(tl(sk3)) = nil )
    | ~ strictorderedP(tl(sk3))
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3))) ),
    inference(superposition,[status(thm)],[c_65177,c_288]) ).

tcf(c_66272,plain,
    ( ( tl(sk3) = nil )
    | ~ ssItem(hd(tl(sk3)))
    | ~ ssList(tl(tl(sk3)))
    | ( tl(tl(sk3)) != tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_65177,c_267]) ).

tcf(c_66274,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(tl(sk3)),X1)
      | ( tl(sk3) = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(tl(sk3)))
      | ~ ssList(tl(tl(sk3)))
      | ~ ssList(app(app(X0,tl(sk3)),cons(X1,X2)))
      | ~ totalorderedP(app(app(X0,cons(hd(tl(sk3)),tl(tl(sk3)))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_65177,c_300]) ).

tcf(c_66275,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(tl(sk3)),X1)
      | ( tl(sk3) = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(tl(sk3)))
      | ~ ssList(tl(tl(sk3)))
      | ~ ssList(app(app(X0,tl(sk3)),cons(X1,X2)))
      | ~ strictorderedP(app(app(X0,cons(hd(tl(sk3)),tl(tl(sk3)))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_65177,c_287]) ).

tcf(c_66276,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk3) = nil )
      | ( hd(tl(sk3)) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(tl(sk3)))
      | ~ ssList(tl(tl(sk3)))
      | ( cons(X0,X1) != tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_65177,c_265]) ).

tcf(c_66277,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk3) = nil )
      | ( tl(tl(sk3)) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(tl(sk3)))
      | ~ ssList(tl(tl(sk3)))
      | ( cons(X0,X1) != tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_65177,c_264]) ).

tcf(c_66278,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(tl(sk3)))
      | ( tl(sk3) = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(tl(sk3)))
      | ~ ssList(tl(tl(sk3)))
      | ~ ssList(app(app(X0,cons(X1,X2)),tl(sk3)))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_300]) ).

tcf(c_66279,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(tl(sk3)))
      | ( tl(sk3) = nil )
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(tl(sk3)))
      | ~ ssList(tl(tl(sk3)))
      | ~ ssList(app(app(X0,cons(X1,X2)),tl(sk3)))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(tl(sk3)),tl(tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65177,c_287]) ).

tcf(c_66554,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18773]) ).

tcf(c_66555,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18497]) ).

tcf(c_66556,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18185]) ).

tcf(c_66557,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_16330]) ).

tcf(c_66558,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15966]) ).

tcf(c_66559,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15593]) ).

tcf(c_66560,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),nil),X0) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4541]) ).

tcf(c_66561,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3154]) ).

tcf(c_66562,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4037]) ).

tcf(c_66563,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3952]) ).

tcf(c_66564,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3050]) ).

tcf(c_66565,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0),nil) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3049]) ).

tcf(c_66566,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),sk4),X0) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4540]) ).

tcf(c_66567,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),sk3),X0) = app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4539]) ).

tcf(c_66568,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),X0) = app(X1,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_271]) ).

tcf(c_66569,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(cons(X1,X0),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_266]) ).

tcf(c_66570,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),X0) = tl(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_274]) ).

tcf(c_66571,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_283]) ).

tcf(c_66572,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_61402]) ).

tcf(c_66573,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_61324]) ).

tcf(c_66574,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3118]) ).

tcf(c_66575,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),app(sk4,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_34548]) ).

tcf(c_66576,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),app(sk4,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_34490]) ).

tcf(c_66577,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),app(sk3,sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_34149]) ).

tcf(c_66578,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),app(sk3,sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_34101]) ).

tcf(c_66579,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_19899]) ).

tcf(c_66580,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_19024]) ).

tcf(c_66581,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_19014]) ).

tcf(c_66582,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_17999]) ).

tcf(c_66583,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18774]) ).

tcf(c_66584,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_57010]) ).

tcf(c_66585,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_57009]) ).

tcf(c_66586,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_57008]) ).

tcf(c_66587,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18772]) ).

tcf(c_66588,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15409]) ).

tcf(c_66589,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18498]) ).

tcf(c_66590,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_54564]) ).

tcf(c_66591,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_54563]) ).

tcf(c_66592,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_54562]) ).

tcf(c_66593,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18496]) ).

tcf(c_66594,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18186]) ).

tcf(c_66595,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_48819]) ).

tcf(c_66596,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_48818]) ).

tcf(c_66597,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_48817]) ).

tcf(c_66598,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18184]) ).

tcf(c_66599,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_17287]) ).

tcf(c_66600,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_16680]) ).

tcf(c_66601,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_16670]) ).

tcf(c_66602,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_16331]) ).

tcf(c_66603,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_45260]) ).

tcf(c_66604,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_45259]) ).

tcf(c_66605,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_45258]) ).

tcf(c_66606,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_16329]) ).

tcf(c_66607,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15967]) ).

tcf(c_66608,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_40467]) ).

tcf(c_66609,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_40466]) ).

tcf(c_66610,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_40465]) ).

tcf(c_66611,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15965]) ).

tcf(c_66612,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15594]) ).

tcf(c_66613,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_37606]) ).

tcf(c_66614,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_37605]) ).

tcf(c_66615,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_37604]) ).

tcf(c_66616,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15592]) ).

tcf(c_66617,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_18000]) ).

tcf(c_66618,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_17998]) ).

tcf(c_66619,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_17997]) ).

tcf(c_66620,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_35790]) ).

tcf(c_66621,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_35787]) ).

tcf(c_66622,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),nil)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4463]) ).

tcf(c_66623,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3155]) ).

tcf(c_66624,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_33403]) ).

tcf(c_66625,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_33402]) ).

tcf(c_66626,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_33401]) ).

tcf(c_66627,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(sk3))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_32111]) ).

tcf(c_66628,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_32098]) ).

tcf(c_66629,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15410]) ).

tcf(c_66630,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15408]) ).

tcf(c_66631,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15407]) ).

tcf(c_66632,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3153]) ).

tcf(c_66633,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4038]) ).

tcf(c_66634,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_17993]) ).

tcf(c_66635,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_17992]) ).

tcf(c_66636,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_17991]) ).

tcf(c_66637,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4036]) ).

tcf(c_66638,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3953]) ).

tcf(c_66639,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15403]) ).

tcf(c_66640,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15402]) ).

tcf(c_66641,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_15401]) ).

tcf(c_66642,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3951]) ).

tcf(c_66643,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3423]) ).

tcf(c_66644,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_13452]) ).

tcf(c_66645,plain,
    ( ( app(app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_12354]) ).

tcf(c_66646,plain,
    ( ( app(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_12353]) ).

tcf(c_66647,plain,
    ( ( app(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_12352]) ).

tcf(c_66648,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3199]) ).

tcf(c_66649,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3066]) ).

tcf(c_66650,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_8061]) ).

tcf(c_66651,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_8048]) ).

tcf(c_66652,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_5745]) ).

tcf(c_66653,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_8047]) ).

tcf(c_66654,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk4,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_5738]) ).

tcf(c_66655,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_5737]) ).

tcf(c_66656,plain,
    ( ( app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = tl(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4136]) ).

tcf(c_66657,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),sk4)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4462]) ).

tcf(c_66658,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),sk3)) = app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4461]) ).

tcf(c_66659,plain,
    ( ( app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = tl(app(sk3,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4284]) ).

tcf(c_66662,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3019]) ).

tcf(c_66663,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3452]) ).

tcf(c_66664,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3444]) ).

tcf(c_66665,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3065]) ).

tcf(c_66666,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3215]) ).

tcf(c_66667,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3)) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3207]) ).

tcf(c_66668,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_253]) ).

tcf(c_66669,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_275]) ).

tcf(c_66670,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) = cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3018]) ).

tcf(c_66671,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3191]) ).

tcf(c_66672,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3183]) ).

tcf(c_66673,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_284]) ).

tcf(c_66674,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_276]) ).

tcf(c_66675,plain,
    ( ( app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),nil) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_258]) ).

tcf(c_66676,plain,
    ( ( app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_257]) ).

tcf(c_66939,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ( hd(app(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))),X0)) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_66571,c_18201]) ).

tcf(c_66954,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_66669,c_18201]) ).

tcf(c_67465,plain,
    ! [X0: $i] :
      ( ( app(sk4,tl(sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( app(sk4,tl(sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_65158,c_270]) ).

tcf(c_67466,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( app(X0,app(sk4,tl(sk3))) != app(sk4,tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65158,c_269]) ).

tcf(c_67467,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( app(X0,app(sk4,tl(sk3))) != app(sk4,tl(sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_67466,c_259]) ).

tcf(c_67472,plain,
    ! [X0: $i] :
      ( ( app(sk4,tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( app(sk4,tl(sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_67465,c_259]) ).

tcf(c_67485,plain,
    ! [X0: $i] :
      ( ( app(sk3,tl(sk3)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( app(sk3,tl(sk3)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_65160,c_270]) ).

tcf(c_67486,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( app(X0,app(sk3,tl(sk3))) != app(sk3,tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65160,c_269]) ).

tcf(c_67487,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( app(X0,app(sk3,tl(sk3))) != app(sk3,tl(sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_67486,c_259]) ).

tcf(c_67492,plain,
    ! [X0: $i] :
      ( ( app(sk3,tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,tl(sk3)))
      | ( app(sk3,tl(sk3)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_67485,c_259]) ).

tcf(c_67498,plain,
    ( ssList(app(tl(sk4),tl(sk3)))
    | ( app(sk4,tl(sk3)) = nil )
    | ~ ssList(app(sk4,tl(sk3))) ),
    inference(superposition,[status(thm)],[c_65164,c_278]) ).

tcf(c_67499,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,tl(sk3)) = nil )
      | ( app(sk4,tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( hd(app(sk4,tl(sk3))) != hd(X0) )
      | ( app(tl(sk4),tl(sk3)) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_65164,c_273]) ).

tcf(c_67503,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,tl(sk3)) = nil )
      | ( app(sk4,tl(sk3)) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,tl(sk3)))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),tl(sk3)) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_67499,c_14921]) ).

tcf(c_67512,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,tl(sk4)))))
      | ( cons(hd(sk4),app(sk4,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,tl(sk4))))
      | ~ ssList(cons(hd(sk4),app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_66119,c_280]) ).

tcf(c_67513,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,tl(sk4)))))
      | ( cons(hd(sk4),app(sk4,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,tl(sk4))))
      | ~ ssList(cons(hd(sk4),app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_66119,c_279]) ).

tcf(c_67532,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,tl(sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_62824]) ).

tcf(c_67533,plain,
    hd(cons(hd(sk4),app(sk3,tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_62824]) ).

tcf(c_67534,plain,
    hd(cons(hd(sk3),app(sk3,tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_62824]) ).

tcf(c_67541,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,tl(sk3))))))
      | ( app(sk3,app(sk4,app(sk4,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,tl(sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65099,c_280]) ).

tcf(c_67542,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,tl(sk3))))))
      | ( app(sk3,app(sk4,app(sk4,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,tl(sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65099,c_279]) ).

tcf(c_67558,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,tl(sk3))))))
      | ( app(sk3,app(sk4,app(sk3,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,tl(sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65100,c_280]) ).

tcf(c_67559,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,tl(sk3))))))
      | ( app(sk3,app(sk4,app(sk3,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,tl(sk3)))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65100,c_279]) ).

tcf(c_67575,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,tl(sk3))))))
      | ( app(sk3,app(sk3,app(sk4,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,tl(sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65104,c_280]) ).

tcf(c_67576,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,tl(sk3))))))
      | ( app(sk3,app(sk3,app(sk4,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,tl(sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65104,c_279]) ).

tcf(c_67592,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,tl(sk3))))))
      | ( app(sk3,app(sk3,app(sk3,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,tl(sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65105,c_280]) ).

tcf(c_67593,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,tl(sk3))))))
      | ( app(sk3,app(sk3,app(sk3,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,tl(sk3)))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65105,c_279]) ).

tcf(c_67610,plain,
    ( ssList(app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))
    | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_10213,c_278]) ).

tcf(c_67611,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = nil )
      | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4))))
      | ( hd(app(sk4,cons(hd(sk4),app(sk3,sk4)))) != hd(X0) )
      | ( app(tl(sk4),cons(hd(sk4),app(sk3,sk4))) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_10213,c_273]) ).

tcf(c_67615,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = nil )
      | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4))))
      | ( hd(X0) != hd(sk4) )
      | ( app(tl(sk4),cons(hd(sk4),app(sk3,sk4))) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_67611,c_10218]) ).

tcf(c_67647,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),sk3)) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_246,c_62769]) ).

tcf(c_67648,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),sk4)) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_247,c_62769]) ).

tcf(c_67649,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),nil)) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_259,c_62769]) ).

tcf(c_67650,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(sk4) = nil )
      | ( hd(app(tl(sk4),tl(X0))) = hd(tl(sk4)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_62769]) ).

tcf(c_67651,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk4) = nil )
      | ( hd(app(tl(sk4),app(X1,X0))) = hd(tl(sk4)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_62769]) ).

tcf(c_67652,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk4) = nil )
      | ( hd(app(tl(sk4),cons(X1,X0))) = hd(tl(sk4)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_62769]) ).

tcf(c_67653,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),tl(sk4))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_62769]) ).

tcf(c_67654,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk3),sk3))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_62769]) ).

tcf(c_67655,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk4),sk3))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_62769]) ).

tcf(c_67656,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk3),sk4))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_62769]) ).

tcf(c_67657,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk4),sk4))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_62769]) ).

tcf(c_67658,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),tl(sk3))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_62769]) ).

tcf(c_67659,plain,
    ( ( tl(sk4) = nil )
    | ( app(sk3,sk3) = nil )
    | ( hd(app(tl(sk4),app(tl(sk3),sk3))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_62769]) ).

tcf(c_67660,plain,
    ( ( tl(sk4) = nil )
    | ( app(sk3,sk4) = nil )
    | ( hd(app(tl(sk4),app(tl(sk3),sk4))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_62769]) ).

tcf(c_67661,plain,
    ( ( tl(sk4) = nil )
    | ( app(sk4,sk3) = nil )
    | ( hd(app(tl(sk4),app(tl(sk4),sk3))) = hd(tl(sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_62769]) ).

tcf(c_67662,plain,
    ( ( tl(sk4) = nil )
    | ( app(sk4,sk4) = nil )
    | ( hd(app(tl(sk4),app(tl(sk4),sk4))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_62769]) ).

tcf(c_67663,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_5886,c_62769]) ).

tcf(c_67664,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk3,sk3)))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_62769]) ).

tcf(c_67665,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk3,sk4)))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_62769]) ).

tcf(c_67666,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk3,sk3)))) = hd(tl(sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_62769]) ).

tcf(c_67667,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_7540,c_62769]) ).

tcf(c_67668,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk3,sk4)))) = hd(tl(sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_62769]) ).

tcf(c_67669,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk4,sk3)))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_62769]) ).

tcf(c_67670,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk4,sk4)))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_62769]) ).

tcf(c_67671,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk4,sk3)))) = hd(tl(sk4)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_62769]) ).

tcf(c_67672,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk4,sk4)))) = hd(tl(sk4)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_62769]) ).

tcf(c_67673,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_10188,c_62769]) ).

tcf(c_67674,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_10606,c_62769]) ).

tcf(c_67675,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),sk3))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_62769]) ).

tcf(c_67676,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),sk4))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_62769]) ).

tcf(c_67677,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_62769]) ).

tcf(c_67678,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_16922,c_62769]) ).

tcf(c_67679,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_19123,c_62769]) ).

tcf(c_67680,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_17697,c_62769]) ).

tcf(c_67681,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_20483,c_62769]) ).

tcf(c_67682,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),sk3))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_62769]) ).

tcf(c_67683,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),sk4))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_62769]) ).

tcf(c_67684,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),sk3))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_50099,c_62769]) ).

tcf(c_67685,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),sk4))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_51167,c_62769]) ).

tcf(c_67686,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_42609,c_62769]) ).

tcf(c_67687,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_43441,c_62769]) ).

tcf(c_67688,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_62769]) ).

tcf(c_67689,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_62769]) ).

tcf(c_67690,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_64396,c_62769]) ).

tcf(c_67691,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_52696,c_62769]) ).

tcf(c_67692,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_53971,c_62769]) ).

tcf(c_67693,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_59405,c_62769]) ).

tcf(c_67694,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_62769]) ).

tcf(c_67695,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_62769]) ).

tcf(c_67696,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_44714,c_62769]) ).

tcf(c_67697,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_46613,c_62769]) ).

tcf(c_67698,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_61722,c_62769]) ).

tcf(c_67892,plain,
    ( ssItem(hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ~ ssList(app(tl(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_67647,c_286]) ).

tcf(c_67893,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(tl(sk4),sk3)))
      | ( tl(sk4) = nil )
      | ( app(tl(sk4),sk3) = nil )
      | ~ ssItem(X0)
      | ~ totalorderedP(app(tl(sk4),sk3))
      | ~ ssList(app(tl(sk4),sk3))
      | ~ leq(X0,hd(tl(sk4))) ),
    inference(superposition,[status(thm)],[c_67647,c_280]) ).

tcf(c_67894,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(tl(sk4),sk3)))
      | ( tl(sk4) = nil )
      | ( app(tl(sk4),sk3) = nil )
      | ~ ssItem(X0)
      | ~ strictorderedP(app(tl(sk4),sk3))
      | ~ ssList(app(tl(sk4),sk3))
      | ~ lt(X0,hd(tl(sk4))) ),
    inference(superposition,[status(thm)],[c_67647,c_279]) ).

tcf(c_67919,plain,
    ( ssItem(hd(tl(sk4)))
    | ( tl(sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ~ ssList(app(tl(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_67648,c_286]) ).

tcf(c_67920,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(tl(sk4),sk4)))
      | ( tl(sk4) = nil )
      | ( app(tl(sk4),sk4) = nil )
      | ~ ssItem(X0)
      | ~ totalorderedP(app(tl(sk4),sk4))
      | ~ ssList(app(tl(sk4),sk4))
      | ~ leq(X0,hd(tl(sk4))) ),
    inference(superposition,[status(thm)],[c_67648,c_280]) ).

tcf(c_67921,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(tl(sk4),sk4)))
      | ( tl(sk4) = nil )
      | ( app(tl(sk4),sk4) = nil )
      | ~ ssItem(X0)
      | ~ strictorderedP(app(tl(sk4),sk4))
      | ~ ssList(app(tl(sk4),sk4))
      | ~ lt(X0,hd(tl(sk4))) ),
    inference(superposition,[status(thm)],[c_67648,c_279]) ).

tcf(c_67966,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),sk3)) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_246,c_65079]) ).

tcf(c_67967,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),sk4)) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_247,c_65079]) ).

tcf(c_67968,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),nil)) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_259,c_65079]) ).

tcf(c_67969,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(sk3) = nil )
      | ( hd(app(tl(sk3),tl(X0))) = hd(tl(sk3)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_65079]) ).

tcf(c_67970,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk3) = nil )
      | ( hd(app(tl(sk3),app(X1,X0))) = hd(tl(sk3)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_65079]) ).

tcf(c_67971,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(sk3) = nil )
      | ( hd(app(tl(sk3),cons(X1,X0))) = hd(tl(sk3)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_65079]) ).

tcf(c_67972,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),tl(sk4))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_65079]) ).

tcf(c_67973,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk3),sk3))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_65079]) ).

tcf(c_67974,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk4),sk3))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_65079]) ).

tcf(c_67975,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk3),sk4))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_65079]) ).

tcf(c_67976,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk4),sk4))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_65079]) ).

tcf(c_67977,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),tl(sk3))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_65079]) ).

tcf(c_67978,plain,
    ( ( tl(sk3) = nil )
    | ( app(sk3,sk3) = nil )
    | ( hd(app(tl(sk3),app(tl(sk3),sk3))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_65079]) ).

tcf(c_67979,plain,
    ( ( tl(sk3) = nil )
    | ( app(sk3,sk4) = nil )
    | ( hd(app(tl(sk3),app(tl(sk3),sk4))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_65079]) ).

tcf(c_67980,plain,
    ( ( tl(sk3) = nil )
    | ( app(sk4,sk3) = nil )
    | ( hd(app(tl(sk3),app(tl(sk4),sk3))) = hd(tl(sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_65079]) ).

tcf(c_67981,plain,
    ( ( tl(sk3) = nil )
    | ( app(sk4,sk4) = nil )
    | ( hd(app(tl(sk3),app(tl(sk4),sk4))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_65079]) ).

tcf(c_67982,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk4),app(sk3,sk3)))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_5886,c_65079]) ).

tcf(c_67983,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk3,sk3)))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_65079]) ).

tcf(c_67984,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk3,sk4)))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_65079]) ).

tcf(c_67985,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk3,sk3)))) = hd(tl(sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_65079]) ).

tcf(c_67986,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk4),app(sk4,sk3)))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_7540,c_65079]) ).

tcf(c_67987,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk3,sk4)))) = hd(tl(sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_65079]) ).

tcf(c_67988,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk4,sk3)))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_65079]) ).

tcf(c_67989,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk4,sk4)))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_65079]) ).

tcf(c_67990,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk4,sk3)))) = hd(tl(sk3)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_65079]) ).

tcf(c_67991,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk4,sk4)))) = hd(tl(sk3)) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_65079]) ).

tcf(c_67992,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk4),app(sk3,sk4)))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_10188,c_65079]) ).

tcf(c_67993,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk4),app(sk4,sk4)))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_10606,c_65079]) ).

tcf(c_67994,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk3))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_65079]) ).

tcf(c_67995,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk4))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_65079]) ).

tcf(c_67996,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_65079]) ).

tcf(c_67997,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk3),app(sk4,sk4)))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_16922,c_65079]) ).

tcf(c_67998,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk3),app(sk4,sk3)))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_19123,c_65079]) ).

tcf(c_67999,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk3),app(sk3,sk4)))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_17697,c_65079]) ).

tcf(c_68000,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk3),app(sk3,sk3)))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_20483,c_65079]) ).

tcf(c_68001,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk3))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_65079]) ).

tcf(c_68002,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk4))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_65079]) ).

tcf(c_68003,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk3))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_50099,c_65079]) ).

tcf(c_68004,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk4))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_51167,c_65079]) ).

tcf(c_68005,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_42609,c_65079]) ).

tcf(c_68006,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_43441,c_65079]) ).

tcf(c_68007,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_65079]) ).

tcf(c_68008,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_65079]) ).

tcf(c_68009,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_64396,c_65079]) ).

tcf(c_68010,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_52696,c_65079]) ).

tcf(c_68011,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_53971,c_65079]) ).

tcf(c_68012,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_59405,c_65079]) ).

tcf(c_68013,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_65079]) ).

tcf(c_68014,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_65079]) ).

tcf(c_68015,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_44714,c_65079]) ).

tcf(c_68016,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_46613,c_65079]) ).

tcf(c_68017,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_61722,c_65079]) ).

tcf(c_68389,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,tl(sk4)))))
      | ( cons(hd(sk3),app(sk4,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,tl(sk4))))
      | ~ ssList(cons(hd(sk3),app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_66120,c_280]) ).

tcf(c_68390,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,tl(sk4)))))
      | ( cons(hd(sk3),app(sk4,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,tl(sk4))))
      | ~ ssList(cons(hd(sk3),app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_66120,c_279]) ).

tcf(c_68406,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,tl(sk4)))))
      | ( cons(hd(sk4),app(sk3,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,tl(sk4))))
      | ~ ssList(cons(hd(sk4),app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_67533,c_280]) ).

tcf(c_68407,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,tl(sk4)))))
      | ( cons(hd(sk4),app(sk3,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,tl(sk4))))
      | ~ ssList(cons(hd(sk4),app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_67533,c_279]) ).

tcf(c_68427,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,tl(sk4)))))
      | ( cons(hd(sk3),app(sk3,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,tl(sk4))))
      | ~ ssList(cons(hd(sk3),app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_67534,c_280]) ).

tcf(c_68428,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,tl(sk4)))))
      | ( cons(hd(sk3),app(sk3,tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,tl(sk4))))
      | ~ ssList(cons(hd(sk3),app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_67534,c_279]) ).

tcf(c_68483,plain,
    ( ssItem(hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ~ ssList(app(tl(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_67966,c_286]) ).

tcf(c_68484,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(tl(sk3),sk3)))
      | ( tl(sk3) = nil )
      | ( app(tl(sk3),sk3) = nil )
      | ~ ssItem(X0)
      | ~ totalorderedP(app(tl(sk3),sk3))
      | ~ ssList(app(tl(sk3),sk3))
      | ~ leq(X0,hd(tl(sk3))) ),
    inference(superposition,[status(thm)],[c_67966,c_280]) ).

tcf(c_68485,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(tl(sk3),sk3)))
      | ( tl(sk3) = nil )
      | ( app(tl(sk3),sk3) = nil )
      | ~ ssItem(X0)
      | ~ strictorderedP(app(tl(sk3),sk3))
      | ~ ssList(app(tl(sk3),sk3))
      | ~ lt(X0,hd(tl(sk3))) ),
    inference(superposition,[status(thm)],[c_67966,c_279]) ).

tcf(c_68546,plain,
    ( ssItem(hd(tl(sk3)))
    | ( tl(sk3) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ~ ssList(app(tl(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_67967,c_286]) ).

tcf(c_68547,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(tl(sk3),sk4)))
      | ( tl(sk3) = nil )
      | ( app(tl(sk3),sk4) = nil )
      | ~ ssItem(X0)
      | ~ totalorderedP(app(tl(sk3),sk4))
      | ~ ssList(app(tl(sk3),sk4))
      | ~ leq(X0,hd(tl(sk3))) ),
    inference(superposition,[status(thm)],[c_67967,c_280]) ).

tcf(c_68548,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(tl(sk3),sk4)))
      | ( tl(sk3) = nil )
      | ( app(tl(sk3),sk4) = nil )
      | ~ ssItem(X0)
      | ~ strictorderedP(app(tl(sk3),sk4))
      | ~ ssList(app(tl(sk3),sk4))
      | ~ lt(X0,hd(tl(sk3))) ),
    inference(superposition,[status(thm)],[c_67967,c_279]) ).

tcf(c_68570,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,tl(sk3))))))
      | ( app(sk4,app(sk4,app(sk4,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,tl(sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65117,c_280]) ).

tcf(c_68571,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,tl(sk3))))))
      | ( app(sk4,app(sk4,app(sk4,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,tl(sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65117,c_279]) ).

tcf(c_68587,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,tl(sk3))))))
      | ( app(sk4,app(sk4,app(sk3,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,tl(sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65118,c_280]) ).

tcf(c_68588,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,tl(sk3))))))
      | ( app(sk4,app(sk4,app(sk3,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,tl(sk3)))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65118,c_279]) ).

tcf(c_68604,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,tl(sk3))))))
      | ( app(sk4,app(sk3,app(sk4,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,tl(sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65122,c_280]) ).

tcf(c_68605,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,tl(sk3))))))
      | ( app(sk4,app(sk3,app(sk4,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,tl(sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65122,c_279]) ).

tcf(c_68621,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,tl(sk3))))))
      | ( app(sk4,app(sk3,app(sk3,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,tl(sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65123,c_280]) ).

tcf(c_68622,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,tl(sk3))))))
      | ( app(sk4,app(sk3,app(sk3,tl(sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,tl(sk3)))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65123,c_279]) ).

tcf(c_68655,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,tl(sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_65133]) ).

tcf(c_68656,plain,
    hd(cons(hd(sk4),app(sk4,tl(sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_65133]) ).

tcf(c_68657,plain,
    hd(cons(hd(sk3),app(sk4,tl(sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_65133]) ).

tcf(c_68679,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,tl(sk3)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_65134]) ).

tcf(c_68680,plain,
    hd(cons(hd(sk4),app(sk3,tl(sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_65134]) ).

tcf(c_68681,plain,
    hd(cons(hd(sk3),app(sk3,tl(sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_65134]) ).

tcf(c_68686,plain,
    ( ssList(app(tl(sk3),cons(hd(sk4),app(sk3,sk4))))
    | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_10216,c_278]) ).

tcf(c_68687,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = nil )
      | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4))))
      | ( hd(app(sk3,cons(hd(sk4),app(sk3,sk4)))) != hd(X0) )
      | ( app(tl(sk3),cons(hd(sk4),app(sk3,sk4))) != tl(X0) ) ),
    inference(superposition,[status(thm)],[c_10216,c_273]) ).

tcf(c_68691,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = nil )
      | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4))))
      | ( hd(X0) != hd(sk3) )
      | ( app(tl(sk3),cons(hd(sk4),app(sk3,sk4))) != tl(X0) ) ),
    inference(light_normalisation,[status(thm)],[c_68687,c_10217]) ).

tcf(c_68708,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(cons(hd(tl(X0)),nil),sk3) = cons(hd(tl(X0)),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3460]) ).

tcf(c_68709,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(cons(hd(app(X1,X0)),nil),sk3) = cons(hd(app(X1,X0)),sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3460]) ).

tcf(c_68710,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(cons(hd(cons(X1,X0)),nil),sk3) = cons(hd(cons(X1,X0)),sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3460]) ).

tcf(c_68711,plain,
    ( ( tl(sk4) = nil )
    | ( app(cons(hd(tl(sk4)),nil),sk3) = cons(hd(tl(sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3460]) ).

tcf(c_68712,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk3)),nil),sk3) = cons(hd(cons(hd(sk3),sk3)),sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3460]) ).

tcf(c_68713,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk3)),nil),sk3) = cons(hd(cons(hd(sk4),sk3)),sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3460]) ).

tcf(c_68714,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk4)),nil),sk3) = cons(hd(cons(hd(sk3),sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3460]) ).

tcf(c_68715,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk4)),nil),sk3) = cons(hd(cons(hd(sk4),sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3460]) ).

tcf(c_68716,plain,
    ( ( tl(sk3) = nil )
    | ( app(cons(hd(tl(sk3)),nil),sk3) = cons(hd(tl(sk3)),sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3460]) ).

tcf(c_68717,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(cons(hd(app(tl(sk3),sk3)),nil),sk3) = cons(hd(app(tl(sk3),sk3)),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3460]) ).

tcf(c_68718,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(cons(hd(app(tl(sk3),sk4)),nil),sk3) = cons(hd(app(tl(sk3),sk4)),sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3460]) ).

tcf(c_68719,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(cons(hd(app(tl(sk4),sk3)),nil),sk3) = cons(hd(app(tl(sk4),sk3)),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3460]) ).

tcf(c_68720,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(cons(hd(app(tl(sk4),sk4)),nil),sk3) = cons(hd(app(tl(sk4),sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3460]) ).

tcf(c_68721,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil),sk3) = cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3460]) ).

tcf(c_68722,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk3))),nil),sk3) = cons(hd(app(sk3,app(sk3,sk3))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3460]) ).

tcf(c_68723,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk4))),nil),sk3) = cons(hd(app(sk3,app(sk3,sk4))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3460]) ).

tcf(c_68724,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk3))),nil),sk3) = cons(hd(app(sk4,app(sk3,sk3))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3460]) ).

tcf(c_68725,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil),sk3) = cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3460]) ).

tcf(c_68726,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk4))),nil),sk3) = cons(hd(app(sk4,app(sk3,sk4))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3460]) ).

tcf(c_68727,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk3))),nil),sk3) = cons(hd(app(sk3,app(sk4,sk3))),sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3460]) ).

tcf(c_68728,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk4))),nil),sk3) = cons(hd(app(sk3,app(sk4,sk4))),sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3460]) ).

tcf(c_68729,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk3))),nil),sk3) = cons(hd(app(sk4,app(sk4,sk3))),sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3460]) ).

tcf(c_68730,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk4))),nil),sk3) = cons(hd(app(sk4,app(sk4,sk4))),sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3460]) ).

tcf(c_68731,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil),sk3) = cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3460]) ).

tcf(c_68732,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil),sk3) = cons(hd(cons(hd(sk4),app(sk4,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3460]) ).

tcf(c_68733,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil),sk3) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3460]) ).

tcf(c_68734,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil),sk3) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3460]) ).

tcf(c_68735,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil),sk3) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3460]) ).

tcf(c_68736,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk4))),nil),sk3) = cons(hd(cons(hd(sk3),app(sk4,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3460]) ).

tcf(c_68737,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk3))),nil),sk3) = cons(hd(cons(hd(sk3),app(sk4,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3460]) ).

tcf(c_68738,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk4))),nil),sk3) = cons(hd(cons(hd(sk3),app(sk3,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3460]) ).

tcf(c_68739,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk3))),nil),sk3) = cons(hd(cons(hd(sk3),app(sk3,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3460]) ).

tcf(c_68740,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil),sk3) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3460]) ).

tcf(c_68741,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil),sk3) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3460]) ).

tcf(c_68742,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil),sk3) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3460]) ).

tcf(c_68743,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil),sk3) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3460]) ).

tcf(c_68744,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil),sk3) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3460]) ).

tcf(c_68745,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil),sk3) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3460]) ).

tcf(c_68746,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil),sk3) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3460]) ).

tcf(c_68747,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil),sk3) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3460]) ).

tcf(c_68748,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil),sk3) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3460]) ).

tcf(c_68749,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil),sk3) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3460]) ).

tcf(c_68750,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil),sk3) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3460]) ).

tcf(c_68751,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil),sk3) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3460]) ).

tcf(c_68752,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil),sk3) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3460]) ).

tcf(c_68753,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil),sk3) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3460]) ).

tcf(c_68754,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil),sk3) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3460]) ).

tcf(c_68755,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil),sk3) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3460]) ).

tcf(c_68756,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil),sk3) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3460]) ).

tcf(c_68862,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(cons(hd(tl(X0)),nil),sk4) = cons(hd(tl(X0)),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3470]) ).

tcf(c_68863,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(cons(hd(app(X1,X0)),nil),sk4) = cons(hd(app(X1,X0)),sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3470]) ).

tcf(c_68864,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(cons(hd(cons(X1,X0)),nil),sk4) = cons(hd(cons(X1,X0)),sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3470]) ).

tcf(c_68865,plain,
    ( ( tl(sk4) = nil )
    | ( app(cons(hd(tl(sk4)),nil),sk4) = cons(hd(tl(sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3470]) ).

tcf(c_68866,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk3)),nil),sk4) = cons(hd(cons(hd(sk3),sk3)),sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3470]) ).

tcf(c_68867,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk3)),nil),sk4) = cons(hd(cons(hd(sk4),sk3)),sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3470]) ).

tcf(c_68868,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk4)),nil),sk4) = cons(hd(cons(hd(sk3),sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3470]) ).

tcf(c_68869,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk4)),nil),sk4) = cons(hd(cons(hd(sk4),sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3470]) ).

tcf(c_68870,plain,
    ( ( tl(sk3) = nil )
    | ( app(cons(hd(tl(sk3)),nil),sk4) = cons(hd(tl(sk3)),sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3470]) ).

tcf(c_68871,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(cons(hd(app(tl(sk3),sk3)),nil),sk4) = cons(hd(app(tl(sk3),sk3)),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3470]) ).

tcf(c_68872,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(cons(hd(app(tl(sk3),sk4)),nil),sk4) = cons(hd(app(tl(sk3),sk4)),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3470]) ).

tcf(c_68873,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(cons(hd(app(tl(sk4),sk3)),nil),sk4) = cons(hd(app(tl(sk4),sk3)),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3470]) ).

tcf(c_68874,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(cons(hd(app(tl(sk4),sk4)),nil),sk4) = cons(hd(app(tl(sk4),sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3470]) ).

tcf(c_68875,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil),sk4) = cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3470]) ).

tcf(c_68876,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk3))),nil),sk4) = cons(hd(app(sk3,app(sk3,sk3))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3470]) ).

tcf(c_68877,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk4))),nil),sk4) = cons(hd(app(sk3,app(sk3,sk4))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3470]) ).

tcf(c_68878,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk3))),nil),sk4) = cons(hd(app(sk4,app(sk3,sk3))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3470]) ).

tcf(c_68879,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil),sk4) = cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3470]) ).

tcf(c_68880,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk4))),nil),sk4) = cons(hd(app(sk4,app(sk3,sk4))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3470]) ).

tcf(c_68881,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk3))),nil),sk4) = cons(hd(app(sk3,app(sk4,sk3))),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3470]) ).

tcf(c_68882,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk4))),nil),sk4) = cons(hd(app(sk3,app(sk4,sk4))),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3470]) ).

tcf(c_68883,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk3))),nil),sk4) = cons(hd(app(sk4,app(sk4,sk3))),sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3470]) ).

tcf(c_68884,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk4))),nil),sk4) = cons(hd(app(sk4,app(sk4,sk4))),sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3470]) ).

tcf(c_68885,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil),sk4) = cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3470]) ).

tcf(c_68886,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil),sk4) = cons(hd(cons(hd(sk4),app(sk4,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3470]) ).

tcf(c_68887,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil),sk4) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3470]) ).

tcf(c_68888,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil),sk4) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3470]) ).

tcf(c_68889,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil),sk4) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3470]) ).

tcf(c_68890,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk4))),nil),sk4) = cons(hd(cons(hd(sk3),app(sk4,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3470]) ).

tcf(c_68891,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk3))),nil),sk4) = cons(hd(cons(hd(sk3),app(sk4,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3470]) ).

tcf(c_68892,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk4))),nil),sk4) = cons(hd(cons(hd(sk3),app(sk3,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3470]) ).

tcf(c_68893,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk3))),nil),sk4) = cons(hd(cons(hd(sk3),app(sk3,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3470]) ).

tcf(c_68894,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil),sk4) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3470]) ).

tcf(c_68895,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil),sk4) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3470]) ).

tcf(c_68896,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil),sk4) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3470]) ).

tcf(c_68897,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil),sk4) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3470]) ).

tcf(c_68898,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil),sk4) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3470]) ).

tcf(c_68899,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil),sk4) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3470]) ).

tcf(c_68900,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil),sk4) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3470]) ).

tcf(c_68901,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil),sk4) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3470]) ).

tcf(c_68902,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil),sk4) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3470]) ).

tcf(c_68903,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil),sk4) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3470]) ).

tcf(c_68904,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil),sk4) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3470]) ).

tcf(c_68905,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil),sk4) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3470]) ).

tcf(c_68906,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil),sk4) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3470]) ).

tcf(c_68907,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil),sk4) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3470]) ).

tcf(c_68908,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil),sk4) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3470]) ).

tcf(c_68909,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil),sk4) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3470]) ).

tcf(c_68910,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil),sk4) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3470]) ).

tcf(c_69044,plain,
    ( strictorderedP(tl(sk4))
    | ( tl(sk4) = nil )
    | ~ strictorderedP(sk4) ),
    inference(global_subsumption_just,[status(thm)],[c_3622,c_40997]) ).

tcf(c_69061,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(cons(hd(tl(X0)),nil),nil) = cons(hd(tl(X0)),nil) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_3653]) ).

tcf(c_69062,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(cons(hd(app(X1,X0)),nil),nil) = cons(hd(app(X1,X0)),nil) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_3653]) ).

tcf(c_69063,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(cons(hd(cons(X1,X0)),nil),nil) = cons(hd(cons(X1,X0)),nil) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_3653]) ).

tcf(c_69064,plain,
    ( ( tl(sk4) = nil )
    | ( app(cons(hd(tl(sk4)),nil),nil) = cons(hd(tl(sk4)),nil) ) ),
    inference(superposition,[status(thm)],[c_62750,c_3653]) ).

tcf(c_69065,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk3)),nil),nil) = cons(hd(cons(hd(sk3),sk3)),nil) ) ),
    inference(superposition,[status(thm)],[c_13784,c_3653]) ).

tcf(c_69066,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk3)),nil),nil) = cons(hd(cons(hd(sk4),sk3)),nil) ) ),
    inference(superposition,[status(thm)],[c_4358,c_3653]) ).

tcf(c_69067,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk3),sk4)),nil),nil) = cons(hd(cons(hd(sk3),sk4)),nil) ) ),
    inference(superposition,[status(thm)],[c_12796,c_3653]) ).

tcf(c_69068,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(cons(hd(cons(hd(sk4),sk4)),nil),nil) = cons(hd(cons(hd(sk4),sk4)),nil) ) ),
    inference(superposition,[status(thm)],[c_4223,c_3653]) ).

tcf(c_69069,plain,
    ( ( tl(sk3) = nil )
    | ( app(cons(hd(tl(sk3)),nil),nil) = cons(hd(tl(sk3)),nil) ) ),
    inference(superposition,[status(thm)],[c_65060,c_3653]) ).

tcf(c_69070,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(cons(hd(app(tl(sk3),sk3)),nil),nil) = cons(hd(app(tl(sk3),sk3)),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_3653]) ).

tcf(c_69071,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(cons(hd(app(tl(sk3),sk4)),nil),nil) = cons(hd(app(tl(sk3),sk4)),nil) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_3653]) ).

tcf(c_69072,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(cons(hd(app(tl(sk4),sk3)),nil),nil) = cons(hd(app(tl(sk4),sk3)),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_3653]) ).

tcf(c_69073,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(cons(hd(app(tl(sk4),sk4)),nil),nil) = cons(hd(app(tl(sk4),sk4)),nil) ) ),
    inference(superposition,[status(thm)],[c_22091,c_3653]) ).

tcf(c_69074,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk3))),nil),nil) = cons(hd(cons(hd(sk4),app(sk3,sk3))),nil) ) ),
    inference(superposition,[status(thm)],[c_5886,c_3653]) ).

tcf(c_69075,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk3))),nil),nil) = cons(hd(app(sk3,app(sk3,sk3))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_3653]) ).

tcf(c_69076,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,sk4))),nil),nil) = cons(hd(app(sk3,app(sk3,sk4))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_3653]) ).

tcf(c_69077,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk3))),nil),nil) = cons(hd(app(sk4,app(sk3,sk3))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_3653]) ).

tcf(c_69078,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk3))),nil),nil) = cons(hd(cons(hd(sk4),app(sk4,sk3))),nil) ) ),
    inference(superposition,[status(thm)],[c_7540,c_3653]) ).

tcf(c_69079,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,sk4))),nil),nil) = cons(hd(app(sk4,app(sk3,sk4))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_3653]) ).

tcf(c_69080,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk3))),nil),nil) = cons(hd(app(sk3,app(sk4,sk3))),nil) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_3653]) ).

tcf(c_69081,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,sk4))),nil),nil) = cons(hd(app(sk3,app(sk4,sk4))),nil) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_3653]) ).

tcf(c_69082,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk3))),nil),nil) = cons(hd(app(sk4,app(sk4,sk3))),nil) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_3653]) ).

tcf(c_69083,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,sk4))),nil),nil) = cons(hd(app(sk4,app(sk4,sk4))),nil) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_3653]) ).

tcf(c_69084,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk3,sk4))),nil),nil) = cons(hd(cons(hd(sk4),app(sk3,sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_10188,c_3653]) ).

tcf(c_69085,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk4),app(sk4,sk4))),nil),nil) = cons(hd(cons(hd(sk4),app(sk4,sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_10606,c_3653]) ).

tcf(c_69086,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_3653]) ).

tcf(c_69087,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_3653]) ).

tcf(c_69088,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_3653]) ).

tcf(c_69089,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk4))),nil),nil) = cons(hd(cons(hd(sk3),app(sk4,sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_16922,c_3653]) ).

tcf(c_69090,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk4,sk3))),nil),nil) = cons(hd(cons(hd(sk3),app(sk4,sk3))),nil) ) ),
    inference(superposition,[status(thm)],[c_19123,c_3653]) ).

tcf(c_69091,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk4))),nil),nil) = cons(hd(cons(hd(sk3),app(sk3,sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_17697,c_3653]) ).

tcf(c_69092,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(cons(hd(cons(hd(sk3),app(sk3,sk3))),nil),nil) = cons(hd(cons(hd(sk3),app(sk3,sk3))),nil) ) ),
    inference(superposition,[status(thm)],[c_20483,c_3653]) ).

tcf(c_69093,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_3653]) ).

tcf(c_69094,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_3653]) ).

tcf(c_69095,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_50099,c_3653]) ).

tcf(c_69096,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_51167,c_3653]) ).

tcf(c_69097,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_42609,c_3653]) ).

tcf(c_69098,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_43441,c_3653]) ).

tcf(c_69099,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_3653]) ).

tcf(c_69100,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_3653]) ).

tcf(c_69101,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil),nil) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) ) ),
    inference(superposition,[status(thm)],[c_64396,c_3653]) ).

tcf(c_69102,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) ) ),
    inference(superposition,[status(thm)],[c_52696,c_3653]) ).

tcf(c_69103,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) ) ),
    inference(superposition,[status(thm)],[c_53971,c_3653]) ).

tcf(c_69104,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil),nil) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) ) ),
    inference(superposition,[status(thm)],[c_59405,c_3653]) ).

tcf(c_69105,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_3653]) ).

tcf(c_69106,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil),nil) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_3653]) ).

tcf(c_69107,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) ) ),
    inference(superposition,[status(thm)],[c_44714,c_3653]) ).

tcf(c_69108,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) ) ),
    inference(superposition,[status(thm)],[c_46613,c_3653]) ).

tcf(c_69109,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil),nil) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) ) ),
    inference(superposition,[status(thm)],[c_61722,c_3653]) ).

tcf(c_69202,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk4,tl(sk3)))))
      | ( cons(hd(sk4),app(sk4,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk4,tl(sk3))))
      | ~ ssList(cons(hd(sk4),app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68656,c_280]) ).

tcf(c_69203,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk4,tl(sk3)))))
      | ( cons(hd(sk4),app(sk4,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk4,tl(sk3))))
      | ~ ssList(cons(hd(sk4),app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68656,c_279]) ).

tcf(c_69219,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk4,tl(sk3)))))
      | ( cons(hd(sk3),app(sk4,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk4,tl(sk3))))
      | ~ ssList(cons(hd(sk3),app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68657,c_280]) ).

tcf(c_69220,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk4,tl(sk3)))))
      | ( cons(hd(sk3),app(sk4,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk4,tl(sk3))))
      | ~ ssList(cons(hd(sk3),app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68657,c_279]) ).

tcf(c_69260,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,tl(sk3)))))
      | ( cons(hd(sk4),app(sk3,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,tl(sk3))))
      | ~ ssList(cons(hd(sk4),app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68680,c_280]) ).

tcf(c_69261,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,tl(sk3)))))
      | ( cons(hd(sk4),app(sk3,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,tl(sk3))))
      | ~ ssList(cons(hd(sk4),app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68680,c_279]) ).

tcf(c_69277,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,tl(sk3)))))
      | ( cons(hd(sk3),app(sk3,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,tl(sk3))))
      | ~ ssList(cons(hd(sk3),app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68681,c_280]) ).

tcf(c_69278,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,tl(sk3)))))
      | ( cons(hd(sk3),app(sk3,tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,tl(sk3))))
      | ~ ssList(cons(hd(sk3),app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68681,c_279]) ).

tcf(c_69295,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_62849,c_255]) ).

tcf(c_69296,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_62849,c_254]) ).

tcf(c_69297,plain,
    ( ssList(app(sk4,app(sk4,tl(sk4))))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_62849,c_272]) ).

tcf(c_69298,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,tl(sk4))) != app(app(sk4,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_62849,c_270]) ).

tcf(c_69299,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,tl(sk4))) != app(X0,tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62849,c_269]) ).

tcf(c_69300,plain,
    ( ( tl(sk4) = sk4 )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk4))) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_62849,c_9527]) ).

tcf(c_69301,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk4))) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_62849,c_9248]) ).

tcf(c_69302,plain,
    ( ssList(app(sk4,app(sk4,tl(sk4))))
    | ~ ssList(app(sk4,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69297,c_62750]) ).

tcf(c_69305,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69296,c_62750]) ).

tcf(c_69309,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69295,c_62750]) ).

tcf(c_69313,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk4))) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69301,c_62750]) ).

tcf(c_69317,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk4))) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69300,c_3659,c_62750]) ).

tcf(c_69320,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,tl(sk4))) != app(X0,tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69299,c_62750]) ).

tcf(c_69325,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,tl(sk4))) != app(app(sk4,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69298,c_62750]) ).

tcf(c_69334,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_62851,c_255]) ).

tcf(c_69335,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_62851,c_254]) ).

tcf(c_69336,plain,
    ( ssList(app(sk3,app(sk4,tl(sk4))))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_62851,c_272]) ).

tcf(c_69337,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,tl(sk4))) != app(app(sk3,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_62851,c_270]) ).

tcf(c_69338,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,tl(sk4))) != app(X0,tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62851,c_269]) ).

tcf(c_69339,plain,
    ( ( tl(sk4) = sk4 )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk4))) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_62851,c_8552]) ).

tcf(c_69340,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk4))) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_62851,c_8271]) ).

tcf(c_69341,plain,
    ( ssList(app(sk3,app(sk4,tl(sk4))))
    | ~ ssList(app(sk3,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69336,c_62750]) ).

tcf(c_69344,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69335,c_62750]) ).

tcf(c_69348,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69334,c_62750]) ).

tcf(c_69352,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk4))) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69340,c_62750]) ).

tcf(c_69356,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk4))) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69339,c_3659,c_62750]) ).

tcf(c_69359,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,tl(sk4))) != app(X0,tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69338,c_62750]) ).

tcf(c_69364,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,tl(sk4))) != app(app(sk3,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69337,c_62750]) ).

tcf(c_69469,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_62852,c_255]) ).

tcf(c_69470,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_62852,c_254]) ).

tcf(c_69471,plain,
    ( ssList(app(sk4,app(sk3,tl(sk4))))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_62852,c_272]) ).

tcf(c_69472,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,tl(sk4))) != app(app(sk4,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_62852,c_270]) ).

tcf(c_69473,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,tl(sk4))) != app(X0,tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62852,c_269]) ).

tcf(c_69474,plain,
    ( ( tl(sk4) = sk4 )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk4))) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_62852,c_7768]) ).

tcf(c_69475,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk4))) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_62852,c_7262]) ).

tcf(c_69476,plain,
    ( ssList(app(sk4,app(sk3,tl(sk4))))
    | ~ ssList(app(sk4,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69471,c_62750]) ).

tcf(c_69479,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69470,c_62750]) ).

tcf(c_69483,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69469,c_62750]) ).

tcf(c_69487,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk4))) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69475,c_62750]) ).

tcf(c_69491,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk4))) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69474,c_3659,c_62750]) ).

tcf(c_69494,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,tl(sk4))) != app(X0,tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69473,c_62750]) ).

tcf(c_69499,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,tl(sk4))) != app(app(sk4,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69472,c_62750]) ).

tcf(c_69508,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_62853,c_255]) ).

tcf(c_69509,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk4))) != nil ) ),
    inference(superposition,[status(thm)],[c_62853,c_254]) ).

tcf(c_69510,plain,
    ( ssList(app(sk3,app(sk3,tl(sk4))))
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_62853,c_272]) ).

tcf(c_69511,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,tl(sk4))) != app(app(sk3,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_62853,c_270]) ).

tcf(c_69512,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,tl(sk4))) != app(X0,tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62853,c_269]) ).

tcf(c_69513,plain,
    ( ( tl(sk4) = sk4 )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk4))) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_62853,c_6948]) ).

tcf(c_69514,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(tl(sk4))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk4))) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_62853,c_6605]) ).

tcf(c_69515,plain,
    ( ssList(app(sk3,app(sk3,tl(sk4))))
    | ~ ssList(app(sk3,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69510,c_62750]) ).

tcf(c_69518,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69509,c_62750]) ).

tcf(c_69522,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk4))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69508,c_62750]) ).

tcf(c_69526,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk4))) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69514,c_62750]) ).

tcf(c_69530,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk4))) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69513,c_3659,c_62750]) ).

tcf(c_69533,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,tl(sk4))) != app(X0,tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69512,c_62750]) ).

tcf(c_69538,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,tl(sk4))) != app(app(sk3,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69511,c_62750]) ).

tcf(c_69547,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_65159,c_255]) ).

tcf(c_69548,plain,
    ( ( tl(sk3) = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_65159,c_254]) ).

tcf(c_69549,plain,
    ( ssList(app(sk4,app(sk4,tl(sk3))))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_65159,c_272]) ).

tcf(c_69550,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,tl(sk3))) != app(app(sk4,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_65159,c_270]) ).

tcf(c_69551,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,tl(sk3))) != app(X0,tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65159,c_269]) ).

tcf(c_69552,plain,
    ( ( tl(sk3) = sk4 )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk3))) != app(sk4,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_65159,c_9527]) ).

tcf(c_69553,plain,
    ( ( tl(sk3) = sk3 )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk3))) != app(sk4,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_65159,c_9248]) ).

tcf(c_69554,plain,
    ( ssList(app(sk4,app(sk4,tl(sk3))))
    | ~ ssList(app(sk4,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69549,c_65060]) ).

tcf(c_69557,plain,
    ( ( tl(sk3) = nil )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69548,c_65060]) ).

tcf(c_69561,plain,
    ( ( app(sk4,sk4) = nil )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69547,c_65060]) ).

tcf(c_69565,plain,
    ( ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk3))) != app(sk4,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69553,c_10973,c_65060]) ).

tcf(c_69568,plain,
    ( ( tl(sk3) = sk4 )
    | ~ ssList(app(sk4,sk4))
    | ( app(sk4,app(sk4,tl(sk3))) != app(sk4,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69552,c_65060]) ).

tcf(c_69572,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,tl(sk3))) != app(X0,tl(sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69551,c_65060]) ).

tcf(c_69577,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk4))
      | ( app(sk4,app(sk4,tl(sk3))) != app(app(sk4,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69550,c_65060]) ).

tcf(c_69586,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_65161,c_255]) ).

tcf(c_69587,plain,
    ( ( tl(sk3) = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_65161,c_254]) ).

tcf(c_69588,plain,
    ( ssList(app(sk3,app(sk4,tl(sk3))))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_65161,c_272]) ).

tcf(c_69589,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,tl(sk3))) != app(app(sk3,sk4),X0) ) ),
    inference(superposition,[status(thm)],[c_65161,c_270]) ).

tcf(c_69590,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,tl(sk3))) != app(X0,tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65161,c_269]) ).

tcf(c_69591,plain,
    ( ( tl(sk3) = sk4 )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk3))) != app(sk3,app(sk4,sk4)) ) ),
    inference(superposition,[status(thm)],[c_65161,c_8552]) ).

tcf(c_69592,plain,
    ( ( tl(sk3) = sk3 )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk3))) != app(sk3,app(sk4,sk3)) ) ),
    inference(superposition,[status(thm)],[c_65161,c_8271]) ).

tcf(c_69593,plain,
    ( ssList(app(sk3,app(sk4,tl(sk3))))
    | ~ ssList(app(sk3,sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69588,c_65060]) ).

tcf(c_69596,plain,
    ( ( tl(sk3) = nil )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69587,c_65060]) ).

tcf(c_69600,plain,
    ( ( app(sk3,sk4) = nil )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69586,c_65060]) ).

tcf(c_69604,plain,
    ( ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk3))) != app(sk3,app(sk4,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69592,c_10973,c_65060]) ).

tcf(c_69607,plain,
    ( ( tl(sk3) = sk4 )
    | ~ ssList(app(sk3,sk4))
    | ( app(sk3,app(sk4,tl(sk3))) != app(sk3,app(sk4,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69591,c_65060]) ).

tcf(c_69611,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,tl(sk3))) != app(X0,tl(sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69590,c_65060]) ).

tcf(c_69616,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk4))
      | ( app(sk3,app(sk4,tl(sk3))) != app(app(sk3,sk4),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69589,c_65060]) ).

tcf(c_69625,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_65162,c_255]) ).

tcf(c_69626,plain,
    ( ( tl(sk3) = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_65162,c_254]) ).

tcf(c_69627,plain,
    ( ssList(app(sk4,app(sk3,tl(sk3))))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_65162,c_272]) ).

tcf(c_69628,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,tl(sk3))) != app(app(sk4,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_65162,c_270]) ).

tcf(c_69629,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,tl(sk3))) != app(X0,tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65162,c_269]) ).

tcf(c_69630,plain,
    ( ( tl(sk3) = sk4 )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk3))) != app(sk4,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_65162,c_7768]) ).

tcf(c_69631,plain,
    ( ( tl(sk3) = sk3 )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk3))) != app(sk4,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_65162,c_7262]) ).

tcf(c_69632,plain,
    ( ssList(app(sk4,app(sk3,tl(sk3))))
    | ~ ssList(app(sk4,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69627,c_65060]) ).

tcf(c_69635,plain,
    ( ( tl(sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69626,c_65060]) ).

tcf(c_69639,plain,
    ( ( app(sk4,sk3) = nil )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69625,c_65060]) ).

tcf(c_69643,plain,
    ( ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk3))) != app(sk4,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69631,c_10973,c_65060]) ).

tcf(c_69646,plain,
    ( ( tl(sk3) = sk4 )
    | ~ ssList(app(sk4,sk3))
    | ( app(sk4,app(sk3,tl(sk3))) != app(sk4,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69630,c_65060]) ).

tcf(c_69650,plain,
    ! [X0: $i] :
      ( ( app(sk4,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,tl(sk3))) != app(X0,tl(sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69629,c_65060]) ).

tcf(c_69655,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk4,sk3))
      | ( app(sk4,app(sk3,tl(sk3))) != app(app(sk4,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69628,c_65060]) ).

tcf(c_69682,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_65163,c_255]) ).

tcf(c_69683,plain,
    ( ( tl(sk3) = nil )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk3))) != nil ) ),
    inference(superposition,[status(thm)],[c_65163,c_254]) ).

tcf(c_69684,plain,
    ( ssList(app(sk3,app(sk3,tl(sk3))))
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_65163,c_272]) ).

tcf(c_69685,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,tl(sk3))) != app(app(sk3,sk3),X0) ) ),
    inference(superposition,[status(thm)],[c_65163,c_270]) ).

tcf(c_69686,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk3))
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,tl(sk3))) != app(X0,tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65163,c_269]) ).

tcf(c_69687,plain,
    ( ( tl(sk3) = sk4 )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk3))) != app(sk3,app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_65163,c_6948]) ).

tcf(c_69688,plain,
    ( ( tl(sk3) = sk3 )
    | ~ ssList(tl(sk3))
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk3))) != app(sk3,app(sk3,sk3)) ) ),
    inference(superposition,[status(thm)],[c_65163,c_6605]) ).

tcf(c_69689,plain,
    ( ssList(app(sk3,app(sk3,tl(sk3))))
    | ~ ssList(app(sk3,sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69684,c_65060]) ).

tcf(c_69692,plain,
    ( ( tl(sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69683,c_65060]) ).

tcf(c_69696,plain,
    ( ( app(sk3,sk3) = nil )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk3))) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69682,c_65060]) ).

tcf(c_69700,plain,
    ( ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk3))) != app(sk3,app(sk3,sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69688,c_10973,c_65060]) ).

tcf(c_69703,plain,
    ( ( tl(sk3) = sk4 )
    | ~ ssList(app(sk3,sk3))
    | ( app(sk3,app(sk3,tl(sk3))) != app(sk3,app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69687,c_65060]) ).

tcf(c_69707,plain,
    ! [X0: $i] :
      ( ( app(sk3,sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,tl(sk3))) != app(X0,tl(sk3)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69686,c_65060]) ).

tcf(c_69712,plain,
    ! [X0: $i] :
      ( ( tl(sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3))
      | ( app(sk3,app(sk3,tl(sk3))) != app(app(sk3,sk3),X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_69685,c_65060]) ).

tcf(c_69719,plain,
    app(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4),nil) = cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4),
    inference(global_subsumption_just,[status(thm)],[c_10220,c_10190,c_10220]) ).

tcf(c_69722,plain,
    ssList(app(sk4,app(sk4,tl(sk4)))),
    inference(global_subsumption_just,[status(thm)],[c_69302,c_247,c_20236,c_69302]) ).

tcf(c_69724,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk4,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_18773]) ).

tcf(c_69725,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk4,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_18497]) ).

tcf(c_69726,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk4,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_18185]) ).

tcf(c_69727,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk4,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_16330]) ).

tcf(c_69728,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk4,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_15966]) ).

tcf(c_69729,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk4,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_15593]) ).

tcf(c_69730,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,tl(sk4))),nil),X0) = app(app(sk4,app(sk4,tl(sk4))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_4541]) ).

tcf(c_69731,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk4,tl(sk4))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3154]) ).

tcf(c_69732,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk4,tl(sk4))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_4037]) ).

tcf(c_69733,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk4,tl(sk4))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3952]) ).

tcf(c_69734,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk4,tl(sk4))),X0)) = app(app(sk4,app(sk4,tl(sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3050]) ).

tcf(c_69735,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,tl(sk4))),X0),nil) = app(app(sk4,app(sk4,tl(sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3049]) ).

tcf(c_69736,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,tl(sk4))),sk4),X0) = app(app(sk4,app(sk4,tl(sk4))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_4540]) ).

tcf(c_69737,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,tl(sk4))),sk3),X0) = app(app(sk4,app(sk4,tl(sk4))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_4539]) ).

tcf(c_69738,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk4,tl(sk4)))),X0) = app(X1,app(app(sk4,app(sk4,tl(sk4))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_271]) ).

tcf(c_69739,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk4,tl(sk4))))) = app(cons(X1,X0),app(sk4,app(sk4,tl(sk4)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_266]) ).

tcf(c_69740,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk4))) = nil )
      | ( app(tl(app(sk4,app(sk4,tl(sk4)))),X0) = tl(app(app(sk4,app(sk4,tl(sk4))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_274]) ).

tcf(c_69741,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk4))) = nil )
      | ( hd(app(app(sk4,app(sk4,tl(sk4))),X0)) = hd(app(sk4,app(sk4,tl(sk4)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_283]) ).

tcf(c_69742,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk4)))),nil),nil) = cons(hd(app(sk4,app(sk4,tl(sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3653]) ).

tcf(c_69743,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk4)))),nil),sk4) = cons(hd(app(sk4,app(sk4,tl(sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3470]) ).

tcf(c_69744,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk4)))),nil),sk3) = cons(hd(app(sk4,app(sk4,tl(sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3460]) ).

tcf(c_69745,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk4,tl(sk4))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_69722,c_65079]) ).

tcf(c_69746,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk4,tl(sk4))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_69722,c_62769]) ).

tcf(c_69747,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk4)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_61402]) ).

tcf(c_69748,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk4)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_61324]) ).

tcf(c_69749,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk4))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk4,tl(sk4)))))) = tl(app(sk4,app(sk4,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3118]) ).

tcf(c_69750,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),app(sk4,sk4))) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_34548]) ).

tcf(c_69751,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),app(sk4,sk3))) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_34490]) ).

tcf(c_69752,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),app(sk3,sk4))) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_34149]) ).

tcf(c_69753,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),app(sk3,sk3))) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_34101]) ).

tcf(c_69754,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,tl(sk4)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_19899]) ).

tcf(c_69755,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,tl(sk4)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_19024]) ).

tcf(c_69756,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,tl(sk4)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_19014]) ).

tcf(c_69757,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_17999]) ).

tcf(c_69758,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_18774]) ).

tcf(c_69759,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_57010]) ).

tcf(c_69760,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_57009]) ).

tcf(c_69761,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_57008]) ).

tcf(c_69762,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk4,tl(sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_18772]) ).

tcf(c_69763,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_15409]) ).

tcf(c_69764,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_18498]) ).

tcf(c_69765,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_54564]) ).

tcf(c_69766,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_54563]) ).

tcf(c_69767,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_54562]) ).

tcf(c_69768,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,tl(sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_18496]) ).

tcf(c_69769,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_18186]) ).

tcf(c_69770,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_48819]) ).

tcf(c_69771,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_48818]) ).

tcf(c_69772,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_48817]) ).

tcf(c_69773,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk4,tl(sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_18184]) ).

tcf(c_69774,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,tl(sk4)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_17287]) ).

tcf(c_69775,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,tl(sk4)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_16680]) ).

tcf(c_69776,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,tl(sk4)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_16670]) ).

tcf(c_69777,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_16331]) ).

tcf(c_69778,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_45260]) ).

tcf(c_69779,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_45259]) ).

tcf(c_69780,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_45258]) ).

tcf(c_69781,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk4,tl(sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_16329]) ).

tcf(c_69782,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_15967]) ).

tcf(c_69783,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_40467]) ).

tcf(c_69784,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_40466]) ).

tcf(c_69785,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_40465]) ).

tcf(c_69786,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk4,tl(sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_15965]) ).

tcf(c_69787,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_15594]) ).

tcf(c_69788,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_37606]) ).

tcf(c_69789,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_37605]) ).

tcf(c_69790,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_37604]) ).

tcf(c_69791,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk4,tl(sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_15592]) ).

tcf(c_69792,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_18000]) ).

tcf(c_69793,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_17998]) ).

tcf(c_69794,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_17997]) ).

tcf(c_69795,plain,
    app(sk3,app(nil,app(sk4,app(sk4,tl(sk4))))) = app(sk3,app(sk4,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_69722,c_35790]) ).

tcf(c_69796,plain,
    app(sk4,app(nil,app(sk4,app(sk4,tl(sk4))))) = app(sk4,app(sk4,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_69722,c_35787]) ).

tcf(c_69797,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,tl(sk4))),nil)) = app(cons(X0,app(sk4,app(sk4,tl(sk4)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_4463]) ).

tcf(c_69798,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk4,tl(sk4)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3155]) ).

tcf(c_69799,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk4,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_33403]) ).

tcf(c_69800,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk4,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_33402]) ).

tcf(c_69801,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk4,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_33401]) ).

tcf(c_69802,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),tl(sk3))) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_32111]) ).

tcf(c_69803,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),tl(sk4))) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_32098]) ).

tcf(c_69804,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_15410]) ).

tcf(c_69805,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_15408]) ).

tcf(c_69806,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_15407]) ).

tcf(c_69807,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk4))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk4,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3153]) ).

tcf(c_69808,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk4,tl(sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_4038]) ).

tcf(c_69809,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_17993]) ).

tcf(c_69810,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_17992]) ).

tcf(c_69811,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_17991]) ).

tcf(c_69812,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk4,tl(sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_4036]) ).

tcf(c_69813,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk4,tl(sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3953]) ).

tcf(c_69814,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_15403]) ).

tcf(c_69815,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_15402]) ).

tcf(c_69816,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_15401]) ).

tcf(c_69817,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk4,tl(sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3951]) ).

tcf(c_69818,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),nil)) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3423]) ).

tcf(c_69819,plain,
    app(nil,app(nil,app(sk4,app(sk4,tl(sk4))))) = app(nil,app(sk4,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_69722,c_13452]) ).

tcf(c_69820,plain,
    app(app(nil,app(sk4,app(sk4,tl(sk4)))),nil) = app(nil,app(sk4,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_69722,c_12354]) ).

tcf(c_69821,plain,
    app(app(sk4,app(sk4,app(sk4,tl(sk4)))),nil) = app(sk4,app(sk4,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_69722,c_12353]) ).

tcf(c_69822,plain,
    app(app(sk3,app(sk4,app(sk4,tl(sk4)))),nil) = app(sk3,app(sk4,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_69722,c_12352]) ).

tcf(c_69823,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk4)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_69722,c_3199]) ).

tcf(c_69824,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(nil,tl(app(sk4,app(sk4,tl(sk4))))) = tl(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3066]) ).

tcf(c_69825,plain,
    app(nil,app(sk4,app(sk4,app(sk4,tl(sk4))))) = app(sk4,app(sk4,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_69722,c_8061]) ).

tcf(c_69826,plain,
    app(app(sk4,sk4),app(sk4,app(sk4,tl(sk4)))) = app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_69722,c_8048]) ).

tcf(c_69827,plain,
    app(nil,app(sk3,app(sk4,app(sk4,tl(sk4))))) = app(sk3,app(sk4,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_69722,c_5745]) ).

tcf(c_69828,plain,
    app(app(sk3,sk4),app(sk4,app(sk4,tl(sk4)))) = app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_69722,c_8047]) ).

tcf(c_69829,plain,
    app(app(sk4,sk3),app(sk4,app(sk4,tl(sk4)))) = app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_69722,c_5738]) ).

tcf(c_69830,plain,
    app(app(sk3,sk3),app(sk4,app(sk4,tl(sk4)))) = app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_69722,c_5737]) ).

tcf(c_69831,plain,
    app(tl(sk4),app(sk4,app(sk4,tl(sk4)))) = tl(app(sk4,app(sk4,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_69722,c_4136]) ).

tcf(c_69832,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,tl(sk4))),sk4)) = app(cons(X0,app(sk4,app(sk4,tl(sk4)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_4462]) ).

tcf(c_69833,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,tl(sk4))),sk3)) = app(cons(X0,app(sk4,app(sk4,tl(sk4)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_4461]) ).

tcf(c_69834,plain,
    app(tl(sk3),app(sk4,app(sk4,tl(sk4)))) = tl(app(sk3,app(sk4,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_69722,c_4284]) ).

tcf(c_69837,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk4,tl(sk4))))) = cons(X0,app(sk4,app(sk4,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3019]) ).

tcf(c_69838,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk4)))),sk4),nil) = cons(hd(app(sk4,app(sk4,tl(sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3452]) ).

tcf(c_69839,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk4)))),sk3),nil) = cons(hd(app(sk4,app(sk4,tl(sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3444]) ).

tcf(c_69840,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(tl(app(sk4,app(sk4,tl(sk4)))),nil) = tl(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3065]) ).

tcf(c_69841,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),sk4)) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3215]) ).

tcf(c_69842,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),sk3)) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_3207]) ).

tcf(c_69843,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk4,tl(sk4)))) = cons(X0,app(sk4,app(sk4,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_253]) ).

tcf(c_69844,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( cons(hd(app(sk4,app(sk4,tl(sk4)))),tl(app(sk4,app(sk4,tl(sk4))))) = app(sk4,app(sk4,tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_275]) ).

tcf(c_69845,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk4,tl(sk4)))),nil) = cons(X0,app(sk4,app(sk4,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_3018]) ).

tcf(c_69846,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk4)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_69722,c_3191]) ).

tcf(c_69847,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk4)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_69722,c_3183]) ).

tcf(c_69848,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,tl(sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_284]) ).

tcf(c_69849,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk4,tl(sk4))))) = app(sk4,app(sk4,tl(sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_69722,c_276]) ).

tcf(c_69850,plain,
    app(app(sk4,app(sk4,tl(sk4))),nil) = app(sk4,app(sk4,tl(sk4))),
    inference(superposition,[status(thm)],[c_69722,c_258]) ).

tcf(c_69851,plain,
    app(nil,app(sk4,app(sk4,tl(sk4)))) = app(sk4,app(sk4,tl(sk4))),
    inference(superposition,[status(thm)],[c_69722,c_257]) ).

tcf(c_69975,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk4))) = nil )
      | ( hd(app(app(sk4,app(sk4,tl(sk4))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_69741,c_39968]) ).

tcf(c_69987,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk4,tl(sk4))))) = app(sk4,app(sk4,tl(sk4))) ) ),
    inference(light_normalisation,[status(thm)],[c_69844,c_39968]) ).

tcf(c_70418,plain,
    ssList(app(sk3,app(sk4,tl(sk4)))),
    inference(global_subsumption_just,[status(thm)],[c_69341,c_247,c_246,c_42153,c_69341]) ).

tcf(c_70420,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk4,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_18773]) ).

tcf(c_70421,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk4,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_18497]) ).

tcf(c_70422,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk4,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_18185]) ).

tcf(c_70423,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk4,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_16330]) ).

tcf(c_70424,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk4,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_15966]) ).

tcf(c_70425,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk4,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_15593]) ).

tcf(c_70426,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,tl(sk4))),nil),X0) = app(app(sk3,app(sk4,tl(sk4))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_4541]) ).

tcf(c_70427,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk4,tl(sk4))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3154]) ).

tcf(c_70428,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk4,tl(sk4))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_4037]) ).

tcf(c_70429,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk4,tl(sk4))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3952]) ).

tcf(c_70430,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk4,tl(sk4))),X0)) = app(app(sk3,app(sk4,tl(sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3050]) ).

tcf(c_70431,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,tl(sk4))),X0),nil) = app(app(sk3,app(sk4,tl(sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3049]) ).

tcf(c_70432,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,tl(sk4))),sk4),X0) = app(app(sk3,app(sk4,tl(sk4))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_4540]) ).

tcf(c_70433,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,tl(sk4))),sk3),X0) = app(app(sk3,app(sk4,tl(sk4))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_4539]) ).

tcf(c_70434,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk4,tl(sk4)))),X0) = app(X1,app(app(sk3,app(sk4,tl(sk4))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_271]) ).

tcf(c_70435,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk4,tl(sk4))))) = app(cons(X1,X0),app(sk3,app(sk4,tl(sk4)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_266]) ).

tcf(c_70436,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk4))) = nil )
      | ( app(tl(app(sk3,app(sk4,tl(sk4)))),X0) = tl(app(app(sk3,app(sk4,tl(sk4))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_274]) ).

tcf(c_70437,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk4))) = nil )
      | ( hd(app(app(sk3,app(sk4,tl(sk4))),X0)) = hd(app(sk3,app(sk4,tl(sk4)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_283]) ).

tcf(c_70438,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk4)))),nil),nil) = cons(hd(app(sk3,app(sk4,tl(sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3653]) ).

tcf(c_70439,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk4)))),nil),sk4) = cons(hd(app(sk3,app(sk4,tl(sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3470]) ).

tcf(c_70440,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk4)))),nil),sk3) = cons(hd(app(sk3,app(sk4,tl(sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3460]) ).

tcf(c_70441,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk4,tl(sk4))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_70418,c_65079]) ).

tcf(c_70442,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk4,tl(sk4))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_70418,c_62769]) ).

tcf(c_70443,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk4)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_61402]) ).

tcf(c_70444,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk4)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_61324]) ).

tcf(c_70445,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk4))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk4,tl(sk4)))))) = tl(app(sk3,app(sk4,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3118]) ).

tcf(c_70446,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),app(sk4,sk4))) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_34548]) ).

tcf(c_70447,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),app(sk4,sk3))) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_34490]) ).

tcf(c_70448,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),app(sk3,sk4))) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_34149]) ).

tcf(c_70449,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),app(sk3,sk3))) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_34101]) ).

tcf(c_70450,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,tl(sk4)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_19899]) ).

tcf(c_70451,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,tl(sk4)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_19024]) ).

tcf(c_70452,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,tl(sk4)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_19014]) ).

tcf(c_70453,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_17999]) ).

tcf(c_70454,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_18774]) ).

tcf(c_70455,plain,
    hd(app(sk3,app(nil,app(nil,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_57010]) ).

tcf(c_70456,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_57009]) ).

tcf(c_70457,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_57008]) ).

tcf(c_70458,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk4,tl(sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_18772]) ).

tcf(c_70459,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_15409]) ).

tcf(c_70460,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_18498]) ).

tcf(c_70461,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_54564]) ).

tcf(c_70462,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_54563]) ).

tcf(c_70463,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_54562]) ).

tcf(c_70464,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,tl(sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_18496]) ).

tcf(c_70465,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_18186]) ).

tcf(c_70466,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_48819]) ).

tcf(c_70467,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_48818]) ).

tcf(c_70468,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_48817]) ).

tcf(c_70469,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,tl(sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_18184]) ).

tcf(c_70470,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,tl(sk4)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_17287]) ).

tcf(c_70471,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,tl(sk4)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_16680]) ).

tcf(c_70472,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,tl(sk4)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_16670]) ).

tcf(c_70473,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_16331]) ).

tcf(c_70474,plain,
    hd(app(sk4,app(nil,app(nil,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_45260]) ).

tcf(c_70475,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_45259]) ).

tcf(c_70476,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_45258]) ).

tcf(c_70477,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk4,tl(sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_16329]) ).

tcf(c_70478,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_15967]) ).

tcf(c_70479,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_40467]) ).

tcf(c_70480,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_40466]) ).

tcf(c_70481,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_40465]) ).

tcf(c_70482,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk4,tl(sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_15965]) ).

tcf(c_70483,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_15594]) ).

tcf(c_70484,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_37606]) ).

tcf(c_70485,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_37605]) ).

tcf(c_70486,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_37604]) ).

tcf(c_70487,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk4,tl(sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_15592]) ).

tcf(c_70488,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_18000]) ).

tcf(c_70489,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_17998]) ).

tcf(c_70490,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_17997]) ).

tcf(c_70491,plain,
    app(sk3,app(nil,app(sk3,app(sk4,tl(sk4))))) = app(sk3,app(sk3,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_70418,c_35790]) ).

tcf(c_70492,plain,
    app(sk4,app(nil,app(sk3,app(sk4,tl(sk4))))) = app(sk4,app(sk3,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_70418,c_35787]) ).

tcf(c_70493,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,tl(sk4))),nil)) = app(cons(X0,app(sk3,app(sk4,tl(sk4)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_4463]) ).

tcf(c_70494,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk4,tl(sk4)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3155]) ).

tcf(c_70495,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk4,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_33403]) ).

tcf(c_70496,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk4,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_33402]) ).

tcf(c_70497,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk4,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_33401]) ).

tcf(c_70498,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),tl(sk3))) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_32111]) ).

tcf(c_70499,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),tl(sk4))) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_32098]) ).

tcf(c_70500,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_15410]) ).

tcf(c_70501,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_15408]) ).

tcf(c_70502,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_15407]) ).

tcf(c_70503,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk4))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk4,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3153]) ).

tcf(c_70504,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk4,tl(sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_4038]) ).

tcf(c_70505,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_17993]) ).

tcf(c_70506,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_17992]) ).

tcf(c_70507,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_17991]) ).

tcf(c_70508,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk4,tl(sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_4036]) ).

tcf(c_70509,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk4,tl(sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3953]) ).

tcf(c_70510,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_15403]) ).

tcf(c_70511,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_15402]) ).

tcf(c_70512,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_15401]) ).

tcf(c_70513,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk4,tl(sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3951]) ).

tcf(c_70514,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),nil)) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3423]) ).

tcf(c_70515,plain,
    app(nil,app(nil,app(sk3,app(sk4,tl(sk4))))) = app(nil,app(sk3,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_70418,c_13452]) ).

tcf(c_70516,plain,
    app(app(nil,app(sk3,app(sk4,tl(sk4)))),nil) = app(nil,app(sk3,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_70418,c_12354]) ).

tcf(c_70517,plain,
    app(app(sk4,app(sk3,app(sk4,tl(sk4)))),nil) = app(sk4,app(sk3,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_70418,c_12353]) ).

tcf(c_70518,plain,
    app(app(sk3,app(sk3,app(sk4,tl(sk4)))),nil) = app(sk3,app(sk3,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_70418,c_12352]) ).

tcf(c_70519,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk4)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_70418,c_3199]) ).

tcf(c_70520,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(nil,tl(app(sk3,app(sk4,tl(sk4))))) = tl(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3066]) ).

tcf(c_70521,plain,
    app(nil,app(sk4,app(sk3,app(sk4,tl(sk4))))) = app(sk4,app(sk3,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_70418,c_8061]) ).

tcf(c_70522,plain,
    app(app(sk4,sk4),app(sk3,app(sk4,tl(sk4)))) = app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_70418,c_8048]) ).

tcf(c_70523,plain,
    app(nil,app(sk3,app(sk3,app(sk4,tl(sk4))))) = app(sk3,app(sk3,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_70418,c_5745]) ).

tcf(c_70524,plain,
    app(app(sk3,sk4),app(sk3,app(sk4,tl(sk4)))) = app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_70418,c_8047]) ).

tcf(c_70525,plain,
    app(app(sk4,sk3),app(sk3,app(sk4,tl(sk4)))) = app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_70418,c_5738]) ).

tcf(c_70526,plain,
    app(app(sk3,sk3),app(sk3,app(sk4,tl(sk4)))) = app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_70418,c_5737]) ).

tcf(c_70527,plain,
    app(tl(sk4),app(sk3,app(sk4,tl(sk4)))) = tl(app(sk4,app(sk3,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_70418,c_4136]) ).

tcf(c_70528,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,tl(sk4))),sk4)) = app(cons(X0,app(sk3,app(sk4,tl(sk4)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_4462]) ).

tcf(c_70529,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,tl(sk4))),sk3)) = app(cons(X0,app(sk3,app(sk4,tl(sk4)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_4461]) ).

tcf(c_70530,plain,
    app(tl(sk3),app(sk3,app(sk4,tl(sk4)))) = tl(app(sk3,app(sk3,app(sk4,tl(sk4))))),
    inference(superposition,[status(thm)],[c_70418,c_4284]) ).

tcf(c_70533,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk4,tl(sk4))))) = cons(X0,app(sk3,app(sk4,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3019]) ).

tcf(c_70534,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk4)))),sk4),nil) = cons(hd(app(sk3,app(sk4,tl(sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3452]) ).

tcf(c_70535,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk4)))),sk3),nil) = cons(hd(app(sk3,app(sk4,tl(sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3444]) ).

tcf(c_70536,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(tl(app(sk3,app(sk4,tl(sk4)))),nil) = tl(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3065]) ).

tcf(c_70537,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),sk4)) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3215]) ).

tcf(c_70538,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),sk3)) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_3207]) ).

tcf(c_70539,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk4,tl(sk4)))) = cons(X0,app(sk3,app(sk4,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_253]) ).

tcf(c_70540,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( cons(hd(app(sk3,app(sk4,tl(sk4)))),tl(app(sk3,app(sk4,tl(sk4))))) = app(sk3,app(sk4,tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_275]) ).

tcf(c_70541,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk4,tl(sk4)))),nil) = cons(X0,app(sk3,app(sk4,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_3018]) ).

tcf(c_70542,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk4)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_70418,c_3191]) ).

tcf(c_70543,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk4)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_70418,c_3183]) ).

tcf(c_70544,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,tl(sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_284]) ).

tcf(c_70545,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk4,tl(sk4))))) = app(sk3,app(sk4,tl(sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_70418,c_276]) ).

tcf(c_70546,plain,
    app(app(sk3,app(sk4,tl(sk4))),nil) = app(sk3,app(sk4,tl(sk4))),
    inference(superposition,[status(thm)],[c_70418,c_258]) ).

tcf(c_70547,plain,
    app(nil,app(sk3,app(sk4,tl(sk4)))) = app(sk3,app(sk4,tl(sk4))),
    inference(superposition,[status(thm)],[c_70418,c_257]) ).

tcf(c_70671,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk4))) = nil )
      | ( hd(app(app(sk3,app(sk4,tl(sk4))),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_70437,c_53363]) ).

tcf(c_70683,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk4,tl(sk4))))) = app(sk3,app(sk4,tl(sk4))) ) ),
    inference(light_normalisation,[status(thm)],[c_70540,c_53363]) ).

tcf(c_71362,plain,
    ssList(app(sk4,app(sk3,tl(sk4)))),
    inference(global_subsumption_just,[status(thm)],[c_69476,c_247,c_246,c_55093,c_69476]) ).

tcf(c_71364,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk3,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_18773]) ).

tcf(c_71365,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk3,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_18497]) ).

tcf(c_71366,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk3,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_18185]) ).

tcf(c_71367,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk3,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_16330]) ).

tcf(c_71368,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk3,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_15966]) ).

tcf(c_71369,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk3,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_15593]) ).

tcf(c_71370,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,tl(sk4))),nil),X0) = app(app(sk4,app(sk3,tl(sk4))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_4541]) ).

tcf(c_71371,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk3,tl(sk4))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3154]) ).

tcf(c_71372,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk3,tl(sk4))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_4037]) ).

tcf(c_71373,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk3,tl(sk4))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3952]) ).

tcf(c_71374,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk3,tl(sk4))),X0)) = app(app(sk4,app(sk3,tl(sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3050]) ).

tcf(c_71375,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,tl(sk4))),X0),nil) = app(app(sk4,app(sk3,tl(sk4))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3049]) ).

tcf(c_71376,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,tl(sk4))),sk4),X0) = app(app(sk4,app(sk3,tl(sk4))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_4540]) ).

tcf(c_71377,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,tl(sk4))),sk3),X0) = app(app(sk4,app(sk3,tl(sk4))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_4539]) ).

tcf(c_71378,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk3,tl(sk4)))),X0) = app(X1,app(app(sk4,app(sk3,tl(sk4))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_271]) ).

tcf(c_71379,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk3,tl(sk4))))) = app(cons(X1,X0),app(sk4,app(sk3,tl(sk4)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_266]) ).

tcf(c_71380,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk4))) = nil )
      | ( app(tl(app(sk4,app(sk3,tl(sk4)))),X0) = tl(app(app(sk4,app(sk3,tl(sk4))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_274]) ).

tcf(c_71381,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk4))) = nil )
      | ( hd(app(app(sk4,app(sk3,tl(sk4))),X0)) = hd(app(sk4,app(sk3,tl(sk4)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_283]) ).

tcf(c_71382,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk4)))),nil),nil) = cons(hd(app(sk4,app(sk3,tl(sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3653]) ).

tcf(c_71383,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk4)))),nil),sk4) = cons(hd(app(sk4,app(sk3,tl(sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3470]) ).

tcf(c_71384,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk4)))),nil),sk3) = cons(hd(app(sk4,app(sk3,tl(sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3460]) ).

tcf(c_71385,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk3,tl(sk4))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_71362,c_65079]) ).

tcf(c_71386,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk3,tl(sk4))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_71362,c_62769]) ).

tcf(c_71387,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk4)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_61402]) ).

tcf(c_71388,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk4)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_61324]) ).

tcf(c_71389,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk4))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk3,tl(sk4)))))) = tl(app(sk4,app(sk3,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3118]) ).

tcf(c_71390,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),app(sk4,sk4))) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_34548]) ).

tcf(c_71391,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),app(sk4,sk3))) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_34490]) ).

tcf(c_71392,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),app(sk3,sk4))) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_34149]) ).

tcf(c_71393,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),app(sk3,sk3))) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_34101]) ).

tcf(c_71394,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,tl(sk4)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_19899]) ).

tcf(c_71395,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,tl(sk4)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_19024]) ).

tcf(c_71396,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,tl(sk4)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_19014]) ).

tcf(c_71397,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk3,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_17999]) ).

tcf(c_71398,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_18774]) ).

tcf(c_71399,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_57010]) ).

tcf(c_71400,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_57009]) ).

tcf(c_71401,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_57008]) ).

tcf(c_71402,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk3,tl(sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_18772]) ).

tcf(c_71403,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk3,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_15409]) ).

tcf(c_71404,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_18498]) ).

tcf(c_71405,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_54564]) ).

tcf(c_71406,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_54563]) ).

tcf(c_71407,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_54562]) ).

tcf(c_71408,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk3,tl(sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_18496]) ).

tcf(c_71409,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_18186]) ).

tcf(c_71410,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_48819]) ).

tcf(c_71411,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_48818]) ).

tcf(c_71412,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_48817]) ).

tcf(c_71413,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk3,tl(sk4))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_18184]) ).

tcf(c_71414,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,tl(sk4)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_17287]) ).

tcf(c_71415,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,tl(sk4)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_16680]) ).

tcf(c_71416,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,tl(sk4)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_16670]) ).

tcf(c_71417,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_16331]) ).

tcf(c_71418,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_45260]) ).

tcf(c_71419,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_45259]) ).

tcf(c_71420,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_45258]) ).

tcf(c_71421,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk3,tl(sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_16329]) ).

tcf(c_71422,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_15967]) ).

tcf(c_71423,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_40467]) ).

tcf(c_71424,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_40466]) ).

tcf(c_71425,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_40465]) ).

tcf(c_71426,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk3,tl(sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_15965]) ).

tcf(c_71427,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_15594]) ).

tcf(c_71428,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_37606]) ).

tcf(c_71429,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_37605]) ).

tcf(c_71430,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_37604]) ).

tcf(c_71431,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk3,tl(sk4))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_15592]) ).

tcf(c_71432,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk3,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_18000]) ).

tcf(c_71433,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk3,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_17998]) ).

tcf(c_71434,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk3,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_17997]) ).

tcf(c_71435,plain,
    app(sk3,app(nil,app(sk4,app(sk3,tl(sk4))))) = app(sk3,app(sk4,app(sk3,tl(sk4)))),
    inference(superposition,[status(thm)],[c_71362,c_35790]) ).

tcf(c_71436,plain,
    app(sk4,app(nil,app(sk4,app(sk3,tl(sk4))))) = app(sk4,app(sk4,app(sk3,tl(sk4)))),
    inference(superposition,[status(thm)],[c_71362,c_35787]) ).

tcf(c_71437,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,tl(sk4))),nil)) = app(cons(X0,app(sk4,app(sk3,tl(sk4)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_4463]) ).

tcf(c_71438,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk3,tl(sk4)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3155]) ).

tcf(c_71439,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk3,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_33403]) ).

tcf(c_71440,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk3,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_33402]) ).

tcf(c_71441,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk3,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_33401]) ).

tcf(c_71442,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),tl(sk3))) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_32111]) ).

tcf(c_71443,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),tl(sk4))) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_32098]) ).

tcf(c_71444,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk3,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_15410]) ).

tcf(c_71445,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk3,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_15408]) ).

tcf(c_71446,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk3,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_15407]) ).

tcf(c_71447,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk4))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk3,tl(sk4)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3153]) ).

tcf(c_71448,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk3,tl(sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_4038]) ).

tcf(c_71449,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_17993]) ).

tcf(c_71450,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_17992]) ).

tcf(c_71451,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_17991]) ).

tcf(c_71452,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk3,tl(sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_4036]) ).

tcf(c_71453,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk3,tl(sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3953]) ).

tcf(c_71454,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_15403]) ).

tcf(c_71455,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_15402]) ).

tcf(c_71456,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_15401]) ).

tcf(c_71457,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk3,tl(sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3951]) ).

tcf(c_71458,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),nil)) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3423]) ).

tcf(c_71459,plain,
    app(nil,app(nil,app(sk4,app(sk3,tl(sk4))))) = app(nil,app(sk4,app(sk3,tl(sk4)))),
    inference(superposition,[status(thm)],[c_71362,c_13452]) ).

tcf(c_71460,plain,
    app(app(nil,app(sk4,app(sk3,tl(sk4)))),nil) = app(nil,app(sk4,app(sk3,tl(sk4)))),
    inference(superposition,[status(thm)],[c_71362,c_12354]) ).

tcf(c_71461,plain,
    app(app(sk4,app(sk4,app(sk3,tl(sk4)))),nil) = app(sk4,app(sk4,app(sk3,tl(sk4)))),
    inference(superposition,[status(thm)],[c_71362,c_12353]) ).

tcf(c_71462,plain,
    app(app(sk3,app(sk4,app(sk3,tl(sk4)))),nil) = app(sk3,app(sk4,app(sk3,tl(sk4)))),
    inference(superposition,[status(thm)],[c_71362,c_12352]) ).

tcf(c_71463,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk4)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_71362,c_3199]) ).

tcf(c_71464,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(nil,tl(app(sk4,app(sk3,tl(sk4))))) = tl(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3066]) ).

tcf(c_71465,plain,
    app(nil,app(sk4,app(sk4,app(sk3,tl(sk4))))) = app(sk4,app(sk4,app(sk3,tl(sk4)))),
    inference(superposition,[status(thm)],[c_71362,c_8061]) ).

tcf(c_71466,plain,
    app(app(sk4,sk4),app(sk4,app(sk3,tl(sk4)))) = app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4))))),
    inference(superposition,[status(thm)],[c_71362,c_8048]) ).

tcf(c_71467,plain,
    app(nil,app(sk3,app(sk4,app(sk3,tl(sk4))))) = app(sk3,app(sk4,app(sk3,tl(sk4)))),
    inference(superposition,[status(thm)],[c_71362,c_5745]) ).

tcf(c_71468,plain,
    app(app(sk3,sk4),app(sk4,app(sk3,tl(sk4)))) = app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4))))),
    inference(superposition,[status(thm)],[c_71362,c_8047]) ).

tcf(c_71469,plain,
    app(app(sk4,sk3),app(sk4,app(sk3,tl(sk4)))) = app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4))))),
    inference(superposition,[status(thm)],[c_71362,c_5738]) ).

tcf(c_71470,plain,
    app(app(sk3,sk3),app(sk4,app(sk3,tl(sk4)))) = app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4))))),
    inference(superposition,[status(thm)],[c_71362,c_5737]) ).

tcf(c_71471,plain,
    app(tl(sk4),app(sk4,app(sk3,tl(sk4)))) = tl(app(sk4,app(sk4,app(sk3,tl(sk4))))),
    inference(superposition,[status(thm)],[c_71362,c_4136]) ).

tcf(c_71472,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,tl(sk4))),sk4)) = app(cons(X0,app(sk4,app(sk3,tl(sk4)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_4462]) ).

tcf(c_71473,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,tl(sk4))),sk3)) = app(cons(X0,app(sk4,app(sk3,tl(sk4)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_4461]) ).

tcf(c_71474,plain,
    app(tl(sk3),app(sk4,app(sk3,tl(sk4)))) = tl(app(sk3,app(sk4,app(sk3,tl(sk4))))),
    inference(superposition,[status(thm)],[c_71362,c_4284]) ).

tcf(c_71477,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk3,tl(sk4))))) = cons(X0,app(sk4,app(sk3,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3019]) ).

tcf(c_71478,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk4)))),sk4),nil) = cons(hd(app(sk4,app(sk3,tl(sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3452]) ).

tcf(c_71479,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk4)))),sk3),nil) = cons(hd(app(sk4,app(sk3,tl(sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3444]) ).

tcf(c_71480,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(tl(app(sk4,app(sk3,tl(sk4)))),nil) = tl(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3065]) ).

tcf(c_71481,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),sk4)) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3215]) ).

tcf(c_71482,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),sk3)) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_3207]) ).

tcf(c_71483,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk3,tl(sk4)))) = cons(X0,app(sk4,app(sk3,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_253]) ).

tcf(c_71484,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( cons(hd(app(sk4,app(sk3,tl(sk4)))),tl(app(sk4,app(sk3,tl(sk4))))) = app(sk4,app(sk3,tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_275]) ).

tcf(c_71485,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk3,tl(sk4)))),nil) = cons(X0,app(sk4,app(sk3,tl(sk4)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_3018]) ).

tcf(c_71486,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk4)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_71362,c_3191]) ).

tcf(c_71487,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk4)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_71362,c_3183]) ).

tcf(c_71488,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,tl(sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_284]) ).

tcf(c_71489,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk3,tl(sk4))))) = app(sk4,app(sk3,tl(sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_71362,c_276]) ).

tcf(c_71490,plain,
    app(app(sk4,app(sk3,tl(sk4))),nil) = app(sk4,app(sk3,tl(sk4))),
    inference(superposition,[status(thm)],[c_71362,c_258]) ).

tcf(c_71491,plain,
    app(nil,app(sk4,app(sk3,tl(sk4)))) = app(sk4,app(sk3,tl(sk4))),
    inference(superposition,[status(thm)],[c_71362,c_257]) ).

tcf(c_71615,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk4))) = nil )
      | ( hd(app(app(sk4,app(sk3,tl(sk4))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_71381,c_37428]) ).

tcf(c_71627,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk3,tl(sk4))))) = app(sk4,app(sk3,tl(sk4))) ) ),
    inference(light_normalisation,[status(thm)],[c_71484,c_37428]) ).

tcf(c_72090,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk3,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18773]) ).

tcf(c_72091,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk3,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18497]) ).

tcf(c_72092,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk3,tl(sk4))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18185]) ).

tcf(c_72093,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk3,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_16330]) ).

tcf(c_72094,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk3,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15966]) ).

tcf(c_72095,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk3,tl(sk4))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15593]) ).

tcf(c_72096,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,tl(sk4))),nil),X0) = app(app(sk3,app(sk3,tl(sk4))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4541]) ).

tcf(c_72097,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk3,tl(sk4))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3154]) ).

tcf(c_72098,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk3,tl(sk4))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4037]) ).

tcf(c_72099,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk3,tl(sk4))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3952]) ).

tcf(c_72100,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk3,tl(sk4))),X0)) = app(app(sk3,app(sk3,tl(sk4))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3050]) ).

tcf(c_72101,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,tl(sk4))),X0),nil) = app(app(sk3,app(sk3,tl(sk4))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3049]) ).

tcf(c_72102,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,tl(sk4))),sk4),X0) = app(app(sk3,app(sk3,tl(sk4))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4540]) ).

tcf(c_72103,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,tl(sk4))),sk3),X0) = app(app(sk3,app(sk3,tl(sk4))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4539]) ).

tcf(c_72104,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk3,tl(sk4)))),X0) = app(X1,app(app(sk3,app(sk3,tl(sk4))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_271]) ).

tcf(c_72105,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk3,tl(sk4))))) = app(cons(X1,X0),app(sk3,app(sk3,tl(sk4)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_266]) ).

tcf(c_72106,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk4))) = nil )
      | ( app(tl(app(sk3,app(sk3,tl(sk4)))),X0) = tl(app(app(sk3,app(sk3,tl(sk4))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_274]) ).

tcf(c_72107,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk4))) = nil )
      | ( hd(app(app(sk3,app(sk3,tl(sk4))),X0)) = hd(app(sk3,app(sk3,tl(sk4)))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_283]) ).

tcf(c_72108,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk4)))),nil),nil) = cons(hd(app(sk3,app(sk3,tl(sk4)))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3653]) ).

tcf(c_72109,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk4)))),nil),sk4) = cons(hd(app(sk3,app(sk3,tl(sk4)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3470]) ).

tcf(c_72110,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk4)))),nil),sk3) = cons(hd(app(sk3,app(sk3,tl(sk4)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3460]) ).

tcf(c_72111,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk3,tl(sk4))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_65079]) ).

tcf(c_72112,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk3,tl(sk4))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_62769]) ).

tcf(c_72113,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk4)))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_61402]) ).

tcf(c_72114,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk4)))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_61324]) ).

tcf(c_72115,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk4))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk3,tl(sk4)))))) = tl(app(sk3,app(sk3,tl(sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3118]) ).

tcf(c_72116,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),app(sk4,sk4))) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_34548]) ).

tcf(c_72117,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),app(sk4,sk3))) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_34490]) ).

tcf(c_72118,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),app(sk3,sk4))) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_34149]) ).

tcf(c_72119,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),app(sk3,sk3))) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_34101]) ).

tcf(c_72120,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,tl(sk4)))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_19899]) ).

tcf(c_72121,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,tl(sk4)))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_19024]) ).

tcf(c_72122,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,tl(sk4)))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_19014]) ).

tcf(c_72123,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_17999]) ).

tcf(c_72124,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18774]) ).

tcf(c_72125,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_57010]) ).

tcf(c_72126,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_57009]) ).

tcf(c_72127,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_57008]) ).

tcf(c_72128,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18772]) ).

tcf(c_72129,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15409]) ).

tcf(c_72130,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18498]) ).

tcf(c_72131,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_54564]) ).

tcf(c_72132,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_54563]) ).

tcf(c_72133,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_54562]) ).

tcf(c_72134,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18496]) ).

tcf(c_72135,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18186]) ).

tcf(c_72136,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_48819]) ).

tcf(c_72137,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_48818]) ).

tcf(c_72138,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_48817]) ).

tcf(c_72139,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk3,tl(sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18184]) ).

tcf(c_72140,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,tl(sk4)))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_17287]) ).

tcf(c_72141,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,tl(sk4)))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_16680]) ).

tcf(c_72142,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,tl(sk4)))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_16670]) ).

tcf(c_72143,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_16331]) ).

tcf(c_72144,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_45260]) ).

tcf(c_72145,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_45259]) ).

tcf(c_72146,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_45258]) ).

tcf(c_72147,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_16329]) ).

tcf(c_72148,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15967]) ).

tcf(c_72149,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_40467]) ).

tcf(c_72150,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_40466]) ).

tcf(c_72151,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_40465]) ).

tcf(c_72152,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15965]) ).

tcf(c_72153,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15594]) ).

tcf(c_72154,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_37606]) ).

tcf(c_72155,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_37605]) ).

tcf(c_72156,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_37604]) ).

tcf(c_72157,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk3,tl(sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15592]) ).

tcf(c_72158,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_18000]) ).

tcf(c_72159,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_17998]) ).

tcf(c_72160,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_17997]) ).

tcf(c_72161,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk3,tl(sk4))))) = app(sk3,app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_35790]) ).

tcf(c_72162,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk3,tl(sk4))))) = app(sk4,app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_35787]) ).

tcf(c_72163,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,tl(sk4))),nil)) = app(cons(X0,app(sk3,app(sk3,tl(sk4)))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4463]) ).

tcf(c_72164,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk3,tl(sk4)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3155]) ).

tcf(c_72165,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk3,tl(sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_33403]) ).

tcf(c_72166,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk3,tl(sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_33402]) ).

tcf(c_72167,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk3,tl(sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_33401]) ).

tcf(c_72168,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),tl(sk3))) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_32111]) ).

tcf(c_72169,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),tl(sk4))) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_32098]) ).

tcf(c_72170,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15410]) ).

tcf(c_72171,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15408]) ).

tcf(c_72172,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15407]) ).

tcf(c_72173,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk4))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk3,tl(sk4)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3153]) ).

tcf(c_72174,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4038]) ).

tcf(c_72175,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_17993]) ).

tcf(c_72176,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_17992]) ).

tcf(c_72177,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_17991]) ).

tcf(c_72178,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4036]) ).

tcf(c_72179,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3953]) ).

tcf(c_72180,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15403]) ).

tcf(c_72181,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15402]) ).

tcf(c_72182,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_15401]) ).

tcf(c_72183,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3951]) ).

tcf(c_72184,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),nil)) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3423]) ).

tcf(c_72185,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk3,tl(sk4))))) = app(nil,app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_13452]) ).

tcf(c_72186,plain,
    ( ( app(app(nil,app(sk3,app(sk3,tl(sk4)))),nil) = app(nil,app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_12354]) ).

tcf(c_72187,plain,
    ( ( app(app(sk4,app(sk3,app(sk3,tl(sk4)))),nil) = app(sk4,app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_12353]) ).

tcf(c_72188,plain,
    ( ( app(app(sk3,app(sk3,app(sk3,tl(sk4)))),nil) = app(sk3,app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_12352]) ).

tcf(c_72189,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk4)))),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3199]) ).

tcf(c_72190,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(nil,tl(app(sk3,app(sk3,tl(sk4))))) = tl(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3066]) ).

tcf(c_72191,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk3,tl(sk4))))) = app(sk4,app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_8061]) ).

tcf(c_72192,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk3,tl(sk4)))) = app(sk4,app(sk4,app(sk3,app(sk3,tl(sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_8048]) ).

tcf(c_72193,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk3,tl(sk4))))) = app(sk3,app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_5745]) ).

tcf(c_72194,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk3,tl(sk4)))) = app(sk3,app(sk4,app(sk3,app(sk3,tl(sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_8047]) ).

tcf(c_72195,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk3,tl(sk4)))) = app(sk4,app(sk3,app(sk3,app(sk3,tl(sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_5738]) ).

tcf(c_72196,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk3,tl(sk4)))) = app(sk3,app(sk3,app(sk3,app(sk3,tl(sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_5737]) ).

tcf(c_72197,plain,
    ( ( app(tl(sk4),app(sk3,app(sk3,tl(sk4)))) = tl(app(sk4,app(sk3,app(sk3,tl(sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4136]) ).

tcf(c_72198,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,tl(sk4))),sk4)) = app(cons(X0,app(sk3,app(sk3,tl(sk4)))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4462]) ).

tcf(c_72199,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,tl(sk4))),sk3)) = app(cons(X0,app(sk3,app(sk3,tl(sk4)))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4461]) ).

tcf(c_72200,plain,
    ( ( app(tl(sk3),app(sk3,app(sk3,tl(sk4)))) = tl(app(sk3,app(sk3,app(sk3,tl(sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4284]) ).

tcf(c_72203,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk3,tl(sk4))))) = cons(X0,app(sk3,app(sk3,tl(sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3019]) ).

tcf(c_72204,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk4)))),sk4),nil) = cons(hd(app(sk3,app(sk3,tl(sk4)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3452]) ).

tcf(c_72205,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk4)))),sk3),nil) = cons(hd(app(sk3,app(sk3,tl(sk4)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3444]) ).

tcf(c_72206,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(tl(app(sk3,app(sk3,tl(sk4)))),nil) = tl(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3065]) ).

tcf(c_72207,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),sk4)) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3215]) ).

tcf(c_72208,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),sk3)) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3207]) ).

tcf(c_72209,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk3,tl(sk4)))) = cons(X0,app(sk3,app(sk3,tl(sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_253]) ).

tcf(c_72210,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( cons(hd(app(sk3,app(sk3,tl(sk4)))),tl(app(sk3,app(sk3,tl(sk4))))) = app(sk3,app(sk3,tl(sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_275]) ).

tcf(c_72211,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk3,tl(sk4)))),nil) = cons(X0,app(sk3,app(sk3,tl(sk4)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3018]) ).

tcf(c_72212,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk4)))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3191]) ).

tcf(c_72213,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk4)))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_3183]) ).

tcf(c_72214,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,tl(sk4))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_284]) ).

tcf(c_72215,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk3,tl(sk4))))) = app(sk3,app(sk3,tl(sk4))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_276]) ).

tcf(c_72216,plain,
    ( ( app(app(sk3,app(sk3,tl(sk4))),nil) = app(sk3,app(sk3,tl(sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_258]) ).

tcf(c_72217,plain,
    ( ( app(nil,app(sk3,app(sk3,tl(sk4)))) = app(sk3,app(sk3,tl(sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_257]) ).

tcf(c_72486,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk4))) = nil )
      | ( hd(app(app(sk3,app(sk3,tl(sk4))),X0)) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_72107,c_48433]) ).

tcf(c_72500,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk3,tl(sk4))))) = app(sk3,app(sk3,tl(sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_72210,c_48433]) ).

tcf(c_72733,plain,
    ssList(app(sk4,app(sk4,tl(sk3)))),
    inference(global_subsumption_just,[status(thm)],[c_69554,c_247,c_20236,c_69554]) ).

tcf(c_72735,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk4,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_18773]) ).

tcf(c_72736,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk4,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_18497]) ).

tcf(c_72737,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk4,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_18185]) ).

tcf(c_72738,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk4,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_16330]) ).

tcf(c_72739,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk4,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_15966]) ).

tcf(c_72740,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk4,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_15593]) ).

tcf(c_72741,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,tl(sk3))),nil),X0) = app(app(sk4,app(sk4,tl(sk3))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_4541]) ).

tcf(c_72742,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk4,tl(sk3))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3154]) ).

tcf(c_72743,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk4,tl(sk3))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_4037]) ).

tcf(c_72744,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk4,tl(sk3))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3952]) ).

tcf(c_72745,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk4,tl(sk3))),X0)) = app(app(sk4,app(sk4,tl(sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3050]) ).

tcf(c_72746,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,tl(sk3))),X0),nil) = app(app(sk4,app(sk4,tl(sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3049]) ).

tcf(c_72747,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,tl(sk3))),sk4),X0) = app(app(sk4,app(sk4,tl(sk3))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_4540]) ).

tcf(c_72748,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk4,tl(sk3))),sk3),X0) = app(app(sk4,app(sk4,tl(sk3))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_4539]) ).

tcf(c_72749,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk4,tl(sk3)))),X0) = app(X1,app(app(sk4,app(sk4,tl(sk3))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_271]) ).

tcf(c_72750,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk4,tl(sk3))))) = app(cons(X1,X0),app(sk4,app(sk4,tl(sk3)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_266]) ).

tcf(c_72751,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk3))) = nil )
      | ( app(tl(app(sk4,app(sk4,tl(sk3)))),X0) = tl(app(app(sk4,app(sk4,tl(sk3))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_274]) ).

tcf(c_72752,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk3))) = nil )
      | ( hd(app(app(sk4,app(sk4,tl(sk3))),X0)) = hd(app(sk4,app(sk4,tl(sk3)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_283]) ).

tcf(c_72753,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk3)))),nil),nil) = cons(hd(app(sk4,app(sk4,tl(sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3653]) ).

tcf(c_72754,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk3)))),nil),sk4) = cons(hd(app(sk4,app(sk4,tl(sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3470]) ).

tcf(c_72755,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk3)))),nil),sk3) = cons(hd(app(sk4,app(sk4,tl(sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3460]) ).

tcf(c_72756,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk4,tl(sk3))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_72733,c_65079]) ).

tcf(c_72757,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk4,tl(sk3))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_72733,c_62769]) ).

tcf(c_72758,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk3)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_61402]) ).

tcf(c_72759,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk3)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_61324]) ).

tcf(c_72760,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk3))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk4,tl(sk3)))))) = tl(app(sk4,app(sk4,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3118]) ).

tcf(c_72761,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),app(sk4,sk4))) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_34548]) ).

tcf(c_72762,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),app(sk4,sk3))) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_34490]) ).

tcf(c_72763,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),app(sk3,sk4))) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_34149]) ).

tcf(c_72764,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),app(sk3,sk3))) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_34101]) ).

tcf(c_72765,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,tl(sk3)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_19899]) ).

tcf(c_72766,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,tl(sk3)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_19024]) ).

tcf(c_72767,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk4,tl(sk3)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_19014]) ).

tcf(c_72768,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_17999]) ).

tcf(c_72769,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_18774]) ).

tcf(c_72770,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_57010]) ).

tcf(c_72771,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_57009]) ).

tcf(c_72772,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_57008]) ).

tcf(c_72773,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk4,tl(sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_18772]) ).

tcf(c_72774,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_15409]) ).

tcf(c_72775,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_18498]) ).

tcf(c_72776,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_54564]) ).

tcf(c_72777,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_54563]) ).

tcf(c_72778,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_54562]) ).

tcf(c_72779,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk4,tl(sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_18496]) ).

tcf(c_72780,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_18186]) ).

tcf(c_72781,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_48819]) ).

tcf(c_72782,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_48818]) ).

tcf(c_72783,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_48817]) ).

tcf(c_72784,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk4,tl(sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_18184]) ).

tcf(c_72785,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,tl(sk3)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_17287]) ).

tcf(c_72786,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,tl(sk3)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_16680]) ).

tcf(c_72787,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk4,tl(sk3)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_16670]) ).

tcf(c_72788,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_16331]) ).

tcf(c_72789,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_45260]) ).

tcf(c_72790,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_45259]) ).

tcf(c_72791,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_45258]) ).

tcf(c_72792,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk4,tl(sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_16329]) ).

tcf(c_72793,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_15967]) ).

tcf(c_72794,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_40467]) ).

tcf(c_72795,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_40466]) ).

tcf(c_72796,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_40465]) ).

tcf(c_72797,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk4,tl(sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_15965]) ).

tcf(c_72798,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_15594]) ).

tcf(c_72799,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_37606]) ).

tcf(c_72800,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_37605]) ).

tcf(c_72801,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_37604]) ).

tcf(c_72802,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk4,tl(sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_15592]) ).

tcf(c_72803,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_18000]) ).

tcf(c_72804,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_17998]) ).

tcf(c_72805,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_17997]) ).

tcf(c_72806,plain,
    app(sk3,app(nil,app(sk4,app(sk4,tl(sk3))))) = app(sk3,app(sk4,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_72733,c_35790]) ).

tcf(c_72807,plain,
    app(sk4,app(nil,app(sk4,app(sk4,tl(sk3))))) = app(sk4,app(sk4,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_72733,c_35787]) ).

tcf(c_72808,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,tl(sk3))),nil)) = app(cons(X0,app(sk4,app(sk4,tl(sk3)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_4463]) ).

tcf(c_72809,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk4,tl(sk3)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3155]) ).

tcf(c_72810,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk4,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_33403]) ).

tcf(c_72811,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk4,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_33402]) ).

tcf(c_72812,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk4,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_33401]) ).

tcf(c_72813,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),tl(sk3))) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_32111]) ).

tcf(c_72814,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),tl(sk4))) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_32098]) ).

tcf(c_72815,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_15410]) ).

tcf(c_72816,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_15408]) ).

tcf(c_72817,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_15407]) ).

tcf(c_72818,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk3))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk4,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3153]) ).

tcf(c_72819,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk4,tl(sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_4038]) ).

tcf(c_72820,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_17993]) ).

tcf(c_72821,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_17992]) ).

tcf(c_72822,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_17991]) ).

tcf(c_72823,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk4,tl(sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_4036]) ).

tcf(c_72824,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk4,tl(sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3953]) ).

tcf(c_72825,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_15403]) ).

tcf(c_72826,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_15402]) ).

tcf(c_72827,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_15401]) ).

tcf(c_72828,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk4,tl(sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3951]) ).

tcf(c_72829,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),nil)) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3423]) ).

tcf(c_72830,plain,
    app(nil,app(nil,app(sk4,app(sk4,tl(sk3))))) = app(nil,app(sk4,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_72733,c_13452]) ).

tcf(c_72831,plain,
    app(app(nil,app(sk4,app(sk4,tl(sk3)))),nil) = app(nil,app(sk4,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_72733,c_12354]) ).

tcf(c_72832,plain,
    app(app(sk4,app(sk4,app(sk4,tl(sk3)))),nil) = app(sk4,app(sk4,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_72733,c_12353]) ).

tcf(c_72833,plain,
    app(app(sk3,app(sk4,app(sk4,tl(sk3)))),nil) = app(sk3,app(sk4,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_72733,c_12352]) ).

tcf(c_72834,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk3)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_72733,c_3199]) ).

tcf(c_72835,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(nil,tl(app(sk4,app(sk4,tl(sk3))))) = tl(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3066]) ).

tcf(c_72836,plain,
    app(nil,app(sk4,app(sk4,app(sk4,tl(sk3))))) = app(sk4,app(sk4,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_72733,c_8061]) ).

tcf(c_72837,plain,
    app(app(sk4,sk4),app(sk4,app(sk4,tl(sk3)))) = app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_72733,c_8048]) ).

tcf(c_72838,plain,
    app(nil,app(sk3,app(sk4,app(sk4,tl(sk3))))) = app(sk3,app(sk4,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_72733,c_5745]) ).

tcf(c_72839,plain,
    app(app(sk3,sk4),app(sk4,app(sk4,tl(sk3)))) = app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_72733,c_8047]) ).

tcf(c_72840,plain,
    app(app(sk4,sk3),app(sk4,app(sk4,tl(sk3)))) = app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_72733,c_5738]) ).

tcf(c_72841,plain,
    app(app(sk3,sk3),app(sk4,app(sk4,tl(sk3)))) = app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_72733,c_5737]) ).

tcf(c_72842,plain,
    app(tl(sk4),app(sk4,app(sk4,tl(sk3)))) = tl(app(sk4,app(sk4,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_72733,c_4136]) ).

tcf(c_72843,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,tl(sk3))),sk4)) = app(cons(X0,app(sk4,app(sk4,tl(sk3)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_4462]) ).

tcf(c_72844,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk4,tl(sk3))),sk3)) = app(cons(X0,app(sk4,app(sk4,tl(sk3)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_4461]) ).

tcf(c_72845,plain,
    app(tl(sk3),app(sk4,app(sk4,tl(sk3)))) = tl(app(sk3,app(sk4,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_72733,c_4284]) ).

tcf(c_72848,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk4,tl(sk3))))) = cons(X0,app(sk4,app(sk4,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3019]) ).

tcf(c_72849,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk3)))),sk4),nil) = cons(hd(app(sk4,app(sk4,tl(sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3452]) ).

tcf(c_72850,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk4,tl(sk3)))),sk3),nil) = cons(hd(app(sk4,app(sk4,tl(sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3444]) ).

tcf(c_72851,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(tl(app(sk4,app(sk4,tl(sk3)))),nil) = tl(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3065]) ).

tcf(c_72852,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),sk4)) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3215]) ).

tcf(c_72853,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),sk3)) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_3207]) ).

tcf(c_72854,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk4,tl(sk3)))) = cons(X0,app(sk4,app(sk4,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_253]) ).

tcf(c_72855,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( cons(hd(app(sk4,app(sk4,tl(sk3)))),tl(app(sk4,app(sk4,tl(sk3))))) = app(sk4,app(sk4,tl(sk3))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_275]) ).

tcf(c_72856,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk4,tl(sk3)))),nil) = cons(X0,app(sk4,app(sk4,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_3018]) ).

tcf(c_72857,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk3)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_72733,c_3191]) ).

tcf(c_72858,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk4,tl(sk3)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_72733,c_3183]) ).

tcf(c_72859,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,tl(sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_284]) ).

tcf(c_72860,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk4,tl(sk3))))) = app(sk4,app(sk4,tl(sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_72733,c_276]) ).

tcf(c_72861,plain,
    app(app(sk4,app(sk4,tl(sk3))),nil) = app(sk4,app(sk4,tl(sk3))),
    inference(superposition,[status(thm)],[c_72733,c_258]) ).

tcf(c_72862,plain,
    app(nil,app(sk4,app(sk4,tl(sk3)))) = app(sk4,app(sk4,tl(sk3))),
    inference(superposition,[status(thm)],[c_72733,c_257]) ).

tcf(c_72986,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk3))) = nil )
      | ( hd(app(app(sk4,app(sk4,tl(sk3))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_72752,c_40142]) ).

tcf(c_72998,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk4,tl(sk3))))) = app(sk4,app(sk4,tl(sk3))) ) ),
    inference(light_normalisation,[status(thm)],[c_72855,c_40142]) ).

tcf(c_73351,plain,
    ssList(app(sk3,app(sk4,tl(sk3)))),
    inference(global_subsumption_just,[status(thm)],[c_69593,c_247,c_246,c_42153,c_69593]) ).

tcf(c_73353,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk4,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_18773]) ).

tcf(c_73354,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk4,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_18497]) ).

tcf(c_73355,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk4,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_18185]) ).

tcf(c_73356,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk4,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_16330]) ).

tcf(c_73357,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk4,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_15966]) ).

tcf(c_73358,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk4,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_15593]) ).

tcf(c_73359,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,tl(sk3))),nil),X0) = app(app(sk3,app(sk4,tl(sk3))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_4541]) ).

tcf(c_73360,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk4,tl(sk3))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3154]) ).

tcf(c_73361,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk4,tl(sk3))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_4037]) ).

tcf(c_73362,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk4,tl(sk3))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3952]) ).

tcf(c_73363,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk4,tl(sk3))),X0)) = app(app(sk3,app(sk4,tl(sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3050]) ).

tcf(c_73364,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,tl(sk3))),X0),nil) = app(app(sk3,app(sk4,tl(sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3049]) ).

tcf(c_73365,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,tl(sk3))),sk4),X0) = app(app(sk3,app(sk4,tl(sk3))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_4540]) ).

tcf(c_73366,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk4,tl(sk3))),sk3),X0) = app(app(sk3,app(sk4,tl(sk3))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_4539]) ).

tcf(c_73367,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk4,tl(sk3)))),X0) = app(X1,app(app(sk3,app(sk4,tl(sk3))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_271]) ).

tcf(c_73368,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk4,tl(sk3))))) = app(cons(X1,X0),app(sk3,app(sk4,tl(sk3)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_266]) ).

tcf(c_73369,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk3))) = nil )
      | ( app(tl(app(sk3,app(sk4,tl(sk3)))),X0) = tl(app(app(sk3,app(sk4,tl(sk3))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_274]) ).

tcf(c_73370,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk3))) = nil )
      | ( hd(app(app(sk3,app(sk4,tl(sk3))),X0)) = hd(app(sk3,app(sk4,tl(sk3)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_283]) ).

tcf(c_73371,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk3)))),nil),nil) = cons(hd(app(sk3,app(sk4,tl(sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3653]) ).

tcf(c_73372,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk3)))),nil),sk4) = cons(hd(app(sk3,app(sk4,tl(sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3470]) ).

tcf(c_73373,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk3)))),nil),sk3) = cons(hd(app(sk3,app(sk4,tl(sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3460]) ).

tcf(c_73374,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk4,tl(sk3))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_73351,c_65079]) ).

tcf(c_73375,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk4,tl(sk3))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_73351,c_62769]) ).

tcf(c_73376,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk3)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_61402]) ).

tcf(c_73377,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk3)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_61324]) ).

tcf(c_73378,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk3))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk4,tl(sk3)))))) = tl(app(sk3,app(sk4,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3118]) ).

tcf(c_73379,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),app(sk4,sk4))) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_34548]) ).

tcf(c_73380,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),app(sk4,sk3))) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_34490]) ).

tcf(c_73381,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),app(sk3,sk4))) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_34149]) ).

tcf(c_73382,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),app(sk3,sk3))) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_34101]) ).

tcf(c_73383,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,tl(sk3)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_19899]) ).

tcf(c_73384,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,tl(sk3)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_19024]) ).

tcf(c_73385,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk4,tl(sk3)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_19014]) ).

tcf(c_73386,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_17999]) ).

tcf(c_73387,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_18774]) ).

tcf(c_73388,plain,
    hd(app(sk3,app(nil,app(nil,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_57010]) ).

tcf(c_73389,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_57009]) ).

tcf(c_73390,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_57008]) ).

tcf(c_73391,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk4,tl(sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_18772]) ).

tcf(c_73392,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_15409]) ).

tcf(c_73393,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_18498]) ).

tcf(c_73394,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_54564]) ).

tcf(c_73395,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_54563]) ).

tcf(c_73396,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_54562]) ).

tcf(c_73397,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk4,tl(sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_18496]) ).

tcf(c_73398,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_18186]) ).

tcf(c_73399,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_48819]) ).

tcf(c_73400,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_48818]) ).

tcf(c_73401,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_48817]) ).

tcf(c_73402,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk4,tl(sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_18184]) ).

tcf(c_73403,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,tl(sk3)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_17287]) ).

tcf(c_73404,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,tl(sk3)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_16680]) ).

tcf(c_73405,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk4,tl(sk3)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_16670]) ).

tcf(c_73406,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_16331]) ).

tcf(c_73407,plain,
    hd(app(sk4,app(nil,app(nil,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_45260]) ).

tcf(c_73408,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_45259]) ).

tcf(c_73409,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_45258]) ).

tcf(c_73410,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk4,tl(sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_16329]) ).

tcf(c_73411,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_15967]) ).

tcf(c_73412,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_40467]) ).

tcf(c_73413,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_40466]) ).

tcf(c_73414,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_40465]) ).

tcf(c_73415,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk4,tl(sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_15965]) ).

tcf(c_73416,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_15594]) ).

tcf(c_73417,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_37606]) ).

tcf(c_73418,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_37605]) ).

tcf(c_73419,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_37604]) ).

tcf(c_73420,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk4,tl(sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_15592]) ).

tcf(c_73421,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_18000]) ).

tcf(c_73422,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_17998]) ).

tcf(c_73423,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_17997]) ).

tcf(c_73424,plain,
    app(sk3,app(nil,app(sk3,app(sk4,tl(sk3))))) = app(sk3,app(sk3,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73351,c_35790]) ).

tcf(c_73425,plain,
    app(sk4,app(nil,app(sk3,app(sk4,tl(sk3))))) = app(sk4,app(sk3,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73351,c_35787]) ).

tcf(c_73426,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,tl(sk3))),nil)) = app(cons(X0,app(sk3,app(sk4,tl(sk3)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_4463]) ).

tcf(c_73427,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk4,tl(sk3)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3155]) ).

tcf(c_73428,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk4,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_33403]) ).

tcf(c_73429,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk4,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_33402]) ).

tcf(c_73430,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk4,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_33401]) ).

tcf(c_73431,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),tl(sk3))) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_32111]) ).

tcf(c_73432,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),tl(sk4))) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_32098]) ).

tcf(c_73433,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_15410]) ).

tcf(c_73434,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_15408]) ).

tcf(c_73435,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_15407]) ).

tcf(c_73436,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk3))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk4,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3153]) ).

tcf(c_73437,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk4,tl(sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_4038]) ).

tcf(c_73438,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_17993]) ).

tcf(c_73439,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_17992]) ).

tcf(c_73440,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_17991]) ).

tcf(c_73441,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk4,tl(sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_4036]) ).

tcf(c_73442,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk4,tl(sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3953]) ).

tcf(c_73443,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_15403]) ).

tcf(c_73444,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_15402]) ).

tcf(c_73445,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_15401]) ).

tcf(c_73446,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk4,tl(sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3951]) ).

tcf(c_73447,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),nil)) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3423]) ).

tcf(c_73448,plain,
    app(nil,app(nil,app(sk3,app(sk4,tl(sk3))))) = app(nil,app(sk3,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73351,c_13452]) ).

tcf(c_73449,plain,
    app(app(nil,app(sk3,app(sk4,tl(sk3)))),nil) = app(nil,app(sk3,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73351,c_12354]) ).

tcf(c_73450,plain,
    app(app(sk4,app(sk3,app(sk4,tl(sk3)))),nil) = app(sk4,app(sk3,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73351,c_12353]) ).

tcf(c_73451,plain,
    app(app(sk3,app(sk3,app(sk4,tl(sk3)))),nil) = app(sk3,app(sk3,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73351,c_12352]) ).

tcf(c_73452,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk3)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_73351,c_3199]) ).

tcf(c_73453,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(nil,tl(app(sk3,app(sk4,tl(sk3))))) = tl(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3066]) ).

tcf(c_73454,plain,
    app(nil,app(sk4,app(sk3,app(sk4,tl(sk3))))) = app(sk4,app(sk3,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73351,c_8061]) ).

tcf(c_73455,plain,
    app(app(sk4,sk4),app(sk3,app(sk4,tl(sk3)))) = app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73351,c_8048]) ).

tcf(c_73456,plain,
    app(nil,app(sk3,app(sk3,app(sk4,tl(sk3))))) = app(sk3,app(sk3,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73351,c_5745]) ).

tcf(c_73457,plain,
    app(app(sk3,sk4),app(sk3,app(sk4,tl(sk3)))) = app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73351,c_8047]) ).

tcf(c_73458,plain,
    app(app(sk4,sk3),app(sk3,app(sk4,tl(sk3)))) = app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73351,c_5738]) ).

tcf(c_73459,plain,
    app(app(sk3,sk3),app(sk3,app(sk4,tl(sk3)))) = app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73351,c_5737]) ).

tcf(c_73460,plain,
    app(tl(sk4),app(sk3,app(sk4,tl(sk3)))) = tl(app(sk4,app(sk3,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73351,c_4136]) ).

tcf(c_73461,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,tl(sk3))),sk4)) = app(cons(X0,app(sk3,app(sk4,tl(sk3)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_4462]) ).

tcf(c_73462,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk4,tl(sk3))),sk3)) = app(cons(X0,app(sk3,app(sk4,tl(sk3)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_4461]) ).

tcf(c_73463,plain,
    app(tl(sk3),app(sk3,app(sk4,tl(sk3)))) = tl(app(sk3,app(sk3,app(sk4,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73351,c_4284]) ).

tcf(c_73466,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk4,tl(sk3))))) = cons(X0,app(sk3,app(sk4,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3019]) ).

tcf(c_73467,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk3)))),sk4),nil) = cons(hd(app(sk3,app(sk4,tl(sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3452]) ).

tcf(c_73468,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk4,tl(sk3)))),sk3),nil) = cons(hd(app(sk3,app(sk4,tl(sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3444]) ).

tcf(c_73469,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(tl(app(sk3,app(sk4,tl(sk3)))),nil) = tl(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3065]) ).

tcf(c_73470,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),sk4)) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3215]) ).

tcf(c_73471,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),sk3)) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_3207]) ).

tcf(c_73472,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk4,tl(sk3)))) = cons(X0,app(sk3,app(sk4,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_253]) ).

tcf(c_73473,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( cons(hd(app(sk3,app(sk4,tl(sk3)))),tl(app(sk3,app(sk4,tl(sk3))))) = app(sk3,app(sk4,tl(sk3))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_275]) ).

tcf(c_73474,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk4,tl(sk3)))),nil) = cons(X0,app(sk3,app(sk4,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_3018]) ).

tcf(c_73475,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk3)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_73351,c_3191]) ).

tcf(c_73476,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk4,tl(sk3)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_73351,c_3183]) ).

tcf(c_73477,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,tl(sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_284]) ).

tcf(c_73478,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk4,tl(sk3))))) = app(sk3,app(sk4,tl(sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73351,c_276]) ).

tcf(c_73479,plain,
    app(app(sk3,app(sk4,tl(sk3))),nil) = app(sk3,app(sk4,tl(sk3))),
    inference(superposition,[status(thm)],[c_73351,c_258]) ).

tcf(c_73480,plain,
    app(nil,app(sk3,app(sk4,tl(sk3)))) = app(sk3,app(sk4,tl(sk3))),
    inference(superposition,[status(thm)],[c_73351,c_257]) ).

tcf(c_73604,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk3))) = nil )
      | ( hd(app(app(sk3,app(sk4,tl(sk3))),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_73370,c_53652]) ).

tcf(c_73616,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk4,tl(sk3))))) = app(sk3,app(sk4,tl(sk3))) ) ),
    inference(light_normalisation,[status(thm)],[c_73473,c_53652]) ).

tcf(c_73885,plain,
    ssList(app(sk4,app(sk3,tl(sk3)))),
    inference(global_subsumption_just,[status(thm)],[c_69632,c_247,c_246,c_55093,c_69632]) ).

tcf(c_73887,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk4,app(sk3,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_18773]) ).

tcf(c_73888,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk4,app(sk3,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_18497]) ).

tcf(c_73889,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk4,app(sk3,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_18185]) ).

tcf(c_73890,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk4,app(sk3,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_16330]) ).

tcf(c_73891,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk4,app(sk3,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_15966]) ).

tcf(c_73892,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk4,app(sk3,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_15593]) ).

tcf(c_73893,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,tl(sk3))),nil),X0) = app(app(sk4,app(sk3,tl(sk3))),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_4541]) ).

tcf(c_73894,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk4,app(sk3,tl(sk3))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3154]) ).

tcf(c_73895,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk4,app(sk3,tl(sk3))),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_4037]) ).

tcf(c_73896,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk4,app(sk3,tl(sk3))),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3952]) ).

tcf(c_73897,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk4,app(sk3,tl(sk3))),X0)) = app(app(sk4,app(sk3,tl(sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3050]) ).

tcf(c_73898,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,tl(sk3))),X0),nil) = app(app(sk4,app(sk3,tl(sk3))),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3049]) ).

tcf(c_73899,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,tl(sk3))),sk4),X0) = app(app(sk4,app(sk3,tl(sk3))),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_4540]) ).

tcf(c_73900,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk4,app(sk3,tl(sk3))),sk3),X0) = app(app(sk4,app(sk3,tl(sk3))),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_4539]) ).

tcf(c_73901,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk4,app(sk3,tl(sk3)))),X0) = app(X1,app(app(sk4,app(sk3,tl(sk3))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_271]) ).

tcf(c_73902,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk4,app(sk3,tl(sk3))))) = app(cons(X1,X0),app(sk4,app(sk3,tl(sk3)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_266]) ).

tcf(c_73903,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk3))) = nil )
      | ( app(tl(app(sk4,app(sk3,tl(sk3)))),X0) = tl(app(app(sk4,app(sk3,tl(sk3))),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_274]) ).

tcf(c_73904,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk3))) = nil )
      | ( hd(app(app(sk4,app(sk3,tl(sk3))),X0)) = hd(app(sk4,app(sk3,tl(sk3)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_283]) ).

tcf(c_73905,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk3)))),nil),nil) = cons(hd(app(sk4,app(sk3,tl(sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3653]) ).

tcf(c_73906,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk3)))),nil),sk4) = cons(hd(app(sk4,app(sk3,tl(sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3470]) ).

tcf(c_73907,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk3)))),nil),sk3) = cons(hd(app(sk4,app(sk3,tl(sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3460]) ).

tcf(c_73908,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk4,app(sk3,tl(sk3))))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_73885,c_65079]) ).

tcf(c_73909,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk4,app(sk3,tl(sk3))))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_73885,c_62769]) ).

tcf(c_73910,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk3)))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_61402]) ).

tcf(c_73911,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk3)))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_61324]) ).

tcf(c_73912,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk3))) = nil )
      | ( tl(cons(X0,tl(app(sk4,app(sk3,tl(sk3)))))) = tl(app(sk4,app(sk3,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3118]) ).

tcf(c_73913,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),app(sk4,sk4))) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_34548]) ).

tcf(c_73914,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),app(sk4,sk3))) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_34490]) ).

tcf(c_73915,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),app(sk3,sk4))) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_34149]) ).

tcf(c_73916,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),app(sk3,sk3))) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_34101]) ).

tcf(c_73917,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,tl(sk3)))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_19899]) ).

tcf(c_73918,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,tl(sk3)))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_19024]) ).

tcf(c_73919,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk4,app(sk3,tl(sk3)))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_19014]) ).

tcf(c_73920,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),app(sk4,app(sk3,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_17999]) ).

tcf(c_73921,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_18774]) ).

tcf(c_73922,plain,
    hd(app(sk3,app(nil,app(nil,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_57010]) ).

tcf(c_73923,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_57009]) ).

tcf(c_73924,plain,
    hd(app(sk3,app(nil,app(sk3,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_57008]) ).

tcf(c_73925,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk4,app(sk3,tl(sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_18772]) ).

tcf(c_73926,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),app(sk4,app(sk3,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_15409]) ).

tcf(c_73927,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_18498]) ).

tcf(c_73928,plain,
    hd(app(sk3,app(sk4,app(nil,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_54564]) ).

tcf(c_73929,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_54563]) ).

tcf(c_73930,plain,
    hd(app(sk3,app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_54562]) ).

tcf(c_73931,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk4,app(sk3,tl(sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_18496]) ).

tcf(c_73932,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_18186]) ).

tcf(c_73933,plain,
    hd(app(sk3,app(sk3,app(nil,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_48819]) ).

tcf(c_73934,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_48818]) ).

tcf(c_73935,plain,
    hd(app(sk3,app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_48817]) ).

tcf(c_73936,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk4,app(sk3,tl(sk3))))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_18184]) ).

tcf(c_73937,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,tl(sk3)))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_17287]) ).

tcf(c_73938,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,tl(sk3)))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_16680]) ).

tcf(c_73939,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk4,app(sk3,tl(sk3)))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_16670]) ).

tcf(c_73940,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_16331]) ).

tcf(c_73941,plain,
    hd(app(sk4,app(nil,app(nil,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_45260]) ).

tcf(c_73942,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_45259]) ).

tcf(c_73943,plain,
    hd(app(sk4,app(nil,app(sk3,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_45258]) ).

tcf(c_73944,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk4,app(sk3,tl(sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_16329]) ).

tcf(c_73945,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_15967]) ).

tcf(c_73946,plain,
    hd(app(sk4,app(sk4,app(nil,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_40467]) ).

tcf(c_73947,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_40466]) ).

tcf(c_73948,plain,
    hd(app(sk4,app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_40465]) ).

tcf(c_73949,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk4,app(sk3,tl(sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_15965]) ).

tcf(c_73950,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_15594]) ).

tcf(c_73951,plain,
    hd(app(sk4,app(sk3,app(nil,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_37606]) ).

tcf(c_73952,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_37605]) ).

tcf(c_73953,plain,
    hd(app(sk4,app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_37604]) ).

tcf(c_73954,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk4,app(sk3,tl(sk3))))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_15592]) ).

tcf(c_73955,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),app(sk4,app(sk3,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_18000]) ).

tcf(c_73956,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),app(sk4,app(sk3,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_17998]) ).

tcf(c_73957,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),app(sk4,app(sk3,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_17997]) ).

tcf(c_73958,plain,
    app(sk3,app(nil,app(sk4,app(sk3,tl(sk3))))) = app(sk3,app(sk4,app(sk3,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73885,c_35790]) ).

tcf(c_73959,plain,
    app(sk4,app(nil,app(sk4,app(sk3,tl(sk3))))) = app(sk4,app(sk4,app(sk3,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73885,c_35787]) ).

tcf(c_73960,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,tl(sk3))),nil)) = app(cons(X0,app(sk4,app(sk3,tl(sk3)))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_4463]) ).

tcf(c_73961,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk4,app(sk3,tl(sk3)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3155]) ).

tcf(c_73962,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk4,app(sk3,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_33403]) ).

tcf(c_73963,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk4,app(sk3,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_33402]) ).

tcf(c_73964,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk4,app(sk3,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_33401]) ).

tcf(c_73965,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),tl(sk3))) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_32111]) ).

tcf(c_73966,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),tl(sk4))) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_32098]) ).

tcf(c_73967,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),app(sk4,app(sk3,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_15410]) ).

tcf(c_73968,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),app(sk4,app(sk3,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_15408]) ).

tcf(c_73969,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),app(sk4,app(sk3,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_15407]) ).

tcf(c_73970,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk3))) = nil )
      | ( hd(cons(X0,tl(app(sk4,app(sk3,tl(sk3)))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3153]) ).

tcf(c_73971,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk4,app(sk3,tl(sk3)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_4038]) ).

tcf(c_73972,plain,
    hd(app(sk3,app(nil,app(sk4,app(sk3,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_17993]) ).

tcf(c_73973,plain,
    hd(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_17992]) ).

tcf(c_73974,plain,
    hd(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_17991]) ).

tcf(c_73975,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,tl(app(sk4,app(sk3,tl(sk3)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_4036]) ).

tcf(c_73976,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk4,app(sk3,tl(sk3)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3953]) ).

tcf(c_73977,plain,
    hd(app(sk4,app(nil,app(sk4,app(sk3,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_15403]) ).

tcf(c_73978,plain,
    hd(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_15402]) ).

tcf(c_73979,plain,
    hd(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_15401]) ).

tcf(c_73980,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,tl(app(sk4,app(sk3,tl(sk3)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3951]) ).

tcf(c_73981,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),nil)) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3423]) ).

tcf(c_73982,plain,
    app(nil,app(nil,app(sk4,app(sk3,tl(sk3))))) = app(nil,app(sk4,app(sk3,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73885,c_13452]) ).

tcf(c_73983,plain,
    app(app(nil,app(sk4,app(sk3,tl(sk3)))),nil) = app(nil,app(sk4,app(sk3,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73885,c_12354]) ).

tcf(c_73984,plain,
    app(app(sk4,app(sk4,app(sk3,tl(sk3)))),nil) = app(sk4,app(sk4,app(sk3,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73885,c_12353]) ).

tcf(c_73985,plain,
    app(app(sk3,app(sk4,app(sk3,tl(sk3)))),nil) = app(sk3,app(sk4,app(sk3,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73885,c_12352]) ).

tcf(c_73986,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk3)))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_73885,c_3199]) ).

tcf(c_73987,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(nil,tl(app(sk4,app(sk3,tl(sk3))))) = tl(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3066]) ).

tcf(c_73988,plain,
    app(nil,app(sk4,app(sk4,app(sk3,tl(sk3))))) = app(sk4,app(sk4,app(sk3,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73885,c_8061]) ).

tcf(c_73989,plain,
    app(app(sk4,sk4),app(sk4,app(sk3,tl(sk3)))) = app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73885,c_8048]) ).

tcf(c_73990,plain,
    app(nil,app(sk3,app(sk4,app(sk3,tl(sk3))))) = app(sk3,app(sk4,app(sk3,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73885,c_5745]) ).

tcf(c_73991,plain,
    app(app(sk3,sk4),app(sk4,app(sk3,tl(sk3)))) = app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73885,c_8047]) ).

tcf(c_73992,plain,
    app(app(sk4,sk3),app(sk4,app(sk3,tl(sk3)))) = app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73885,c_5738]) ).

tcf(c_73993,plain,
    app(app(sk3,sk3),app(sk4,app(sk3,tl(sk3)))) = app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73885,c_5737]) ).

tcf(c_73994,plain,
    app(tl(sk4),app(sk4,app(sk3,tl(sk3)))) = tl(app(sk4,app(sk4,app(sk3,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73885,c_4136]) ).

tcf(c_73995,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,tl(sk3))),sk4)) = app(cons(X0,app(sk4,app(sk3,tl(sk3)))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_4462]) ).

tcf(c_73996,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk4,app(sk3,tl(sk3))),sk3)) = app(cons(X0,app(sk4,app(sk3,tl(sk3)))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_4461]) ).

tcf(c_73997,plain,
    app(tl(sk3),app(sk4,app(sk3,tl(sk3)))) = tl(app(sk3,app(sk4,app(sk3,tl(sk3))))),
    inference(superposition,[status(thm)],[c_73885,c_4284]) ).

tcf(c_74000,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk4,app(sk3,tl(sk3))))) = cons(X0,app(sk4,app(sk3,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3019]) ).

tcf(c_74001,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk3)))),sk4),nil) = cons(hd(app(sk4,app(sk3,tl(sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3452]) ).

tcf(c_74002,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk4,app(sk3,tl(sk3)))),sk3),nil) = cons(hd(app(sk4,app(sk3,tl(sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3444]) ).

tcf(c_74003,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(tl(app(sk4,app(sk3,tl(sk3)))),nil) = tl(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3065]) ).

tcf(c_74004,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),sk4)) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3215]) ).

tcf(c_74005,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),sk3)) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_3207]) ).

tcf(c_74006,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk4,app(sk3,tl(sk3)))) = cons(X0,app(sk4,app(sk3,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_253]) ).

tcf(c_74007,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( cons(hd(app(sk4,app(sk3,tl(sk3)))),tl(app(sk4,app(sk3,tl(sk3))))) = app(sk4,app(sk3,tl(sk3))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_275]) ).

tcf(c_74008,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk4,app(sk3,tl(sk3)))),nil) = cons(X0,app(sk4,app(sk3,tl(sk3)))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_3018]) ).

tcf(c_74009,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk3)))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_73885,c_3191]) ).

tcf(c_74010,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk4,app(sk3,tl(sk3)))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_73885,c_3183]) ).

tcf(c_74011,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,tl(sk3))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_284]) ).

tcf(c_74012,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk4,app(sk3,tl(sk3))))) = app(sk4,app(sk3,tl(sk3))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_73885,c_276]) ).

tcf(c_74013,plain,
    app(app(sk4,app(sk3,tl(sk3))),nil) = app(sk4,app(sk3,tl(sk3))),
    inference(superposition,[status(thm)],[c_73885,c_258]) ).

tcf(c_74014,plain,
    app(nil,app(sk4,app(sk3,tl(sk3)))) = app(sk4,app(sk3,tl(sk3))),
    inference(superposition,[status(thm)],[c_73885,c_257]) ).

tcf(c_74138,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk3))) = nil )
      | ( hd(app(app(sk4,app(sk3,tl(sk3))),X0)) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_73904,c_37579]) ).

tcf(c_74150,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( cons(hd(sk4),tl(app(sk4,app(sk3,tl(sk3))))) = app(sk4,app(sk3,tl(sk3))) ) ),
    inference(light_normalisation,[status(thm)],[c_74007,c_37579]) ).

tcf(c_74490,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(app(sk3,app(sk3,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18773]) ).

tcf(c_74491,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(app(sk3,app(sk3,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18497]) ).

tcf(c_74492,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(app(sk3,app(sk3,tl(sk3))),X0)))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18185]) ).

tcf(c_74493,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(app(sk3,app(sk3,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_16330]) ).

tcf(c_74494,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(app(sk3,app(sk3,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15966]) ).

tcf(c_74495,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(app(sk3,app(sk3,tl(sk3))),X0)))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15593]) ).

tcf(c_74496,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,tl(sk3))),nil),X0) = app(app(sk3,app(sk3,tl(sk3))),app(nil,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4541]) ).

tcf(c_74497,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(app(sk3,app(sk3,tl(sk3))),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3154]) ).

tcf(c_74498,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(app(sk3,app(sk3,tl(sk3))),X0))) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4037]) ).

tcf(c_74499,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(app(sk3,app(sk3,tl(sk3))),X0))) = hd(sk4) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3952]) ).

tcf(c_74500,plain,
    ! [X0: $i] :
      ( ( app(nil,app(app(sk3,app(sk3,tl(sk3))),X0)) = app(app(sk3,app(sk3,tl(sk3))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3050]) ).

tcf(c_74501,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,tl(sk3))),X0),nil) = app(app(sk3,app(sk3,tl(sk3))),X0) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3049]) ).

tcf(c_74502,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,tl(sk3))),sk4),X0) = app(app(sk3,app(sk3,tl(sk3))),app(sk4,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4540]) ).

tcf(c_74503,plain,
    ! [X0: $i] :
      ( ( app(app(app(sk3,app(sk3,tl(sk3))),sk3),X0) = app(app(sk3,app(sk3,tl(sk3))),app(sk3,X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4539]) ).

tcf(c_74504,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,app(sk3,app(sk3,tl(sk3)))),X0) = app(X1,app(app(sk3,app(sk3,tl(sk3))),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_271]) ).

tcf(c_74505,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,app(sk3,app(sk3,tl(sk3))))) = app(cons(X1,X0),app(sk3,app(sk3,tl(sk3)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_266]) ).

tcf(c_74506,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk3))) = nil )
      | ( app(tl(app(sk3,app(sk3,tl(sk3)))),X0) = tl(app(app(sk3,app(sk3,tl(sk3))),X0)) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_274]) ).

tcf(c_74507,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk3))) = nil )
      | ( hd(app(app(sk3,app(sk3,tl(sk3))),X0)) = hd(app(sk3,app(sk3,tl(sk3)))) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_283]) ).

tcf(c_74508,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk3)))),nil),nil) = cons(hd(app(sk3,app(sk3,tl(sk3)))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3653]) ).

tcf(c_74509,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk3)))),nil),sk4) = cons(hd(app(sk3,app(sk3,tl(sk3)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3470]) ).

tcf(c_74510,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk3)))),nil),sk3) = cons(hd(app(sk3,app(sk3,tl(sk3)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3460]) ).

tcf(c_74511,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),app(sk3,app(sk3,tl(sk3))))) = hd(tl(sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_65079]) ).

tcf(c_74512,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),app(sk3,app(sk3,tl(sk3))))) = hd(tl(sk4)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_62769]) ).

tcf(c_74513,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk3)))),tl(sk3))) = tl(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_61402]) ).

tcf(c_74514,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk3)))),tl(sk4))) = tl(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_61324]) ).

tcf(c_74515,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk3))) = nil )
      | ( tl(cons(X0,tl(app(sk3,app(sk3,tl(sk3)))))) = tl(app(sk3,app(sk3,tl(sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3118]) ).

tcf(c_74516,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),app(sk4,sk4))) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_34548]) ).

tcf(c_74517,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),app(sk4,sk3))) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_34490]) ).

tcf(c_74518,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),app(sk3,sk4))) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_34149]) ).

tcf(c_74519,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),app(sk3,sk3))) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_34101]) ).

tcf(c_74520,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,tl(sk3)))),nil))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_19899]) ).

tcf(c_74521,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,tl(sk3)))),sk4))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_19024]) ).

tcf(c_74522,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,cons(hd(app(sk3,app(sk3,tl(sk3)))),sk3))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_19014]) ).

tcf(c_74523,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk4),app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_17999]) ).

tcf(c_74524,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18774]) ).

tcf(c_74525,plain,
    ( ( hd(app(sk3,app(nil,app(nil,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_57010]) ).

tcf(c_74526,plain,
    ( ( hd(app(sk3,app(nil,app(sk4,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_57009]) ).

tcf(c_74527,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_57008]) ).

tcf(c_74528,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,app(nil,tl(app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18772]) ).

tcf(c_74529,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk4),app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15409]) ).

tcf(c_74530,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18498]) ).

tcf(c_74531,plain,
    ( ( hd(app(sk3,app(sk4,app(nil,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_54564]) ).

tcf(c_74532,plain,
    ( ( hd(app(sk3,app(sk4,app(sk4,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_54563]) ).

tcf(c_74533,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_54562]) ).

tcf(c_74534,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,app(sk4,tl(app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18496]) ).

tcf(c_74535,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18186]) ).

tcf(c_74536,plain,
    ( ( hd(app(sk3,app(sk3,app(nil,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_48819]) ).

tcf(c_74537,plain,
    ( ( hd(app(sk3,app(sk3,app(sk4,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_48818]) ).

tcf(c_74538,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_48817]) ).

tcf(c_74539,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,app(sk3,tl(app(sk3,app(sk3,tl(sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18184]) ).

tcf(c_74540,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,tl(sk3)))),nil))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_17287]) ).

tcf(c_74541,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,tl(sk3)))),sk4))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_16680]) ).

tcf(c_74542,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,cons(hd(app(sk3,app(sk3,tl(sk3)))),sk3))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_16670]) ).

tcf(c_74543,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_16331]) ).

tcf(c_74544,plain,
    ( ( hd(app(sk4,app(nil,app(nil,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_45260]) ).

tcf(c_74545,plain,
    ( ( hd(app(sk4,app(nil,app(sk4,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_45259]) ).

tcf(c_74546,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_45258]) ).

tcf(c_74547,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,app(nil,tl(app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_16329]) ).

tcf(c_74548,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15967]) ).

tcf(c_74549,plain,
    ( ( hd(app(sk4,app(sk4,app(nil,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_40467]) ).

tcf(c_74550,plain,
    ( ( hd(app(sk4,app(sk4,app(sk4,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_40466]) ).

tcf(c_74551,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_40465]) ).

tcf(c_74552,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,app(sk4,tl(app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15965]) ).

tcf(c_74553,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15594]) ).

tcf(c_74554,plain,
    ( ( hd(app(sk4,app(sk3,app(nil,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_37606]) ).

tcf(c_74555,plain,
    ( ( hd(app(sk4,app(sk3,app(sk4,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_37605]) ).

tcf(c_74556,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_37604]) ).

tcf(c_74557,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,app(sk3,tl(app(sk3,app(sk3,tl(sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15592]) ).

tcf(c_74558,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk4),app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_18000]) ).

tcf(c_74559,plain,
    ( ( hd(app(sk3,app(cons(hd(sk4),sk3),app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_17998]) ).

tcf(c_74560,plain,
    ( ( hd(app(sk3,app(cons(hd(sk3),sk3),app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_17997]) ).

tcf(c_74561,plain,
    ( ( app(sk3,app(nil,app(sk3,app(sk3,tl(sk3))))) = app(sk3,app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_35790]) ).

tcf(c_74562,plain,
    ( ( app(sk4,app(nil,app(sk3,app(sk3,tl(sk3))))) = app(sk4,app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_35787]) ).

tcf(c_74563,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,tl(sk3))),nil)) = app(cons(X0,app(sk3,app(sk3,tl(sk3)))),nil) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4463]) ).

tcf(c_74564,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,app(sk3,app(sk3,tl(sk3)))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3155]) ).

tcf(c_74565,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,app(sk3,app(sk3,tl(sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_33403]) ).

tcf(c_74566,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,app(sk3,app(sk3,tl(sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_33402]) ).

tcf(c_74567,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,app(sk3,tl(sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_33401]) ).

tcf(c_74568,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),tl(sk3))) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_32111]) ).

tcf(c_74569,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),tl(sk4))) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_32098]) ).

tcf(c_74570,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk4),app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15410]) ).

tcf(c_74571,plain,
    ( ( hd(app(sk4,app(cons(hd(sk4),sk3),app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15408]) ).

tcf(c_74572,plain,
    ( ( hd(app(sk4,app(cons(hd(sk3),sk3),app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15407]) ).

tcf(c_74573,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk3))) = nil )
      | ( hd(cons(X0,tl(app(sk3,app(sk3,tl(sk3)))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3153]) ).

tcf(c_74574,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4038]) ).

tcf(c_74575,plain,
    ( ( hd(app(sk3,app(nil,app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_17993]) ).

tcf(c_74576,plain,
    ( ( hd(app(sk3,app(sk4,app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_17992]) ).

tcf(c_74577,plain,
    ( ( hd(app(sk3,app(sk3,app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_17991]) ).

tcf(c_74578,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk3,tl(app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4036]) ).

tcf(c_74579,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3953]) ).

tcf(c_74580,plain,
    ( ( hd(app(sk4,app(nil,app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15403]) ).

tcf(c_74581,plain,
    ( ( hd(app(sk4,app(sk4,app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15402]) ).

tcf(c_74582,plain,
    ( ( hd(app(sk4,app(sk3,app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_15401]) ).

tcf(c_74583,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(app(sk4,tl(app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3951]) ).

tcf(c_74584,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),nil)) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3423]) ).

tcf(c_74585,plain,
    ( ( app(nil,app(nil,app(sk3,app(sk3,tl(sk3))))) = app(nil,app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_13452]) ).

tcf(c_74586,plain,
    ( ( app(app(nil,app(sk3,app(sk3,tl(sk3)))),nil) = app(nil,app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_12354]) ).

tcf(c_74587,plain,
    ( ( app(app(sk4,app(sk3,app(sk3,tl(sk3)))),nil) = app(sk4,app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_12353]) ).

tcf(c_74588,plain,
    ( ( app(app(sk3,app(sk3,app(sk3,tl(sk3)))),nil) = app(sk3,app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_12352]) ).

tcf(c_74589,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk3)))),nil)) = nil )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3199]) ).

tcf(c_74590,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(nil,tl(app(sk3,app(sk3,tl(sk3))))) = tl(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3066]) ).

tcf(c_74591,plain,
    ( ( app(nil,app(sk4,app(sk3,app(sk3,tl(sk3))))) = app(sk4,app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_8061]) ).

tcf(c_74592,plain,
    ( ( app(app(sk4,sk4),app(sk3,app(sk3,tl(sk3)))) = app(sk4,app(sk4,app(sk3,app(sk3,tl(sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_8048]) ).

tcf(c_74593,plain,
    ( ( app(nil,app(sk3,app(sk3,app(sk3,tl(sk3))))) = app(sk3,app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_5745]) ).

tcf(c_74594,plain,
    ( ( app(app(sk3,sk4),app(sk3,app(sk3,tl(sk3)))) = app(sk3,app(sk4,app(sk3,app(sk3,tl(sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_8047]) ).

tcf(c_74595,plain,
    ( ( app(app(sk4,sk3),app(sk3,app(sk3,tl(sk3)))) = app(sk4,app(sk3,app(sk3,app(sk3,tl(sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_5738]) ).

tcf(c_74596,plain,
    ( ( app(app(sk3,sk3),app(sk3,app(sk3,tl(sk3)))) = app(sk3,app(sk3,app(sk3,app(sk3,tl(sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_5737]) ).

tcf(c_74597,plain,
    ( ( app(tl(sk4),app(sk3,app(sk3,tl(sk3)))) = tl(app(sk4,app(sk3,app(sk3,tl(sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4136]) ).

tcf(c_74598,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,tl(sk3))),sk4)) = app(cons(X0,app(sk3,app(sk3,tl(sk3)))),sk4) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4462]) ).

tcf(c_74599,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(app(sk3,app(sk3,tl(sk3))),sk3)) = app(cons(X0,app(sk3,app(sk3,tl(sk3)))),sk3) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4461]) ).

tcf(c_74600,plain,
    ( ( app(tl(sk3),app(sk3,app(sk3,tl(sk3)))) = tl(app(sk3,app(sk3,app(sk3,tl(sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4284]) ).

tcf(c_74603,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,app(sk3,app(sk3,tl(sk3))))) = cons(X0,app(sk3,app(sk3,tl(sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3019]) ).

tcf(c_74604,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk3)))),sk4),nil) = cons(hd(app(sk3,app(sk3,tl(sk3)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3452]) ).

tcf(c_74605,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(cons(hd(app(sk3,app(sk3,tl(sk3)))),sk3),nil) = cons(hd(app(sk3,app(sk3,tl(sk3)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3444]) ).

tcf(c_74606,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(tl(app(sk3,app(sk3,tl(sk3)))),nil) = tl(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3065]) ).

tcf(c_74607,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),sk4)) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3215]) ).

tcf(c_74608,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),sk3)) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3207]) ).

tcf(c_74609,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),app(sk3,app(sk3,tl(sk3)))) = cons(X0,app(sk3,app(sk3,tl(sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_253]) ).

tcf(c_74610,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( cons(hd(app(sk3,app(sk3,tl(sk3)))),tl(app(sk3,app(sk3,tl(sk3))))) = app(sk3,app(sk3,tl(sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_275]) ).

tcf(c_74611,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,app(sk3,app(sk3,tl(sk3)))),nil) = cons(X0,app(sk3,app(sk3,tl(sk3)))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3018]) ).

tcf(c_74612,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk3)))),sk4)) = sk4 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3191]) ).

tcf(c_74613,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( tl(cons(hd(app(sk3,app(sk3,tl(sk3)))),sk3)) = sk3 )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_3183]) ).

tcf(c_74614,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,tl(sk3))))) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_284]) ).

tcf(c_74615,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,app(sk3,app(sk3,tl(sk3))))) = app(sk3,app(sk3,tl(sk3))) )
      | ~ ssItem(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_276]) ).

tcf(c_74616,plain,
    ( ( app(app(sk3,app(sk3,tl(sk3))),nil) = app(sk3,app(sk3,tl(sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_258]) ).

tcf(c_74617,plain,
    ( ( app(nil,app(sk3,app(sk3,tl(sk3)))) = app(sk3,app(sk3,tl(sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_257]) ).

tcf(c_74886,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk3,tl(sk3))) = nil )
      | ( hd(app(app(sk3,app(sk3,tl(sk3))),X0)) = hd(sk3) )
      | ~ ssList(X0)
      | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_74507,c_48789]) ).

tcf(c_74900,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( cons(hd(sk3),tl(app(sk3,app(sk3,tl(sk3))))) = app(sk3,app(sk3,tl(sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(light_normalisation,[status(thm)],[c_74610,c_48789]) ).

tcf(c_75451,plain,
    app(tl(sk3),app(nil,sk3)) = app(tl(sk3),sk3),
    inference(superposition,[status(thm)],[c_246,c_65316]) ).

tcf(c_75452,plain,
    app(tl(sk3),app(nil,sk4)) = app(tl(sk3),sk4),
    inference(superposition,[status(thm)],[c_247,c_65316]) ).

tcf(c_75453,plain,
    app(tl(sk3),app(nil,nil)) = app(tl(sk3),nil),
    inference(superposition,[status(thm)],[c_259,c_65316]) ).

tcf(c_75454,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(tl(sk3),app(nil,tl(X0))) = app(tl(sk3),tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_65316]) ).

tcf(c_75455,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(tl(sk3),app(nil,app(X1,X0))) = app(tl(sk3),app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_65316]) ).

tcf(c_75456,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(tl(sk3),app(nil,cons(X1,X0))) = app(tl(sk3),cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_65316]) ).

tcf(c_75457,plain,
    app(tl(sk3),app(nil,tl(sk4))) = app(tl(sk3),tl(sk4)),
    inference(superposition,[status(thm)],[c_62750,c_65316]) ).

tcf(c_75458,plain,
    app(tl(sk3),app(nil,cons(hd(sk3),sk3))) = app(tl(sk3),cons(hd(sk3),sk3)),
    inference(superposition,[status(thm)],[c_13784,c_65316]) ).

tcf(c_75459,plain,
    app(tl(sk3),app(nil,cons(hd(sk4),sk3))) = app(tl(sk3),cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4358,c_65316]) ).

tcf(c_75460,plain,
    app(tl(sk3),app(nil,cons(hd(sk3),sk4))) = app(tl(sk3),cons(hd(sk3),sk4)),
    inference(superposition,[status(thm)],[c_12796,c_65316]) ).

tcf(c_75461,plain,
    app(tl(sk3),app(nil,cons(hd(sk4),sk4))) = app(tl(sk3),cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4223,c_65316]) ).

tcf(c_75462,plain,
    app(tl(sk3),app(nil,tl(sk3))) = app(tl(sk3),tl(sk3)),
    inference(superposition,[status(thm)],[c_65060,c_65316]) ).

tcf(c_75463,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),app(nil,app(tl(sk3),sk3))) = app(tl(sk3),app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_65316]) ).

tcf(c_75464,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),app(nil,app(tl(sk3),sk4))) = app(tl(sk3),app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_65316]) ).

tcf(c_75465,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk3),app(nil,app(tl(sk4),sk3))) = app(tl(sk3),app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_65316]) ).

tcf(c_75466,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk3),app(nil,app(tl(sk4),sk4))) = app(tl(sk3),app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_65316]) ).

tcf(c_75467,plain,
    app(tl(sk3),app(nil,cons(hd(sk4),app(sk3,sk3)))) = app(tl(sk3),cons(hd(sk4),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_5886,c_65316]) ).

tcf(c_75468,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk3,sk3)))) = app(tl(sk3),app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_65316]) ).

tcf(c_75469,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk3,sk4)))) = app(tl(sk3),app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_65316]) ).

tcf(c_75470,plain,
    ( ( app(tl(sk3),app(nil,app(sk4,app(sk3,sk3)))) = app(tl(sk3),app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_65316]) ).

tcf(c_75471,plain,
    app(tl(sk3),app(nil,cons(hd(sk4),app(sk4,sk3)))) = app(tl(sk3),cons(hd(sk4),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_7540,c_65316]) ).

tcf(c_75472,plain,
    ( ( app(tl(sk3),app(nil,app(sk4,app(sk3,sk4)))) = app(tl(sk3),app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_65316]) ).

tcf(c_75473,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk4,sk3)))) = app(tl(sk3),app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_65316]) ).

tcf(c_75474,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk4,sk4)))) = app(tl(sk3),app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_65316]) ).

tcf(c_75475,plain,
    ( ( app(tl(sk3),app(nil,app(sk4,app(sk4,sk3)))) = app(tl(sk3),app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_65316]) ).

tcf(c_75476,plain,
    ( ( app(tl(sk3),app(nil,app(sk4,app(sk4,sk4)))) = app(tl(sk3),app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_65316]) ).

tcf(c_75477,plain,
    app(tl(sk3),app(nil,cons(hd(sk4),app(sk3,sk4)))) = app(tl(sk3),cons(hd(sk4),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_10188,c_65316]) ).

tcf(c_75478,plain,
    app(tl(sk3),app(nil,cons(hd(sk4),app(sk4,sk4)))) = app(tl(sk3),cons(hd(sk4),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_10606,c_65316]) ).

tcf(c_75479,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk3,cons(hd(sk4),sk3))))) = app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_65316]) ).

tcf(c_75480,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk3,cons(hd(sk4),sk4))))) = app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_65316]) ).

tcf(c_75481,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_65316]) ).

tcf(c_75482,plain,
    app(tl(sk3),app(nil,cons(hd(sk3),app(sk4,sk4)))) = app(tl(sk3),cons(hd(sk3),app(sk4,sk4))),
    inference(superposition,[status(thm)],[c_16922,c_65316]) ).

tcf(c_75483,plain,
    app(tl(sk3),app(nil,cons(hd(sk3),app(sk4,sk3)))) = app(tl(sk3),cons(hd(sk3),app(sk4,sk3))),
    inference(superposition,[status(thm)],[c_19123,c_65316]) ).

tcf(c_75484,plain,
    app(tl(sk3),app(nil,cons(hd(sk3),app(sk3,sk4)))) = app(tl(sk3),cons(hd(sk3),app(sk3,sk4))),
    inference(superposition,[status(thm)],[c_17697,c_65316]) ).

tcf(c_75485,plain,
    app(tl(sk3),app(nil,cons(hd(sk3),app(sk3,sk3)))) = app(tl(sk3),cons(hd(sk3),app(sk3,sk3))),
    inference(superposition,[status(thm)],[c_20483,c_65316]) ).

tcf(c_75486,plain,
    ( ( app(tl(sk3),app(nil,app(sk4,app(sk3,cons(hd(sk4),sk3))))) = app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_65316]) ).

tcf(c_75487,plain,
    ( ( app(tl(sk3),app(nil,app(sk4,app(sk3,cons(hd(sk4),sk4))))) = app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_65316]) ).

tcf(c_75488,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk4,cons(hd(sk4),sk3))))) = app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_50099,c_65316]) ).

tcf(c_75489,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk4,cons(hd(sk4),sk4))))) = app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_51167,c_65316]) ).

tcf(c_75490,plain,
    app(tl(sk3),app(nil,app(sk3,app(sk4,cons(hd(sk4),sk3))))) = app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))),
    inference(superposition,[status(thm)],[c_42609,c_65316]) ).

tcf(c_75491,plain,
    app(tl(sk3),app(nil,app(sk3,app(sk4,cons(hd(sk4),sk4))))) = app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))),
    inference(superposition,[status(thm)],[c_43441,c_65316]) ).

tcf(c_75492,plain,
    ( ( app(tl(sk3),app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_65316]) ).

tcf(c_75493,plain,
    ( ( app(tl(sk3),app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_65316]) ).

tcf(c_75494,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_64396,c_65316]) ).

tcf(c_75495,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_52696,c_65316]) ).

tcf(c_75496,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_53971,c_65316]) ).

tcf(c_75497,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_59405,c_65316]) ).

tcf(c_75498,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_65316]) ).

tcf(c_75499,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_65316]) ).

tcf(c_75500,plain,
    app(tl(sk3),app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),
    inference(superposition,[status(thm)],[c_44714,c_65316]) ).

tcf(c_75501,plain,
    app(tl(sk3),app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),
    inference(superposition,[status(thm)],[c_46613,c_65316]) ).

tcf(c_75502,plain,
    app(tl(sk3),app(nil,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),
    inference(superposition,[status(thm)],[c_61722,c_65316]) ).

tcf(c_75503,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk3,tl(sk4))))) = app(tl(sk3),app(sk4,app(sk3,tl(sk4)))),
    inference(superposition,[status(thm)],[c_71362,c_65316]) ).

tcf(c_75504,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk3,tl(sk3))))) = app(tl(sk3),app(sk4,app(sk3,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73885,c_65316]) ).

tcf(c_75505,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk4,tl(sk4))))) = app(tl(sk3),app(sk4,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_69722,c_65316]) ).

tcf(c_75506,plain,
    app(tl(sk3),app(nil,app(sk4,app(sk4,tl(sk3))))) = app(tl(sk3),app(sk4,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_72733,c_65316]) ).

tcf(c_75507,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk3,tl(sk4))))) = app(tl(sk3),app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_65316]) ).

tcf(c_75508,plain,
    ( ( app(tl(sk3),app(nil,app(sk3,app(sk3,tl(sk3))))) = app(tl(sk3),app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_65316]) ).

tcf(c_75509,plain,
    app(tl(sk3),app(nil,app(sk3,app(sk4,tl(sk4))))) = app(tl(sk3),app(sk3,app(sk4,tl(sk4)))),
    inference(superposition,[status(thm)],[c_70418,c_65316]) ).

tcf(c_75510,plain,
    app(tl(sk3),app(nil,app(sk3,app(sk4,tl(sk3))))) = app(tl(sk3),app(sk3,app(sk4,tl(sk3)))),
    inference(superposition,[status(thm)],[c_73351,c_65316]) ).

tcf(c_75802,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69810,c_280]) ).

tcf(c_75803,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69810,c_279]) ).

tcf(c_75819,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4)))))))
      | ( app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69811,c_280]) ).

tcf(c_75820,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4)))))))
      | ( app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69811,c_279]) ).

tcf(c_75836,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4)))))))
      | ( app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69815,c_280]) ).

tcf(c_75837,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4)))))))
      | ( app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69815,c_279]) ).

tcf(c_75853,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4)))))))
      | ( app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69816,c_280]) ).

tcf(c_75854,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4)))))))
      | ( app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69816,c_279]) ).

tcf(c_75870,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70506,c_280]) ).

tcf(c_75871,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70506,c_279]) ).

tcf(c_75887,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4)))))))
      | ( app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70507,c_280]) ).

tcf(c_75888,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4)))))))
      | ( app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70507,c_279]) ).

tcf(c_75904,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4)))))))
      | ( app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70511,c_280]) ).

tcf(c_75905,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4)))))))
      | ( app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70511,c_279]) ).

tcf(c_75920,plain,
    app(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3),nil) = cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3),
    inference(global_subsumption_just,[status(thm)],[c_10221,c_10190,c_10221]) ).

tcf(c_75927,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,app(sk4,tl(sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_69848]) ).

tcf(c_75928,plain,
    hd(cons(hd(sk4),app(sk4,app(sk4,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_69848]) ).

tcf(c_75929,plain,
    hd(cons(hd(sk3),app(sk4,app(sk4,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_69848]) ).

tcf(c_75937,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,app(sk4,tl(sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_70544]) ).

tcf(c_75938,plain,
    hd(cons(hd(sk4),app(sk3,app(sk4,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_70544]) ).

tcf(c_75939,plain,
    hd(cons(hd(sk3),app(sk3,app(sk4,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_70544]) ).

tcf(c_75947,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,app(sk3,tl(sk4))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_71488]) ).

tcf(c_75948,plain,
    hd(cons(hd(sk4),app(sk4,app(sk3,tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_71488]) ).

tcf(c_75949,plain,
    hd(cons(hd(sk3),app(sk4,app(sk3,tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_71488]) ).

tcf(c_75957,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,app(sk4,tl(sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_72859]) ).

tcf(c_75958,plain,
    hd(cons(hd(sk4),app(sk4,app(sk4,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_72859]) ).

tcf(c_75959,plain,
    hd(cons(hd(sk3),app(sk4,app(sk4,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_72859]) ).

tcf(c_75971,plain,
    hd(app(sk3,app(tl(sk4),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_62760]) ).

tcf(c_75973,plain,
    hd(app(sk3,app(tl(sk4),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_62760]) ).

tcf(c_75974,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(tl(sk4),tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_62760]) ).

tcf(c_75975,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(tl(sk4),app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_62760]) ).

tcf(c_75976,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(tl(sk4),cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_62760]) ).

tcf(c_75977,plain,
    hd(app(sk3,app(tl(sk4),tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_62760]) ).

tcf(c_75978,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_62760]) ).

tcf(c_75979,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_62760]) ).

tcf(c_75980,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_62760]) ).

tcf(c_75981,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_62760]) ).

tcf(c_75982,plain,
    hd(app(sk3,app(tl(sk4),tl(sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_62760]) ).

tcf(c_75983,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(tl(sk4),app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_62760]) ).

tcf(c_75984,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(tl(sk4),app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_62760]) ).

tcf(c_75985,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(tl(sk4),app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_62760]) ).

tcf(c_75986,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(tl(sk4),app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_62760]) ).

tcf(c_75987,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_62760]) ).

tcf(c_75988,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_62760]) ).

tcf(c_75989,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_62760]) ).

tcf(c_75990,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_62760]) ).

tcf(c_75991,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_62760]) ).

tcf(c_75992,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_62760]) ).

tcf(c_75993,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_62760]) ).

tcf(c_75994,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_62760]) ).

tcf(c_75995,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_62760]) ).

tcf(c_75996,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_62760]) ).

tcf(c_75997,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_62760]) ).

tcf(c_75998,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_62760]) ).

tcf(c_75999,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_62760]) ).

tcf(c_76000,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_62760]) ).

tcf(c_76001,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_62760]) ).

tcf(c_76002,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_62760]) ).

tcf(c_76003,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_62760]) ).

tcf(c_76004,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_62760]) ).

tcf(c_76005,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_62760]) ).

tcf(c_76006,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_62760]) ).

tcf(c_76007,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_62760]) ).

tcf(c_76008,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_62760]) ).

tcf(c_76009,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_62760]) ).

tcf(c_76010,plain,
    hd(app(sk3,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_62760]) ).

tcf(c_76011,plain,
    hd(app(sk3,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_62760]) ).

tcf(c_76012,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_62760]) ).

tcf(c_76013,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_62760]) ).

tcf(c_76014,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_62760]) ).

tcf(c_76015,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_62760]) ).

tcf(c_76016,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_62760]) ).

tcf(c_76017,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_62760]) ).

tcf(c_76018,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_62760]) ).

tcf(c_76019,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_62760]) ).

tcf(c_76020,plain,
    hd(app(sk3,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_62760]) ).

tcf(c_76021,plain,
    hd(app(sk3,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_62760]) ).

tcf(c_76022,plain,
    hd(app(sk3,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_62760]) ).

tcf(c_76023,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk3,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_62760]) ).

tcf(c_76024,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk3,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_62760]) ).

tcf(c_76025,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_62760]) ).

tcf(c_76026,plain,
    hd(app(sk3,app(tl(sk4),app(sk4,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_62760]) ).

tcf(c_76027,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_62760]) ).

tcf(c_76028,plain,
    ( ( hd(app(sk3,app(tl(sk4),app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_62760]) ).

tcf(c_76029,plain,
    hd(app(sk3,app(tl(sk4),app(sk3,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_62760]) ).

tcf(c_76030,plain,
    hd(app(sk3,app(tl(sk4),app(sk3,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_62760]) ).

tcf(c_76165,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),sk3))))
      | ( app(sk3,app(tl(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),sk3)))
      | ~ ssList(app(sk3,app(tl(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_75971,c_280]) ).

tcf(c_76166,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),sk3))))
      | ( app(sk3,app(tl(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),sk3)))
      | ~ ssList(app(sk3,app(tl(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_75971,c_279]) ).

tcf(c_76182,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),tl(sk4)))))
      | ( app(sk3,app(tl(sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),tl(sk4))))
      | ~ ssList(app(sk3,app(tl(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_75977,c_280]) ).

tcf(c_76183,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),tl(sk4)))))
      | ( app(sk3,app(tl(sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),tl(sk4))))
      | ~ ssList(app(sk3,app(tl(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_75977,c_279]) ).

tcf(c_76217,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_75978,c_280]) ).

tcf(c_76218,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_75978,c_279]) ).

tcf(c_76234,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_75979,c_280]) ).

tcf(c_76235,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_75979,c_279]) ).

tcf(c_76251,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_75981,c_280]) ).

tcf(c_76252,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_75981,c_279]) ).

tcf(c_76268,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70512,c_280]) ).

tcf(c_76269,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70512,c_279]) ).

tcf(c_76285,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71450,c_280]) ).

tcf(c_76286,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71450,c_279]) ).

tcf(c_76302,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4)))))))
      | ( app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71451,c_280]) ).

tcf(c_76303,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4)))))))
      | ( app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71451,c_279]) ).

tcf(c_76319,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4)))))))
      | ( app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71455,c_280]) ).

tcf(c_76320,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4)))))))
      | ( app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71455,c_279]) ).

tcf(c_76354,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4)))))))
      | ( app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71456,c_280]) ).

tcf(c_76355,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4)))))))
      | ( app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71456,c_279]) ).

tcf(c_76370,plain,
    app(tl(cons(hd(sk4),app(sk3,sk4))),nil) = tl(cons(hd(sk4),app(sk3,sk4))),
    inference(global_subsumption_just,[status(thm)],[c_10222,c_10190,c_10222]) ).

tcf(c_76380,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ( app(tl(cons(hd(sk4),app(sk3,sk4))),X0) != tl(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_76370,c_270]) ).

tcf(c_76381,plain,
    ! [X0: $i] :
      ( ( tl(cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ( tl(cons(hd(sk4),app(sk3,sk4))) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_76370,c_269]) ).

tcf(c_76382,plain,
    ! [X0: $i] :
      ( ( tl(cons(hd(sk4),app(sk3,sk4))) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ( tl(cons(hd(sk4),app(sk3,sk4))) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_76381,c_259]) ).

tcf(c_76387,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ( app(tl(cons(hd(sk4),app(sk3,sk4))),X0) != tl(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_76380,c_259]) ).

tcf(c_76397,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,app(sk4,tl(sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_73477]) ).

tcf(c_76398,plain,
    hd(cons(hd(sk4),app(sk3,app(sk4,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_73477]) ).

tcf(c_76399,plain,
    hd(cons(hd(sk3),app(sk3,app(sk4,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_73477]) ).

tcf(c_76407,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk4,app(sk3,tl(sk3))))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_74011]) ).

tcf(c_76408,plain,
    hd(cons(hd(sk4),app(sk4,app(sk3,tl(sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_74011]) ).

tcf(c_76409,plain,
    hd(cons(hd(sk3),app(sk4,app(sk3,tl(sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_74011]) ).

tcf(c_76421,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk4,tl(sk4))))
      | ( app(app(sk4,app(sk4,tl(sk4))),X0) != app(sk4,app(sk4,tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_69850,c_270]) ).

tcf(c_76422,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk4))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk4,tl(sk4))))
      | ( app(sk4,app(sk4,tl(sk4))) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_69850,c_269]) ).

tcf(c_76423,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk4))) = X0 )
      | ~ ssList(X0)
      | ( app(sk4,app(sk4,tl(sk4))) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_76422,c_259,c_69722]) ).

tcf(c_76427,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(app(sk4,app(sk4,tl(sk4))),X0) != app(sk4,app(sk4,tl(sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_76421,c_259,c_69722]) ).

tcf(c_76440,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk4))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk4,tl(sk4))))
      | ( app(sk4,app(sk4,tl(sk4))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_69851,c_270]) ).

tcf(c_76441,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk4,tl(sk4))))
      | ( app(X0,app(sk4,app(sk4,tl(sk4)))) != app(sk4,app(sk4,tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_69851,c_269]) ).

tcf(c_76442,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,app(sk4,app(sk4,tl(sk4)))) != app(sk4,app(sk4,tl(sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_76441,c_259,c_69722]) ).

tcf(c_76446,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk4))) = X0 )
      | ~ ssList(X0)
      | ( app(sk4,app(sk4,tl(sk4))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_76440,c_259,c_69722]) ).

tcf(c_76463,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),tl(sk3)))))
      | ( app(sk3,app(tl(sk4),tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),tl(sk3))))
      | ~ ssList(app(sk3,app(tl(sk4),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_75982,c_280]) ).

tcf(c_76464,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),tl(sk3)))))
      | ( app(sk3,app(tl(sk4),tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),tl(sk3))))
      | ~ ssList(app(sk3,app(tl(sk4),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_75982,c_279]) ).

tcf(c_76483,plain,
    hd(app(sk4,app(tl(sk4),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_62761]) ).

tcf(c_76484,plain,
    hd(app(sk4,app(tl(sk4),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_62761]) ).

tcf(c_76485,plain,
    hd(app(sk4,app(tl(sk4),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_62761]) ).

tcf(c_76486,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(tl(sk4),tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_62761]) ).

tcf(c_76487,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(tl(sk4),app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_62761]) ).

tcf(c_76488,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(tl(sk4),cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_62761]) ).

tcf(c_76489,plain,
    hd(app(sk4,app(tl(sk4),tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_62761]) ).

tcf(c_76490,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_62761]) ).

tcf(c_76491,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_62761]) ).

tcf(c_76492,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_62761]) ).

tcf(c_76493,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_62761]) ).

tcf(c_76494,plain,
    hd(app(sk4,app(tl(sk4),tl(sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_62761]) ).

tcf(c_76495,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(tl(sk4),app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_62761]) ).

tcf(c_76496,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(tl(sk4),app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_62761]) ).

tcf(c_76497,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(tl(sk4),app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_62761]) ).

tcf(c_76498,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(tl(sk4),app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_62761]) ).

tcf(c_76499,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_62761]) ).

tcf(c_76500,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_62761]) ).

tcf(c_76501,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_62761]) ).

tcf(c_76502,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_62761]) ).

tcf(c_76503,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_62761]) ).

tcf(c_76504,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_62761]) ).

tcf(c_76505,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_62761]) ).

tcf(c_76506,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_62761]) ).

tcf(c_76507,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_62761]) ).

tcf(c_76508,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_62761]) ).

tcf(c_76509,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_62761]) ).

tcf(c_76510,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_62761]) ).

tcf(c_76511,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_62761]) ).

tcf(c_76512,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_62761]) ).

tcf(c_76513,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_62761]) ).

tcf(c_76514,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_62761]) ).

tcf(c_76515,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_62761]) ).

tcf(c_76516,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_62761]) ).

tcf(c_76517,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_62761]) ).

tcf(c_76518,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_62761]) ).

tcf(c_76519,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_62761]) ).

tcf(c_76520,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_62761]) ).

tcf(c_76521,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_62761]) ).

tcf(c_76522,plain,
    hd(app(sk4,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_62761]) ).

tcf(c_76523,plain,
    hd(app(sk4,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_62761]) ).

tcf(c_76524,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_62761]) ).

tcf(c_76525,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_62761]) ).

tcf(c_76526,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_62761]) ).

tcf(c_76527,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_62761]) ).

tcf(c_76528,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_62761]) ).

tcf(c_76529,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_62761]) ).

tcf(c_76530,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_62761]) ).

tcf(c_76531,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_62761]) ).

tcf(c_76532,plain,
    hd(app(sk4,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_62761]) ).

tcf(c_76533,plain,
    hd(app(sk4,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_62761]) ).

tcf(c_76534,plain,
    hd(app(sk4,app(tl(sk4),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_62761]) ).

tcf(c_76535,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk3,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_62761]) ).

tcf(c_76536,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk3,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_62761]) ).

tcf(c_76537,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_62761]) ).

tcf(c_76538,plain,
    hd(app(sk4,app(tl(sk4),app(sk4,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_62761]) ).

tcf(c_76539,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_62761]) ).

tcf(c_76540,plain,
    ( ( hd(app(sk4,app(tl(sk4),app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_62761]) ).

tcf(c_76541,plain,
    hd(app(sk4,app(tl(sk4),app(sk3,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_62761]) ).

tcf(c_76542,plain,
    hd(app(sk4,app(tl(sk4),app(sk3,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_62761]) ).

tcf(c_77168,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),sk3))))
      | ( app(sk4,app(tl(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),sk3)))
      | ~ ssList(app(sk4,app(tl(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_76483,c_280]) ).

tcf(c_77169,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),sk3))))
      | ( app(sk4,app(tl(sk4),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),sk3)))
      | ~ ssList(app(sk4,app(tl(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_76483,c_279]) ).

tcf(c_77269,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),sk4))))
      | ( app(sk4,app(tl(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),sk4)))
      | ~ ssList(app(sk4,app(tl(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_76484,c_280]) ).

tcf(c_77270,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),sk4))))
      | ( app(sk4,app(tl(sk4),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),sk4)))
      | ~ ssList(app(sk4,app(tl(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_76484,c_279]) ).

tcf(c_77286,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_76490,c_280]) ).

tcf(c_77287,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),sk3)))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_76490,c_279]) ).

tcf(c_77303,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_76491,c_280]) ).

tcf(c_77304,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),sk3)))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_76491,c_279]) ).

tcf(c_77338,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_76493,c_280]) ).

tcf(c_77339,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),sk4)))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_76493,c_279]) ).

tcf(c_77367,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3)))))))
      | ( app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72821,c_280]) ).

tcf(c_77368,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3)))))))
      | ( app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72821,c_279]) ).

tcf(c_77384,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3)))))))
      | ( app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72822,c_280]) ).

tcf(c_77385,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3)))))))
      | ( app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72822,c_279]) ).

tcf(c_77428,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3)))))))
      | ( app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72826,c_280]) ).

tcf(c_77429,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3)))))))
      | ( app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72826,c_279]) ).

tcf(c_77445,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3)))))))
      | ( app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72827,c_280]) ).

tcf(c_77446,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3)))))))
      | ( app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72827,c_279]) ).

tcf(c_77462,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3)))))))
      | ( app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73439,c_280]) ).

tcf(c_77463,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3)))))))
      | ( app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73439,c_279]) ).

tcf(c_77478,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4)) = hd(cons(hd(sk4),app(sk3,sk4))),
    inference(global_subsumption_just,[status(thm)],[c_10223,c_10190,c_10223]) ).

tcf(c_77489,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,app(sk4,tl(sk4))))
      | ( app(app(sk3,app(sk4,tl(sk4))),X0) != app(sk3,app(sk4,tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_70546,c_270]) ).

tcf(c_77490,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk4))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,app(sk4,tl(sk4))))
      | ( app(sk3,app(sk4,tl(sk4))) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_70546,c_269]) ).

tcf(c_77491,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk4))) = X0 )
      | ~ ssList(X0)
      | ( app(sk3,app(sk4,tl(sk4))) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77490,c_259,c_70418]) ).

tcf(c_77495,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(app(sk3,app(sk4,tl(sk4))),X0) != app(sk3,app(sk4,tl(sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77489,c_259,c_70418]) ).

tcf(c_77508,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk4))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,app(sk4,tl(sk4))))
      | ( app(sk3,app(sk4,tl(sk4))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_70547,c_270]) ).

tcf(c_77509,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,app(sk4,tl(sk4))))
      | ( app(X0,app(sk3,app(sk4,tl(sk4)))) != app(sk3,app(sk4,tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_70547,c_269]) ).

tcf(c_77510,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,app(sk3,app(sk4,tl(sk4)))) != app(sk3,app(sk4,tl(sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77509,c_259,c_70418]) ).

tcf(c_77514,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk4))) = X0 )
      | ~ ssList(X0)
      | ( app(sk3,app(sk4,tl(sk4))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77508,c_259,c_70418]) ).

tcf(c_77526,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk3,tl(sk4))))
      | ( app(app(sk4,app(sk3,tl(sk4))),X0) != app(sk4,app(sk3,tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_71490,c_270]) ).

tcf(c_77527,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk4))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk3,tl(sk4))))
      | ( app(sk4,app(sk3,tl(sk4))) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_71490,c_269]) ).

tcf(c_77528,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk4))) = X0 )
      | ~ ssList(X0)
      | ( app(sk4,app(sk3,tl(sk4))) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77527,c_259,c_71362]) ).

tcf(c_77532,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(app(sk4,app(sk3,tl(sk4))),X0) != app(sk4,app(sk3,tl(sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77526,c_259,c_71362]) ).

tcf(c_77545,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk4))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk3,tl(sk4))))
      | ( app(sk4,app(sk3,tl(sk4))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_71491,c_270]) ).

tcf(c_77546,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk3,tl(sk4))))
      | ( app(X0,app(sk4,app(sk3,tl(sk4)))) != app(sk4,app(sk3,tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_71491,c_269]) ).

tcf(c_77547,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,app(sk4,app(sk3,tl(sk4)))) != app(sk4,app(sk3,tl(sk4))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77546,c_259,c_71362]) ).

tcf(c_77551,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk4))) = X0 )
      | ~ ssList(X0)
      | ( app(sk4,app(sk3,tl(sk4))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77545,c_259,c_71362]) ).

tcf(c_77556,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),tl(sk4)))))
      | ( app(sk4,app(tl(sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),tl(sk4))))
      | ~ ssList(app(sk4,app(tl(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_76489,c_280]) ).

tcf(c_77557,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),tl(sk4)))))
      | ( app(sk4,app(tl(sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),tl(sk4))))
      | ~ ssList(app(sk4,app(tl(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_76489,c_279]) ).

tcf(c_77573,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),tl(sk3)))))
      | ( app(sk4,app(tl(sk4),tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),tl(sk3))))
      | ~ ssList(app(sk4,app(tl(sk4),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_76494,c_280]) ).

tcf(c_77574,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),tl(sk3)))))
      | ( app(sk4,app(tl(sk4),tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),tl(sk3))))
      | ~ ssList(app(sk4,app(tl(sk4),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_76494,c_279]) ).

tcf(c_77627,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk4),tl(sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk4),tl(sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62780,c_280]) ).

tcf(c_77628,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk4),tl(sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk3),sk4),tl(sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62780,c_279]) ).

tcf(c_77644,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk4),tl(sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk4),tl(sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62786,c_280]) ).

tcf(c_77645,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk4),tl(sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk3),sk4),tl(sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62786,c_279]) ).

tcf(c_77661,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3)))))))
      | ( app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73440,c_280]) ).

tcf(c_77662,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3)))))))
      | ( app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73440,c_279]) ).

tcf(c_77678,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3)))))))
      | ( app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73444,c_280]) ).

tcf(c_77679,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3)))))))
      | ( app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73444,c_279]) ).

tcf(c_77695,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73445,c_280]) ).

tcf(c_77696,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73445,c_279]) ).

tcf(c_77732,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3)))))))
      | ( app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73973,c_280]) ).

tcf(c_77733,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3)))))))
      | ( app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73973,c_279]) ).

tcf(c_77749,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3)))))))
      | ( app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73974,c_280]) ).

tcf(c_77750,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3)))))))
      | ( app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73974,c_279]) ).

tcf(c_77766,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3)))))))
      | ( app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73978,c_280]) ).

tcf(c_77767,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3)))))))
      | ( app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73978,c_279]) ).

tcf(c_77783,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3)))))))
      | ( app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73979,c_280]) ).

tcf(c_77784,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3)))))))
      | ( app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73979,c_279]) ).

tcf(c_77844,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_75987,c_280]) ).

tcf(c_77845,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_75987,c_279]) ).

tcf(c_77860,plain,
    hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3)) = hd(cons(hd(sk4),app(sk3,sk4))),
    inference(global_subsumption_just,[status(thm)],[c_10224,c_10190,c_10224]) ).

tcf(c_77871,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk4,tl(sk3))))
      | ( app(app(sk4,app(sk4,tl(sk3))),X0) != app(sk4,app(sk4,tl(sk3))) ) ),
    inference(superposition,[status(thm)],[c_72861,c_270]) ).

tcf(c_77872,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk4,tl(sk3))))
      | ( app(sk4,app(sk4,tl(sk3))) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_72861,c_269]) ).

tcf(c_77873,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk3))) = X0 )
      | ~ ssList(X0)
      | ( app(sk4,app(sk4,tl(sk3))) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77872,c_259,c_72733]) ).

tcf(c_77877,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(app(sk4,app(sk4,tl(sk3))),X0) != app(sk4,app(sk4,tl(sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77871,c_259,c_72733]) ).

tcf(c_77890,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk4,tl(sk3))))
      | ( app(sk4,app(sk4,tl(sk3))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_72862,c_270]) ).

tcf(c_77891,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk4,tl(sk3))))
      | ( app(X0,app(sk4,app(sk4,tl(sk3)))) != app(sk4,app(sk4,tl(sk3))) ) ),
    inference(superposition,[status(thm)],[c_72862,c_269]) ).

tcf(c_77892,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,app(sk4,app(sk4,tl(sk3)))) != app(sk4,app(sk4,tl(sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77891,c_259,c_72733]) ).

tcf(c_77896,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk4,tl(sk3))) = X0 )
      | ~ ssList(X0)
      | ( app(sk4,app(sk4,tl(sk3))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77890,c_259,c_72733]) ).

tcf(c_77908,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,app(sk4,tl(sk3))))
      | ( app(app(sk3,app(sk4,tl(sk3))),X0) != app(sk3,app(sk4,tl(sk3))) ) ),
    inference(superposition,[status(thm)],[c_73479,c_270]) ).

tcf(c_77909,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,app(sk4,tl(sk3))))
      | ( app(sk3,app(sk4,tl(sk3))) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_73479,c_269]) ).

tcf(c_77910,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk3))) = X0 )
      | ~ ssList(X0)
      | ( app(sk3,app(sk4,tl(sk3))) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77909,c_259,c_73351]) ).

tcf(c_77914,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(app(sk3,app(sk4,tl(sk3))),X0) != app(sk3,app(sk4,tl(sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77908,c_259,c_73351]) ).

tcf(c_77927,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,app(sk4,tl(sk3))))
      | ( app(sk3,app(sk4,tl(sk3))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_73480,c_270]) ).

tcf(c_77928,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk3,app(sk4,tl(sk3))))
      | ( app(X0,app(sk3,app(sk4,tl(sk3)))) != app(sk3,app(sk4,tl(sk3))) ) ),
    inference(superposition,[status(thm)],[c_73480,c_269]) ).

tcf(c_77929,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,app(sk3,app(sk4,tl(sk3)))) != app(sk3,app(sk4,tl(sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77928,c_259,c_73351]) ).

tcf(c_77933,plain,
    ! [X0: $i] :
      ( ( app(sk3,app(sk4,tl(sk3))) = X0 )
      | ~ ssList(X0)
      | ( app(sk3,app(sk4,tl(sk3))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_77927,c_259,c_73351]) ).

tcf(c_77938,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),tl(sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),tl(sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62815,c_280]) ).

tcf(c_77939,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk4),tl(sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk4),tl(sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62815,c_279]) ).

tcf(c_77955,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),tl(sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),tl(sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62816,c_280]) ).

tcf(c_77956,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk4),sk3),tl(sk4)))))
      | ( app(sk3,app(cons(hd(sk4),sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk4),sk3),tl(sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62816,c_279]) ).

tcf(c_78056,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),tl(sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),tl(sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62817,c_280]) ).

tcf(c_78057,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(cons(hd(sk3),sk3),tl(sk4)))))
      | ( app(sk3,app(cons(hd(sk3),sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(cons(hd(sk3),sk3),tl(sk4))))
      | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62817,c_279]) ).

tcf(c_78073,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),tl(sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),tl(sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62827,c_280]) ).

tcf(c_78074,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk4),tl(sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk4),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk4),tl(sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62827,c_279]) ).

tcf(c_78090,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_75991,c_280]) ).

tcf(c_78091,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_75991,c_279]) ).

tcf(c_78107,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_75997,c_280]) ).

tcf(c_78108,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_75997,c_279]) ).

tcf(c_78124,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_75998,c_280]) ).

tcf(c_78125,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_75998,c_279]) ).

tcf(c_78165,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_76002,c_280]) ).

tcf(c_78166,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_76002,c_279]) ).

tcf(c_78182,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_76003,c_280]) ).

tcf(c_78183,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_76003,c_279]) ).

tcf(c_78199,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_76004,c_280]) ).

tcf(c_78200,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_76004,c_279]) ).

tcf(c_78216,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_76005,c_280]) ).

tcf(c_78217,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_76005,c_279]) ).

tcf(c_78233,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_76499,c_280]) ).

tcf(c_78234,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_76499,c_279]) ).

tcf(c_78249,plain,
    cons(hd(cons(hd(sk4),app(sk3,sk4))),tl(cons(hd(sk4),app(sk3,sk4)))) = cons(hd(sk4),app(sk3,sk4)),
    inference(global_subsumption_just,[status(thm)],[c_10226,c_10190,c_10226]) ).

tcf(c_78251,plain,
    cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))) = cons(hd(sk4),app(sk3,sk4)),
    inference(light_normalisation,[status(thm)],[c_78249,c_34150]) ).

tcf(c_78255,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_52397]) ).

tcf(c_78257,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_50771]) ).

tcf(c_78259,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_44436]) ).

tcf(c_78261,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_43119]) ).

tcf(c_78263,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_23849]) ).

tcf(c_78265,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_22996]) ).

tcf(c_78267,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_12044]) ).

tcf(c_78269,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_11277]) ).

tcf(c_78270,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_12667]) ).

tcf(c_78271,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_12660]) ).

tcf(c_78272,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_12629]) ).

tcf(c_78273,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_12622]) ).

tcf(c_78276,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_6196]) ).

tcf(c_78277,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_6189]) ).

tcf(c_78281,plain,
    ( leq(hd(sk4),hd(tl(cons(hd(sk4),app(sk3,sk4)))))
    | ( tl(cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ ssItem(hd(sk4))
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4)))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_78251,c_281]) ).

tcf(c_78282,plain,
    ( totalorderedP(tl(cons(hd(sk4),app(sk3,sk4))))
    | ( tl(cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ ssItem(hd(sk4))
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4)))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_78251,c_301]) ).

tcf(c_78284,plain,
    ( ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ( tl(cons(hd(sk4),app(sk3,sk4))) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(superposition,[status(thm)],[c_78251,c_267]) ).

tcf(c_78286,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2)))
      | ~ totalorderedP(app(app(X0,cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4))))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_78251,c_300]) ).

tcf(c_78287,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2)))
      | ~ strictorderedP(app(app(X0,cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4))))),cons(X1,X2))) ),
    inference(superposition,[status(thm)],[c_78251,c_287]) ).

tcf(c_78288,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(sk4) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ( cons(hd(sk4),app(sk3,sk4)) != cons(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78251,c_265]) ).

tcf(c_78289,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(cons(hd(sk4),app(sk3,sk4))) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ( cons(hd(sk4),app(sk3,sk4)) != cons(X0,X1) ) ),
    inference(superposition,[status(thm)],[c_78251,c_264]) ).

tcf(c_78290,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4))))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_300]) ).

tcf(c_78291,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4))))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_78251,c_287]) ).

tcf(c_78292,plain,
    ( ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ( tl(cons(hd(sk4),app(sk3,sk4))) != cons(hd(sk4),app(sk3,sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78284,c_4059]) ).

tcf(c_78295,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(sk4) = X0 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ( cons(hd(sk4),app(sk3,sk4)) != cons(X0,X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78288,c_4059]) ).

tcf(c_78301,plain,
    ( totalorderedP(tl(cons(hd(sk4),app(sk3,sk4))))
    | ( tl(cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4)))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78282,c_4059]) ).

tcf(c_78306,plain,
    ! [X0: $i,X1: $i] :
      ( ( tl(cons(hd(sk4),app(sk3,sk4))) = X1 )
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ( cons(hd(sk4),app(sk3,sk4)) != cons(X0,X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78289,c_4059]) ).

tcf(c_78312,plain,
    ( leq(hd(sk4),hd(tl(cons(hd(sk4),app(sk3,sk4)))))
    | ( tl(cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4)))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78281,c_4059]) ).

tcf(c_78317,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78277,c_78251]) ).

tcf(c_78318,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk4),sk3),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78317,c_4059]) ).

tcf(c_78323,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78276,c_78251]) ).

tcf(c_78324,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk4),sk4),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78323,c_4059]) ).

tcf(c_78329,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78273,c_78251]) ).

tcf(c_78330,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78329,c_4059]) ).

tcf(c_78335,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78272,c_78251]) ).

tcf(c_78336,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ totalorderedP(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk4),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78335,c_4059]) ).

tcf(c_78341,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78271,c_78251]) ).

tcf(c_78342,plain,
    ( lt(hd(sk3),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78341,c_4059]) ).

tcf(c_78347,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78270,c_78251]) ).

tcf(c_78348,plain,
    ( leq(hd(sk3),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ totalorderedP(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(cons(hd(sk3),sk3),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78347,c_4059]) ).

tcf(c_78353,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78261,c_78251]) ).

tcf(c_78354,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78353,c_4059]) ).

tcf(c_78359,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78259,c_78251]) ).

tcf(c_78360,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78359,c_4059]) ).

tcf(c_78365,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78257,c_78251]) ).

tcf(c_78366,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78365,c_4059]) ).

tcf(c_78371,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78255,c_78251]) ).

tcf(c_78372,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk4,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78371,c_4059]) ).

tcf(c_78377,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78291,c_78251]) ).

tcf(c_78378,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78377,c_4059]) ).

tcf(c_78386,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78290,c_78251]) ).

tcf(c_78387,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(X1,hd(sk4))
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4))))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78386,c_4059]) ).

tcf(c_78395,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ strictorderedP(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2))) ),
    inference(light_normalisation,[status(thm)],[c_78287,c_78251]) ).

tcf(c_78396,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( lt(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ strictorderedP(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78395,c_4059]) ).

tcf(c_78404,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(hd(sk4))
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ totalorderedP(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2))) ),
    inference(light_normalisation,[status(thm)],[c_78286,c_78251]) ).

tcf(c_78405,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( leq(hd(sk4),X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
      | ~ totalorderedP(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2)))
      | ~ ssList(app(app(X0,cons(hd(sk4),app(sk3,sk4))),cons(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78404,c_4059]) ).

tcf(c_78413,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78269,c_78251]) ).

tcf(c_78414,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78413,c_4059]) ).

tcf(c_78420,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78267,c_78251]) ).

tcf(c_78421,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(app(sk3,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk3,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78420,c_4059]) ).

tcf(c_78427,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78265,c_78251]) ).

tcf(c_78428,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk3))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78427,c_4059]) ).

tcf(c_78434,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssItem(hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(light_normalisation,[status(thm)],[c_78263,c_78251]) ).

tcf(c_78435,plain,
    ( lt(hd(sk4),hd(sk4))
    | ~ ssList(app(sk4,sk3))
    | ~ ssList(tl(cons(hd(sk4),app(sk3,sk4))))
    | ~ strictorderedP(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(app(sk4,app(sk3,cons(hd(sk4),sk4))),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78434,c_4059]) ).

tcf(c_78479,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk3,tl(sk3))))
      | ( app(app(sk4,app(sk3,tl(sk3))),X0) != app(sk4,app(sk3,tl(sk3))) ) ),
    inference(superposition,[status(thm)],[c_74013,c_270]) ).

tcf(c_78480,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk3,tl(sk3))))
      | ( app(sk4,app(sk3,tl(sk3))) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_74013,c_269]) ).

tcf(c_78481,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk3))) = X0 )
      | ~ ssList(X0)
      | ( app(sk4,app(sk3,tl(sk3))) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78480,c_259,c_73885]) ).

tcf(c_78485,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(app(sk4,app(sk3,tl(sk3))),X0) != app(sk4,app(sk3,tl(sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78479,c_259,c_73885]) ).

tcf(c_78498,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk3))) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk3,tl(sk3))))
      | ( app(sk4,app(sk3,tl(sk3))) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_74014,c_270]) ).

tcf(c_78499,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sk4,app(sk3,tl(sk3))))
      | ( app(X0,app(sk4,app(sk3,tl(sk3)))) != app(sk4,app(sk3,tl(sk3))) ) ),
    inference(superposition,[status(thm)],[c_74014,c_269]) ).

tcf(c_78500,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,app(sk4,app(sk3,tl(sk3)))) != app(sk4,app(sk3,tl(sk3))) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78499,c_259,c_73885]) ).

tcf(c_78504,plain,
    ! [X0: $i] :
      ( ( app(sk4,app(sk3,tl(sk3))) = X0 )
      | ~ ssList(X0)
      | ( app(sk4,app(sk3,tl(sk3))) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_78498,c_259,c_73885]) ).

tcf(c_78520,plain,
    ( totalorderedP(tl(sk4))
    | ( tl(sk4) = nil )
    | ~ totalorderedP(sk4) ),
    inference(global_subsumption_just,[status(thm)],[c_3859,c_40989]) ).

tcf(c_78537,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(nil,cons(hd(tl(X0)),sk3)) = cons(hd(tl(X0)),sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4014]) ).

tcf(c_78538,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(nil,cons(hd(app(X1,X0)),sk3)) = cons(hd(app(X1,X0)),sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4014]) ).

tcf(c_78539,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(nil,cons(hd(cons(X1,X0)),sk3)) = cons(hd(cons(X1,X0)),sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4014]) ).

tcf(c_78540,plain,
    ( ( tl(sk4) = nil )
    | ( app(nil,cons(hd(tl(sk4)),sk3)) = cons(hd(tl(sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_62750,c_4014]) ).

tcf(c_78541,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),sk3)),sk3)) = cons(hd(cons(hd(sk3),sk3)),sk3) ) ),
    inference(superposition,[status(thm)],[c_13784,c_4014]) ).

tcf(c_78542,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),sk3)),sk3)) = cons(hd(cons(hd(sk4),sk3)),sk3) ) ),
    inference(superposition,[status(thm)],[c_4358,c_4014]) ).

tcf(c_78543,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),sk4)),sk3)) = cons(hd(cons(hd(sk3),sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_12796,c_4014]) ).

tcf(c_78544,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),sk4)),sk3)) = cons(hd(cons(hd(sk4),sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_4223,c_4014]) ).

tcf(c_78545,plain,
    ( ( tl(sk3) = nil )
    | ( app(nil,cons(hd(tl(sk3)),sk3)) = cons(hd(tl(sk3)),sk3) ) ),
    inference(superposition,[status(thm)],[c_65060,c_4014]) ).

tcf(c_78546,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(nil,cons(hd(app(tl(sk3),sk3)),sk3)) = cons(hd(app(tl(sk3),sk3)),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4014]) ).

tcf(c_78547,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(nil,cons(hd(app(tl(sk3),sk4)),sk3)) = cons(hd(app(tl(sk3),sk4)),sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4014]) ).

tcf(c_78548,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(nil,cons(hd(app(tl(sk4),sk3)),sk3)) = cons(hd(app(tl(sk4),sk3)),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4014]) ).

tcf(c_78549,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(nil,cons(hd(app(tl(sk4),sk4)),sk3)) = cons(hd(app(tl(sk4),sk4)),sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_4014]) ).

tcf(c_78550,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3)) = cons(hd(cons(hd(sk4),app(sk3,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_5886,c_4014]) ).

tcf(c_78551,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,sk3))),sk3)) = cons(hd(app(sk3,app(sk3,sk3))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4014]) ).

tcf(c_78552,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,sk4))),sk3)) = cons(hd(app(sk3,app(sk3,sk4))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4014]) ).

tcf(c_78553,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,sk3))),sk3)) = cons(hd(app(sk4,app(sk3,sk3))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4014]) ).

tcf(c_78554,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3)) = cons(hd(cons(hd(sk4),app(sk4,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_7540,c_4014]) ).

tcf(c_78555,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,sk4))),sk3)) = cons(hd(app(sk4,app(sk3,sk4))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4014]) ).

tcf(c_78556,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,sk3))),sk3)) = cons(hd(app(sk3,app(sk4,sk3))),sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4014]) ).

tcf(c_78557,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,sk4))),sk3)) = cons(hd(app(sk3,app(sk4,sk4))),sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4014]) ).

tcf(c_78558,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,sk3))),sk3)) = cons(hd(app(sk4,app(sk4,sk3))),sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4014]) ).

tcf(c_78559,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,sk4))),sk3)) = cons(hd(app(sk4,app(sk4,sk4))),sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4014]) ).

tcf(c_78560,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3)) = cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_10188,c_4014]) ).

tcf(c_78561,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk4,sk4))),sk3)) = cons(hd(cons(hd(sk4),app(sk4,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_10606,c_4014]) ).

tcf(c_78562,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4014]) ).

tcf(c_78563,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4014]) ).

tcf(c_78564,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4014]) ).

tcf(c_78565,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk4,sk4))),sk3)) = cons(hd(cons(hd(sk3),app(sk4,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_16922,c_4014]) ).

tcf(c_78566,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk4,sk3))),sk3)) = cons(hd(cons(hd(sk3),app(sk4,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_19123,c_4014]) ).

tcf(c_78567,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk3,sk4))),sk3)) = cons(hd(cons(hd(sk3),app(sk3,sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_17697,c_4014]) ).

tcf(c_78568,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk3,sk3))),sk3)) = cons(hd(cons(hd(sk3),app(sk3,sk3))),sk3) ) ),
    inference(superposition,[status(thm)],[c_20483,c_4014]) ).

tcf(c_78569,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4014]) ).

tcf(c_78570,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4014]) ).

tcf(c_78571,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_50099,c_4014]) ).

tcf(c_78572,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_51167,c_4014]) ).

tcf(c_78573,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_42609,c_4014]) ).

tcf(c_78574,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_43441,c_4014]) ).

tcf(c_78575,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4014]) ).

tcf(c_78576,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4014]) ).

tcf(c_78577,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_64396,c_4014]) ).

tcf(c_78578,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_52696,c_4014]) ).

tcf(c_78579,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_53971,c_4014]) ).

tcf(c_78580,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_59405,c_4014]) ).

tcf(c_78581,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4014]) ).

tcf(c_78582,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4014]) ).

tcf(c_78583,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_44714,c_4014]) ).

tcf(c_78584,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_46613,c_4014]) ).

tcf(c_78585,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk3) ) ),
    inference(superposition,[status(thm)],[c_61722,c_4014]) ).

tcf(c_78586,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,tl(sk4)))),sk3)) = cons(hd(app(sk4,app(sk3,tl(sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_71362,c_4014]) ).

tcf(c_78587,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,tl(sk3)))),sk3)) = cons(hd(app(sk4,app(sk3,tl(sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_73885,c_4014]) ).

tcf(c_78588,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,tl(sk4)))),sk3)) = cons(hd(app(sk4,app(sk4,tl(sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_69722,c_4014]) ).

tcf(c_78589,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,tl(sk3)))),sk3)) = cons(hd(app(sk4,app(sk4,tl(sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_72733,c_4014]) ).

tcf(c_78590,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,tl(sk4)))),sk3)) = cons(hd(app(sk3,app(sk3,tl(sk4)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4014]) ).

tcf(c_78591,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,tl(sk3)))),sk3)) = cons(hd(app(sk3,app(sk3,tl(sk3)))),sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4014]) ).

tcf(c_78592,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,tl(sk4)))),sk3)) = cons(hd(app(sk3,app(sk4,tl(sk4)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_70418,c_4014]) ).

tcf(c_78593,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,tl(sk3)))),sk3)) = cons(hd(app(sk3,app(sk4,tl(sk3)))),sk3) ) ),
    inference(superposition,[status(thm)],[c_73351,c_4014]) ).

tcf(c_78783,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),tl(sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),tl(sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62828,c_280]) ).

tcf(c_78784,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk4),sk3),tl(sk4)))))
      | ( app(sk4,app(cons(hd(sk4),sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk4),sk3),tl(sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62828,c_279]) ).

tcf(c_78817,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),tl(sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),tl(sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62829,c_280]) ).

tcf(c_78818,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(cons(hd(sk3),sk3),tl(sk4)))))
      | ( app(sk4,app(cons(hd(sk3),sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(cons(hd(sk3),sk3),tl(sk4))))
      | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62829,c_279]) ).

tcf(c_78854,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,cons(hd(X0),tl(sk4)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_62831]) ).

tcf(c_78855,plain,
    hd(app(sk3,cons(hd(sk4),tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4059,c_62831]) ).

tcf(c_78856,plain,
    hd(app(sk3,cons(hd(sk3),tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_62831]) ).

tcf(c_78862,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,cons(hd(sk3),tl(sk4)))))
      | ( app(sk3,cons(hd(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,cons(hd(sk3),tl(sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_78856,c_280]) ).

tcf(c_78863,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,cons(hd(sk3),tl(sk4)))))
      | ( app(sk3,cons(hd(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,cons(hd(sk3),tl(sk4))))
      | ~ ssList(app(sk3,cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_78856,c_279]) ).

tcf(c_78896,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_76503,c_280]) ).

tcf(c_78897,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_76503,c_279]) ).

tcf(c_78961,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_76509,c_280]) ).

tcf(c_78962,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_76509,c_279]) ).

tcf(c_78978,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_76510,c_280]) ).

tcf(c_78979,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_76510,c_279]) ).

tcf(c_78995,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_76514,c_280]) ).

tcf(c_78996,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_76514,c_279]) ).

tcf(c_79012,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_76515,c_280]) ).

tcf(c_79013,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_76515,c_279]) ).

tcf(c_79029,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_76516,c_280]) ).

tcf(c_79030,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_76516,c_279]) ).

tcf(c_79046,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_76517,c_280]) ).

tcf(c_79047,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))))
      | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))))
      | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_76517,c_279]) ).

tcf(c_79063,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38020,c_280]) ).

tcf(c_79064,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38020,c_279]) ).

tcf(c_79079,plain,
    tl(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4)) = sk4,
    inference(global_subsumption_just,[status(thm)],[c_10228,c_10190,c_10228]) ).

tcf(c_79091,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(nil,cons(hd(tl(X0)),sk4)) = cons(hd(tl(X0)),sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4022]) ).

tcf(c_79092,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(nil,cons(hd(app(X1,X0)),sk4)) = cons(hd(app(X1,X0)),sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4022]) ).

tcf(c_79093,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(nil,cons(hd(cons(X1,X0)),sk4)) = cons(hd(cons(X1,X0)),sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4022]) ).

tcf(c_79094,plain,
    ( ( tl(sk4) = nil )
    | ( app(nil,cons(hd(tl(sk4)),sk4)) = cons(hd(tl(sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_62750,c_4022]) ).

tcf(c_79095,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),sk3)),sk4)) = cons(hd(cons(hd(sk3),sk3)),sk4) ) ),
    inference(superposition,[status(thm)],[c_13784,c_4022]) ).

tcf(c_79096,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),sk3)),sk4)) = cons(hd(cons(hd(sk4),sk3)),sk4) ) ),
    inference(superposition,[status(thm)],[c_4358,c_4022]) ).

tcf(c_79097,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),sk4)),sk4)) = cons(hd(cons(hd(sk3),sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_12796,c_4022]) ).

tcf(c_79098,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),sk4)),sk4)) = cons(hd(cons(hd(sk4),sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_4223,c_4022]) ).

tcf(c_79099,plain,
    ( ( tl(sk3) = nil )
    | ( app(nil,cons(hd(tl(sk3)),sk4)) = cons(hd(tl(sk3)),sk4) ) ),
    inference(superposition,[status(thm)],[c_65060,c_4022]) ).

tcf(c_79100,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(nil,cons(hd(app(tl(sk3),sk3)),sk4)) = cons(hd(app(tl(sk3),sk3)),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4022]) ).

tcf(c_79101,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(nil,cons(hd(app(tl(sk3),sk4)),sk4)) = cons(hd(app(tl(sk3),sk4)),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4022]) ).

tcf(c_79102,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(nil,cons(hd(app(tl(sk4),sk3)),sk4)) = cons(hd(app(tl(sk4),sk3)),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4022]) ).

tcf(c_79103,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(nil,cons(hd(app(tl(sk4),sk4)),sk4)) = cons(hd(app(tl(sk4),sk4)),sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_4022]) ).

tcf(c_79104,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4)) = cons(hd(cons(hd(sk4),app(sk3,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_5886,c_4022]) ).

tcf(c_79105,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,sk3))),sk4)) = cons(hd(app(sk3,app(sk3,sk3))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4022]) ).

tcf(c_79106,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,sk4))),sk4)) = cons(hd(app(sk3,app(sk3,sk4))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4022]) ).

tcf(c_79107,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,sk3))),sk4)) = cons(hd(app(sk4,app(sk3,sk3))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4022]) ).

tcf(c_79108,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4)) = cons(hd(cons(hd(sk4),app(sk4,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_7540,c_4022]) ).

tcf(c_79109,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,sk4))),sk4)) = cons(hd(app(sk4,app(sk3,sk4))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4022]) ).

tcf(c_79110,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,sk3))),sk4)) = cons(hd(app(sk3,app(sk4,sk3))),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4022]) ).

tcf(c_79111,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,sk4))),sk4)) = cons(hd(app(sk3,app(sk4,sk4))),sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4022]) ).

tcf(c_79112,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,sk3))),sk4)) = cons(hd(app(sk4,app(sk4,sk3))),sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4022]) ).

tcf(c_79113,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,sk4))),sk4)) = cons(hd(app(sk4,app(sk4,sk4))),sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4022]) ).

tcf(c_79114,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4)) = cons(hd(cons(hd(sk4),app(sk3,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_10188,c_4022]) ).

tcf(c_79115,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk4,sk4))),sk4)) = cons(hd(cons(hd(sk4),app(sk4,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_10606,c_4022]) ).

tcf(c_79116,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4022]) ).

tcf(c_79117,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4022]) ).

tcf(c_79118,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4022]) ).

tcf(c_79119,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk4,sk4))),sk4)) = cons(hd(cons(hd(sk3),app(sk4,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_16922,c_4022]) ).

tcf(c_79120,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk4,sk3))),sk4)) = cons(hd(cons(hd(sk3),app(sk4,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_19123,c_4022]) ).

tcf(c_79121,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk3,sk4))),sk4)) = cons(hd(cons(hd(sk3),app(sk3,sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_17697,c_4022]) ).

tcf(c_79122,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk3,sk3))),sk4)) = cons(hd(cons(hd(sk3),app(sk3,sk3))),sk4) ) ),
    inference(superposition,[status(thm)],[c_20483,c_4022]) ).

tcf(c_79123,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4022]) ).

tcf(c_79124,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4022]) ).

tcf(c_79125,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_50099,c_4022]) ).

tcf(c_79126,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_51167,c_4022]) ).

tcf(c_79127,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_42609,c_4022]) ).

tcf(c_79128,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_43441,c_4022]) ).

tcf(c_79129,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4022]) ).

tcf(c_79130,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4022]) ).

tcf(c_79131,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_64396,c_4022]) ).

tcf(c_79132,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_52696,c_4022]) ).

tcf(c_79133,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_53971,c_4022]) ).

tcf(c_79134,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_59405,c_4022]) ).

tcf(c_79135,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4022]) ).

tcf(c_79136,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4022]) ).

tcf(c_79137,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_44714,c_4022]) ).

tcf(c_79138,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_46613,c_4022]) ).

tcf(c_79139,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),sk4) ) ),
    inference(superposition,[status(thm)],[c_61722,c_4022]) ).

tcf(c_79140,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,tl(sk4)))),sk4)) = cons(hd(app(sk4,app(sk3,tl(sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_71362,c_4022]) ).

tcf(c_79141,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,tl(sk3)))),sk4)) = cons(hd(app(sk4,app(sk3,tl(sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_73885,c_4022]) ).

tcf(c_79142,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,tl(sk4)))),sk4)) = cons(hd(app(sk4,app(sk4,tl(sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_69722,c_4022]) ).

tcf(c_79143,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,tl(sk3)))),sk4)) = cons(hd(app(sk4,app(sk4,tl(sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_72733,c_4022]) ).

tcf(c_79144,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,tl(sk4)))),sk4)) = cons(hd(app(sk3,app(sk3,tl(sk4)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4022]) ).

tcf(c_79145,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,tl(sk3)))),sk4)) = cons(hd(app(sk3,app(sk3,tl(sk3)))),sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4022]) ).

tcf(c_79146,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,tl(sk4)))),sk4)) = cons(hd(app(sk3,app(sk4,tl(sk4)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_70418,c_4022]) ).

tcf(c_79147,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,tl(sk3)))),sk4)) = cons(hd(app(sk3,app(sk4,tl(sk3)))),sk4) ) ),
    inference(superposition,[status(thm)],[c_73351,c_4022]) ).

tcf(c_79316,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),nil),cons(hd(sk4),sk4)) = cons(hd(X0),cons(hd(sk4),sk4)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_4235]) ).

tcf(c_79317,plain,
    app(cons(hd(sk4),nil),cons(hd(sk4),sk4)) = cons(hd(sk4),cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_4059,c_4235]) ).

tcf(c_79318,plain,
    app(cons(hd(sk3),nil),cons(hd(sk4),sk4)) = cons(hd(sk3),cons(hd(sk4),sk4)),
    inference(superposition,[status(thm)],[c_10117,c_4235]) ).

tcf(c_79331,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(tl(sk3),tl(tl(X0))) = tl(app(sk3,tl(tl(X0)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4293]) ).

tcf(c_79332,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(tl(sk3),tl(app(X1,X0))) = tl(app(sk3,tl(app(X1,X0)))) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4293]) ).

tcf(c_79333,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(tl(sk3),tl(cons(X1,X0))) = tl(app(sk3,tl(cons(X1,X0)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4293]) ).

tcf(c_79334,plain,
    ( ( tl(sk4) = nil )
    | ( app(tl(sk3),tl(tl(sk4))) = tl(app(sk3,tl(tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_62750,c_4293]) ).

tcf(c_79335,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk3),sk3))) = tl(app(sk3,tl(cons(hd(sk3),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_13784,c_4293]) ).

tcf(c_79336,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk4),sk3))) = tl(app(sk3,tl(cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_4358,c_4293]) ).

tcf(c_79337,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk3),sk4))) = tl(app(sk3,tl(cons(hd(sk3),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_12796,c_4293]) ).

tcf(c_79338,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk4),sk4))) = tl(app(sk3,tl(cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_4223,c_4293]) ).

tcf(c_79339,plain,
    ( ( tl(sk3) = nil )
    | ( app(tl(sk3),tl(tl(sk3))) = tl(app(sk3,tl(tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_65060,c_4293]) ).

tcf(c_79340,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(tl(sk3),tl(app(tl(sk3),sk3))) = tl(app(sk3,tl(app(tl(sk3),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4293]) ).

tcf(c_79341,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(tl(sk3),tl(app(tl(sk3),sk4))) = tl(app(sk3,tl(app(tl(sk3),sk4)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4293]) ).

tcf(c_79342,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(tl(sk3),tl(app(tl(sk4),sk3))) = tl(app(sk3,tl(app(tl(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4293]) ).

tcf(c_79343,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(tl(sk3),tl(app(tl(sk4),sk4))) = tl(app(sk3,tl(app(tl(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_22091,c_4293]) ).

tcf(c_79344,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk4),app(sk3,sk3)))) = tl(app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_4293]) ).

tcf(c_79345,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk3,sk3)))) = tl(app(sk3,tl(app(sk3,app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4293]) ).

tcf(c_79346,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk3,sk4)))) = tl(app(sk3,tl(app(sk3,app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4293]) ).

tcf(c_79347,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk3,sk3)))) = tl(app(sk3,tl(app(sk4,app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4293]) ).

tcf(c_79348,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk4),app(sk4,sk3)))) = tl(app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_4293]) ).

tcf(c_79349,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk3,sk4)))) = tl(app(sk3,tl(app(sk4,app(sk3,sk4))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4293]) ).

tcf(c_79350,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk4,sk3)))) = tl(app(sk3,tl(app(sk3,app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4293]) ).

tcf(c_79351,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk4,sk4)))) = tl(app(sk3,tl(app(sk3,app(sk4,sk4))))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4293]) ).

tcf(c_79352,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk4,sk3)))) = tl(app(sk3,tl(app(sk4,app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4293]) ).

tcf(c_79353,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk4,sk4)))) = tl(app(sk3,tl(app(sk4,app(sk4,sk4))))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4293]) ).

tcf(c_79354,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk4),app(sk3,sk4)))) = tl(app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_4293]) ).

tcf(c_79355,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk4),app(sk4,sk4)))) = tl(app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_4293]) ).

tcf(c_79356,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))) = tl(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4293]) ).

tcf(c_79357,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))) = tl(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4293]) ).

tcf(c_79358,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4293]) ).

tcf(c_79359,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk3),app(sk4,sk4)))) = tl(app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_4293]) ).

tcf(c_79360,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk3),app(sk4,sk3)))) = tl(app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_4293]) ).

tcf(c_79361,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk3),app(sk3,sk4)))) = tl(app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_4293]) ).

tcf(c_79362,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk3),app(sk3,sk3)))) = tl(app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_4293]) ).

tcf(c_79363,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))) = tl(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4293]) ).

tcf(c_79364,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))) = tl(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4293]) ).

tcf(c_79365,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_4293]) ).

tcf(c_79366,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_4293]) ).

tcf(c_79367,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_4293]) ).

tcf(c_79368,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_4293]) ).

tcf(c_79369,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4293]) ).

tcf(c_79370,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4293]) ).

tcf(c_79371,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk3,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_4293]) ).

tcf(c_79372,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_4293]) ).

tcf(c_79373,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_4293]) ).

tcf(c_79374,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_4293]) ).

tcf(c_79375,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4293]) ).

tcf(c_79376,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk3,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4293]) ).

tcf(c_79377,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_4293]) ).

tcf(c_79378,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_4293]) ).

tcf(c_79379,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_4293]) ).

tcf(c_79380,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk3,tl(sk4))))) = tl(app(sk3,tl(app(sk4,app(sk3,tl(sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_4293]) ).

tcf(c_79381,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk3,tl(sk3))))) = tl(app(sk3,tl(app(sk4,app(sk3,tl(sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_4293]) ).

tcf(c_79382,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk4,tl(sk4))))) = tl(app(sk3,tl(app(sk4,app(sk4,tl(sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_4293]) ).

tcf(c_79383,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(tl(sk3),tl(app(sk4,app(sk4,tl(sk3))))) = tl(app(sk3,tl(app(sk4,app(sk4,tl(sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_4293]) ).

tcf(c_79384,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk3,tl(sk4))))) = tl(app(sk3,tl(app(sk3,app(sk3,tl(sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4293]) ).

tcf(c_79385,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk3,tl(sk3))))) = tl(app(sk3,tl(app(sk3,app(sk3,tl(sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4293]) ).

tcf(c_79386,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk4,tl(sk4))))) = tl(app(sk3,tl(app(sk3,app(sk4,tl(sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_4293]) ).

tcf(c_79387,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(tl(sk3),tl(app(sk3,app(sk4,tl(sk3))))) = tl(app(sk3,tl(app(sk3,app(sk4,tl(sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_4293]) ).

tcf(c_79420,plain,
    app(tl(sk3),tl(cons(hd(sk3),app(sk3,sk3)))) = tl(app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79362,c_20706]) ).

tcf(c_79421,plain,
    app(tl(sk3),tl(cons(hd(sk3),app(sk3,sk4)))) = tl(app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79361,c_17701]) ).

tcf(c_79422,plain,
    app(tl(sk3),tl(cons(hd(sk3),app(sk4,sk3)))) = tl(app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79360,c_19513]) ).

tcf(c_79423,plain,
    app(tl(sk3),tl(cons(hd(sk3),app(sk4,sk4)))) = tl(app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79359,c_16926]) ).

tcf(c_79424,plain,
    app(tl(sk3),tl(cons(hd(sk4),app(sk4,sk4)))) = tl(app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79355,c_10611]) ).

tcf(c_79425,plain,
    app(tl(sk3),tl(cons(hd(sk4),app(sk3,sk4)))) = tl(app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79354,c_10190]) ).

tcf(c_79426,plain,
    app(tl(sk3),tl(cons(hd(sk4),app(sk4,sk3)))) = tl(app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79348,c_7545]) ).

tcf(c_79427,plain,
    app(tl(sk3),tl(cons(hd(sk4),app(sk3,sk3)))) = tl(app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79344,c_5891]) ).

tcf(c_79473,plain,
    app(tl(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79368,c_44126]) ).

tcf(c_79474,plain,
    app(tl(sk3),tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk3,tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79367,c_43038]) ).

tcf(c_79475,plain,
    app(tl(sk3),tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79366,c_51895]) ).

tcf(c_79476,plain,
    app(tl(sk3),tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk3,tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_79365,c_50642]) ).

tcf(c_79642,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( app(cons(hd(X0),nil),cons(hd(sk4),sk3)) = cons(hd(X0),cons(hd(sk4),sk3)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_4371]) ).

tcf(c_79643,plain,
    app(cons(hd(sk4),nil),cons(hd(sk4),sk3)) = cons(hd(sk4),cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_4059,c_4371]) ).

tcf(c_79644,plain,
    app(cons(hd(sk3),nil),cons(hd(sk4),sk3)) = cons(hd(sk3),cons(hd(sk4),sk3)),
    inference(superposition,[status(thm)],[c_10117,c_4371]) ).

tcf(c_79673,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,cons(hd(X0),tl(sk4)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_62836]) ).

tcf(c_79674,plain,
    hd(app(sk4,cons(hd(sk4),tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_62836]) ).

tcf(c_79675,plain,
    hd(app(sk4,cons(hd(sk3),tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10117,c_62836]) ).

tcf(c_79681,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,cons(hd(sk3),tl(sk4)))))
      | ( app(sk4,cons(hd(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,cons(hd(sk3),tl(sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_79675,c_280]) ).

tcf(c_79682,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,cons(hd(sk3),tl(sk4)))))
      | ( app(sk4,cons(hd(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,cons(hd(sk3),tl(sk4))))
      | ~ ssList(app(sk4,cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_79675,c_279]) ).

tcf(c_79758,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(sk4) = nil )
      | ( cons(hd(tl(sk4)),nil) = nil )
      | ( cons(hd(tl(sk4)),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(tl(sk4)),nil))
      | ( tl(X0) != nil )
      | ( hd(cons(hd(tl(sk4)),nil)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_62846,c_273]) ).

tcf(c_79773,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(sk4) = nil )
      | ( cons(hd(tl(sk4)),sk4) = nil )
      | ( cons(hd(tl(sk4)),sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(tl(sk4)),sk4))
      | ( tl(X0) != sk4 )
      | ( hd(cons(hd(tl(sk4)),sk4)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_62869,c_273]) ).

tcf(c_79783,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38026,c_280]) ).

tcf(c_79784,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38026,c_279]) ).

tcf(c_79800,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38027,c_280]) ).

tcf(c_79801,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38027,c_279]) ).

tcf(c_79817,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38031,c_280]) ).

tcf(c_79818,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38031,c_279]) ).

tcf(c_79834,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38032,c_280]) ).

tcf(c_79835,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38032,c_279]) ).

tcf(c_79851,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38033,c_280]) ).

tcf(c_79852,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38033,c_279]) ).

tcf(c_79878,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38034,c_280]) ).

tcf(c_79879,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38034,c_279]) ).

tcf(c_79895,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38647,c_280]) ).

tcf(c_79896,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38647,c_279]) ).

tcf(c_79923,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38651,c_280]) ).

tcf(c_79924,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))
      | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
      | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38651,c_279]) ).

tcf(c_79987,plain,
    tl(cons(hd(cons(hd(sk4),app(sk3,sk4))),sk3)) = sk3,
    inference(global_subsumption_just,[status(thm)],[c_10229,c_10190,c_10229]) ).

tcf(c_79999,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(nil,cons(hd(tl(X0)),nil)) = cons(hd(tl(X0)),nil) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_4817]) ).

tcf(c_80000,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(nil,cons(hd(app(X1,X0)),nil)) = cons(hd(app(X1,X0)),nil) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_4817]) ).

tcf(c_80001,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(nil,cons(hd(cons(X1,X0)),nil)) = cons(hd(cons(X1,X0)),nil) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_4817]) ).

tcf(c_80002,plain,
    ( ( tl(sk4) = nil )
    | ( app(nil,cons(hd(tl(sk4)),nil)) = cons(hd(tl(sk4)),nil) ) ),
    inference(superposition,[status(thm)],[c_62750,c_4817]) ).

tcf(c_80003,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),sk3)),nil)) = cons(hd(cons(hd(sk3),sk3)),nil) ) ),
    inference(superposition,[status(thm)],[c_13784,c_4817]) ).

tcf(c_80004,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),sk3)),nil)) = cons(hd(cons(hd(sk4),sk3)),nil) ) ),
    inference(superposition,[status(thm)],[c_4358,c_4817]) ).

tcf(c_80005,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),sk4)),nil)) = cons(hd(cons(hd(sk3),sk4)),nil) ) ),
    inference(superposition,[status(thm)],[c_12796,c_4817]) ).

tcf(c_80006,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),sk4)),nil)) = cons(hd(cons(hd(sk4),sk4)),nil) ) ),
    inference(superposition,[status(thm)],[c_4223,c_4817]) ).

tcf(c_80007,plain,
    ( ( tl(sk3) = nil )
    | ( app(nil,cons(hd(tl(sk3)),nil)) = cons(hd(tl(sk3)),nil) ) ),
    inference(superposition,[status(thm)],[c_65060,c_4817]) ).

tcf(c_80008,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(nil,cons(hd(app(tl(sk3),sk3)),nil)) = cons(hd(app(tl(sk3),sk3)),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_4817]) ).

tcf(c_80009,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(nil,cons(hd(app(tl(sk3),sk4)),nil)) = cons(hd(app(tl(sk3),sk4)),nil) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_4817]) ).

tcf(c_80010,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(nil,cons(hd(app(tl(sk4),sk3)),nil)) = cons(hd(app(tl(sk4),sk3)),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_4817]) ).

tcf(c_80011,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(nil,cons(hd(app(tl(sk4),sk4)),nil)) = cons(hd(app(tl(sk4),sk4)),nil) ) ),
    inference(superposition,[status(thm)],[c_22091,c_4817]) ).

tcf(c_80012,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk3,sk3))),nil)) = cons(hd(cons(hd(sk4),app(sk3,sk3))),nil) ) ),
    inference(superposition,[status(thm)],[c_5886,c_4817]) ).

tcf(c_80013,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,sk3))),nil)) = cons(hd(app(sk3,app(sk3,sk3))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_4817]) ).

tcf(c_80014,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,sk4))),nil)) = cons(hd(app(sk3,app(sk3,sk4))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_4817]) ).

tcf(c_80015,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,sk3))),nil)) = cons(hd(app(sk4,app(sk3,sk3))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_4817]) ).

tcf(c_80016,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk4,sk3))),nil)) = cons(hd(cons(hd(sk4),app(sk4,sk3))),nil) ) ),
    inference(superposition,[status(thm)],[c_7540,c_4817]) ).

tcf(c_80017,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,sk4))),nil)) = cons(hd(app(sk4,app(sk3,sk4))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_4817]) ).

tcf(c_80018,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,sk3))),nil)) = cons(hd(app(sk3,app(sk4,sk3))),nil) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_4817]) ).

tcf(c_80019,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,sk4))),nil)) = cons(hd(app(sk3,app(sk4,sk4))),nil) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_4817]) ).

tcf(c_80020,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,sk3))),nil)) = cons(hd(app(sk4,app(sk4,sk3))),nil) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_4817]) ).

tcf(c_80021,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,sk4))),nil)) = cons(hd(app(sk4,app(sk4,sk4))),nil) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_4817]) ).

tcf(c_80022,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk3,sk4))),nil)) = cons(hd(cons(hd(sk4),app(sk3,sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_10188,c_4817]) ).

tcf(c_80023,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk4),app(sk4,sk4))),nil)) = cons(hd(cons(hd(sk4),app(sk4,sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_10606,c_4817]) ).

tcf(c_80024,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_4817]) ).

tcf(c_80025,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_4817]) ).

tcf(c_80026,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_4817]) ).

tcf(c_80027,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk4,sk4))),nil)) = cons(hd(cons(hd(sk3),app(sk4,sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_16922,c_4817]) ).

tcf(c_80028,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk4,sk3))),nil)) = cons(hd(cons(hd(sk3),app(sk4,sk3))),nil) ) ),
    inference(superposition,[status(thm)],[c_19123,c_4817]) ).

tcf(c_80029,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk3,sk4))),nil)) = cons(hd(cons(hd(sk3),app(sk3,sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_17697,c_4817]) ).

tcf(c_80030,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),app(sk3,sk3))),nil)) = cons(hd(cons(hd(sk3),app(sk3,sk3))),nil) ) ),
    inference(superposition,[status(thm)],[c_20483,c_4817]) ).

tcf(c_80031,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_4817]) ).

tcf(c_80032,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_4817]) ).

tcf(c_80033,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_50099,c_4817]) ).

tcf(c_80034,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_51167,c_4817]) ).

tcf(c_80035,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_42609,c_4817]) ).

tcf(c_80036,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_43441,c_4817]) ).

tcf(c_80037,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_4817]) ).

tcf(c_80038,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_4817]) ).

tcf(c_80039,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil)) = cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) ) ),
    inference(superposition,[status(thm)],[c_64396,c_4817]) ).

tcf(c_80040,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) ) ),
    inference(superposition,[status(thm)],[c_52696,c_4817]) ).

tcf(c_80041,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) ) ),
    inference(superposition,[status(thm)],[c_53971,c_4817]) ).

tcf(c_80042,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil)) = cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) ) ),
    inference(superposition,[status(thm)],[c_59405,c_4817]) ).

tcf(c_80043,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_4817]) ).

tcf(c_80044,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil)) = cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_4817]) ).

tcf(c_80045,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),nil) ) ),
    inference(superposition,[status(thm)],[c_44714,c_4817]) ).

tcf(c_80046,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),nil) ) ),
    inference(superposition,[status(thm)],[c_46613,c_4817]) ).

tcf(c_80047,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil)) = cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),nil) ) ),
    inference(superposition,[status(thm)],[c_61722,c_4817]) ).

tcf(c_80048,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,tl(sk4)))),nil)) = cons(hd(app(sk4,app(sk3,tl(sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_71362,c_4817]) ).

tcf(c_80049,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk3,tl(sk3)))),nil)) = cons(hd(app(sk4,app(sk3,tl(sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_73885,c_4817]) ).

tcf(c_80050,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,tl(sk4)))),nil)) = cons(hd(app(sk4,app(sk4,tl(sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_69722,c_4817]) ).

tcf(c_80051,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk4,app(sk4,tl(sk3)))),nil)) = cons(hd(app(sk4,app(sk4,tl(sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_72733,c_4817]) ).

tcf(c_80052,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,tl(sk4)))),nil)) = cons(hd(app(sk3,app(sk3,tl(sk4)))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_4817]) ).

tcf(c_80053,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk3,tl(sk3)))),nil)) = cons(hd(app(sk3,app(sk3,tl(sk3)))),nil) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_4817]) ).

tcf(c_80054,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,tl(sk4)))),nil)) = cons(hd(app(sk3,app(sk4,tl(sk4)))),nil) ) ),
    inference(superposition,[status(thm)],[c_70418,c_4817]) ).

tcf(c_80055,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(nil,cons(hd(app(sk3,app(sk4,tl(sk3)))),nil)) = cons(hd(app(sk3,app(sk4,tl(sk3)))),nil) ) ),
    inference(superposition,[status(thm)],[c_73351,c_4817]) ).

tcf(c_80146,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(hd(X0),X0))
      | ( X0 = nil )
      | ~ totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_5405,c_26618]) ).

tcf(c_80156,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),sk3)))
    | ( cons(hd(sk3),sk3) = nil )
    | ~ totalorderedP(cons(hd(sk3),sk3))
    | ~ ssList(cons(hd(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_10138,c_80146]) ).

tcf(c_80157,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),sk3)))
    | ( cons(hd(sk4),sk3) = nil )
    | ~ totalorderedP(cons(hd(sk4),sk3))
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_3488,c_80146]) ).

tcf(c_80158,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),sk4)))
    | ( cons(hd(sk3),sk4) = nil )
    | ~ totalorderedP(cons(hd(sk3),sk4))
    | ~ ssList(cons(hd(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_10137,c_80146]) ).

tcf(c_80159,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),sk4)))
    | ( cons(hd(sk4),sk4) = nil )
    | ~ totalorderedP(cons(hd(sk4),sk4))
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_3537,c_80146]) ).

tcf(c_80160,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),nil)))
    | ( cons(hd(sk4),nil) = nil )
    | ~ totalorderedP(cons(hd(sk4),nil))
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(superposition,[status(thm)],[c_4074,c_80146]) ).

tcf(c_80161,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ( app(sk4,sk3) = nil )
    | ~ totalorderedP(app(sk4,sk3))
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_3948,c_80146]) ).

tcf(c_80162,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,sk4)))
    | ( app(sk4,sk4) = nil )
    | ~ totalorderedP(app(sk4,sk4))
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_3949,c_80146]) ).

tcf(c_80163,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,sk3)))
    | ( app(sk3,sk3) = nil )
    | ~ totalorderedP(app(sk3,sk3))
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4033,c_80146]) ).

tcf(c_80164,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,sk4)))
    | ( app(sk3,sk4) = nil )
    | ~ totalorderedP(app(sk3,sk4))
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4034,c_80146]) ).

tcf(c_80165,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),sk4))))
    | ( app(sk3,cons(hd(sk4),sk4)) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),sk4)))
    | ~ ssList(app(sk3,cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_4227,c_80146]) ).

tcf(c_80166,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),sk4))))
    | ( app(sk4,cons(hd(sk4),sk4)) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),sk4)))
    | ~ ssList(app(sk4,cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_4228,c_80146]) ).

tcf(c_80167,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),sk3))))
    | ( app(sk3,cons(hd(sk4),sk3)) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),sk3)))
    | ~ ssList(app(sk3,cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_4363,c_80146]) ).

tcf(c_80168,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),sk3))))
    | ( app(sk4,cons(hd(sk4),sk3)) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),sk3)))
    | ~ ssList(app(sk4,cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_4364,c_80146]) ).

tcf(c_80169,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk4),sk4))))
    | ( cons(hd(sk4),cons(hd(sk4),sk4)) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),sk4)))
    | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_5647,c_80146]) ).

tcf(c_80170,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk3))))
    | ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk3)))
    | ~ ssList(cons(hd(sk4),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_34102,c_80146]) ).

tcf(c_80171,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),app(sk3,sk3)))))
    | ( app(sk3,cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_6392,c_80146]) ).

tcf(c_80172,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),app(sk3,sk3)))))
    | ( app(sk4,cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_6393,c_80146]) ).

tcf(c_80173,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,sk3))))
    | ( app(sk3,app(sk3,sk3)) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,sk3)))
    | ~ ssList(app(sk3,app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_18181,c_80146]) ).

tcf(c_80174,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,sk3)))))
    | ( app(sk3,app(sk3,app(sk3,sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,sk3))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_49210,c_80146]) ).

tcf(c_80175,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,sk3)))))
    | ( app(sk4,app(sk3,app(sk3,sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,sk3))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_38002,c_80146]) ).

tcf(c_80176,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,sk4))))
    | ( app(sk3,app(sk3,sk4)) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,sk4)))
    | ~ ssList(app(sk3,app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_18182,c_80146]) ).

tcf(c_80177,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,sk4)))))
    | ( app(sk3,app(sk3,app(sk3,sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,sk4))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_49211,c_80146]) ).

tcf(c_80178,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,sk4)))))
    | ( app(sk4,app(sk3,app(sk3,sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,sk4))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_38003,c_80146]) ).

tcf(c_80179,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,sk3))))
    | ( app(sk4,app(sk3,sk3)) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,sk3)))
    | ~ ssList(app(sk4,app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_15589,c_80146]) ).

tcf(c_80180,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,sk3)))))
    | ( app(sk3,app(sk4,app(sk3,sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,sk3))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_54855,c_80146]) ).

tcf(c_80181,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,sk3)))))
    | ( app(sk4,app(sk4,app(sk3,sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,sk3))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_40727,c_80146]) ).

tcf(c_80182,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk3))))
    | ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk3)))
    | ~ ssList(cons(hd(sk4),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_34491,c_80146]) ).

tcf(c_80183,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),app(sk4,sk3)))))
    | ( app(sk3,cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_7590,c_80146]) ).

tcf(c_80184,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),app(sk4,sk3)))))
    | ( app(sk4,cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_7591,c_80146]) ).

tcf(c_80185,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,sk4))))
    | ( app(sk4,app(sk3,sk4)) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,sk4)))
    | ~ ssList(app(sk4,app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_15590,c_80146]) ).

tcf(c_80186,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,sk4)))))
    | ( app(sk3,app(sk4,app(sk3,sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,sk4))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_54856,c_80146]) ).

tcf(c_80187,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,sk4)))))
    | ( app(sk4,app(sk4,app(sk3,sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,sk4))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_40728,c_80146]) ).

tcf(c_80188,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk4),sk3))))
    | ( cons(hd(sk4),cons(hd(sk4),sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),sk3)))
    | ~ ssList(cons(hd(sk4),cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_8020,c_80146]) ).

tcf(c_80189,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,sk3))))
    | ( app(sk3,app(sk4,sk3)) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,sk3)))
    | ~ ssList(app(sk3,app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_18493,c_80146]) ).

tcf(c_80190,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,sk3)))))
    | ( app(sk3,app(sk3,app(sk4,sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,sk3))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_49543,c_80146]) ).

tcf(c_80191,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,sk3)))))
    | ( app(sk4,app(sk3,app(sk4,sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,sk3))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_38633,c_80146]) ).

tcf(c_80192,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,sk4))))
    | ( app(sk3,app(sk4,sk4)) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,sk4)))
    | ~ ssList(app(sk3,app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_18494,c_80146]) ).

tcf(c_80193,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,sk4)))))
    | ( app(sk3,app(sk3,app(sk4,sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,sk4))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_49544,c_80146]) ).

tcf(c_80194,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,sk4)))))
    | ( app(sk4,app(sk3,app(sk4,sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,sk4))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_38634,c_80146]) ).

tcf(c_80195,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,sk3))))
    | ( app(sk4,app(sk4,sk3)) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,sk3)))
    | ~ ssList(app(sk4,app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_15962,c_80146]) ).

tcf(c_80196,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,sk3)))))
    | ( app(sk3,app(sk4,app(sk4,sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,sk3))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_55166,c_80146]) ).

tcf(c_80197,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,sk3)))))
    | ( app(sk4,app(sk4,app(sk4,sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,sk3))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_41208,c_80146]) ).

tcf(c_80198,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,sk4))))
    | ( app(sk4,app(sk4,sk4)) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,sk4)))
    | ~ ssList(app(sk4,app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_15963,c_80146]) ).

tcf(c_80199,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,sk4)))))
    | ( app(sk3,app(sk4,app(sk4,sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,sk4))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_55167,c_80146]) ).

tcf(c_80200,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,sk4)))))
    | ( app(sk4,app(sk4,app(sk4,sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,sk4))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_41209,c_80146]) ).

tcf(c_80201,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),sk3))))
    | ( app(sk3,cons(hd(sk3),sk3)) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),sk3)))
    | ~ ssList(app(sk3,cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_13809,c_80146]) ).

tcf(c_80202,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),sk3))))
    | ( app(sk4,cons(hd(sk3),sk3)) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),sk3)))
    | ~ ssList(app(sk4,cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_13810,c_80146]) ).

tcf(c_80203,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk4),sk3))))
    | ( cons(hd(sk3),cons(hd(sk4),sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),sk3)))
    | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_10122,c_80146]) ).

tcf(c_80204,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk4),sk4))))
    | ( cons(hd(sk3),cons(hd(sk4),sk4)) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),sk4)))
    | ~ ssList(cons(hd(sk3),cons(hd(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_10125,c_80146]) ).

tcf(c_80205,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),nil)))
    | ( cons(hd(sk3),nil) = nil )
    | ~ totalorderedP(cons(hd(sk3),nil))
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(superposition,[status(thm)],[c_10136,c_80146]) ).

tcf(c_80206,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk4))))
    | ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4)))
    | ~ ssList(cons(hd(sk4),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_34150,c_80146]) ).

tcf(c_80207,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),app(sk3,sk4)))))
    | ( app(sk3,cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(sk3,cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_10217,c_80146]) ).

tcf(c_80208,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),app(sk3,sk4)))))
    | ( app(sk4,cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(app(sk4,cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_10218,c_80146]) ).

tcf(c_80209,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk4))))
    | ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk4)))
    | ~ ssList(cons(hd(sk4),app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_34549,c_80146]) ).

tcf(c_80210,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),app(sk4,sk4)))))
    | ( app(sk3,cons(hd(sk4),app(sk4,sk4))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),app(sk4,sk4))))
    | ~ ssList(app(sk3,cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_10683,c_80146]) ).

tcf(c_80211,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),app(sk4,sk4)))))
    | ( app(sk4,cons(hd(sk4),app(sk4,sk4))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),app(sk4,sk4))))
    | ~ ssList(app(sk4,cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_10684,c_80146]) ).

tcf(c_80212,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_18188,c_80146]) ).

tcf(c_80213,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))))
    | ( app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3)))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_49217,c_80146]) ).

tcf(c_80214,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3)))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_38009,c_80146]) ).

tcf(c_80215,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk3),sk3))))
    | ( cons(hd(sk4),cons(hd(sk3),sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),sk3)))
    | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_14346,c_80146]) ).

tcf(c_80216,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk4),app(sk3,sk3)))))
    | ( cons(hd(sk4),cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_11626,c_80146]) ).

tcf(c_80217,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk4),app(sk3,sk3)))))
    | ( cons(hd(sk3),cons(hd(sk4),app(sk3,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),app(sk3,sk3))))
    | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_11627,c_80146]) ).

tcf(c_80218,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk4),app(sk4,sk3)))))
    | ( cons(hd(sk4),cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_11636,c_80146]) ).

tcf(c_80219,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk4),app(sk4,sk3)))))
    | ( cons(hd(sk3),cons(hd(sk4),app(sk4,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),app(sk4,sk3))))
    | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_11637,c_80146]) ).

tcf(c_80220,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))))
    | ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_18190,c_80146]) ).

tcf(c_80221,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))))
    | ( app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4)))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_49219,c_80146]) ).

tcf(c_80222,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4)))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_38011,c_80146]) ).

tcf(c_80223,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk4),app(sk3,sk4)))))
    | ( cons(hd(sk4),cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_12331,c_80146]) ).

tcf(c_80224,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk4),app(sk3,sk4)))))
    | ( cons(hd(sk3),cons(hd(sk4),app(sk3,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),app(sk3,sk4))))
    | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_12332,c_80146]) ).

tcf(c_80225,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk4),app(sk4,sk4)))))
    | ( cons(hd(sk4),cons(hd(sk4),app(sk4,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk4))))
    | ~ ssList(cons(hd(sk4),cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_12341,c_80146]) ).

tcf(c_80226,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk4),app(sk4,sk4)))))
    | ( cons(hd(sk3),cons(hd(sk4),app(sk4,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),app(sk4,sk4))))
    | ~ ssList(cons(hd(sk3),cons(hd(sk4),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_12342,c_80146]) ).

tcf(c_80227,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),sk4))))
    | ( app(sk3,cons(hd(sk3),sk4)) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),sk4)))
    | ~ ssList(app(sk3,cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13181,c_80146]) ).

tcf(c_80228,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),sk4))))
    | ( app(sk4,cons(hd(sk3),sk4)) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),sk4)))
    | ~ ssList(app(sk4,cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13182,c_80146]) ).

tcf(c_80229,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk3),sk4))))
    | ( cons(hd(sk4),cons(hd(sk3),sk4)) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),sk4)))
    | ~ ssList(cons(hd(sk4),cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13439,c_80146]) ).

tcf(c_80230,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk3),sk4))))
    | ( cons(hd(sk3),cons(hd(sk3),sk4)) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),sk4)))
    | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_13440,c_80146]) ).

tcf(c_80231,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk3),sk3))))
    | ( cons(hd(sk3),cons(hd(sk3),sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),sk3)))
    | ~ ssList(cons(hd(sk3),cons(hd(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_14347,c_80146]) ).

tcf(c_80232,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,tl(sk3))))
    | ( app(sk4,tl(sk3)) = nil )
    | ~ totalorderedP(app(sk4,tl(sk3)))
    | ~ ssList(app(sk4,tl(sk3))) ),
    inference(superposition,[status(thm)],[c_14921,c_80146]) ).

tcf(c_80233,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,tl(sk4))))
    | ( app(sk4,tl(sk4)) = nil )
    | ~ totalorderedP(app(sk4,tl(sk4)))
    | ~ ssList(app(sk4,tl(sk4))) ),
    inference(superposition,[status(thm)],[c_14808,c_80146]) ).

tcf(c_80234,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_14822,c_80146]) ).

tcf(c_80235,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_14821,c_80146]) ).

tcf(c_80236,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_14820,c_80146]) ).

tcf(c_80237,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))))
    | ( app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_14819,c_80146]) ).

tcf(c_80238,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),nil))))
    | ( app(sk4,cons(hd(sk4),nil)) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),nil)))
    | ~ ssList(app(sk4,cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_17288,c_80146]) ).

tcf(c_80239,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk3),sk3)))))
    | ( app(sk4,app(sk3,cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),sk3))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_15595,c_80146]) ).

tcf(c_80240,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk4),sk3)))))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_15596,c_80146]) ).

tcf(c_80241,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk3),sk4)))))
    | ( app(sk4,app(sk3,cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),sk4))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_15597,c_80146]) ).

tcf(c_80242,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk4),sk4)))))
    | ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_15598,c_80146]) ).

tcf(c_80243,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_15599,c_80146]) ).

tcf(c_80244,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_15603,c_80146]) ).

tcf(c_80245,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_15609,c_80146]) ).

tcf(c_80246,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4))))))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_15610,c_80146]) ).

tcf(c_80247,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk3),sk3)))))
    | ( app(sk4,app(sk4,cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),sk3))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_15968,c_80146]) ).

tcf(c_80248,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_15969,c_80146]) ).

tcf(c_80249,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk3),sk4)))))
    | ( app(sk4,app(sk4,cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),sk4))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_15970,c_80146]) ).

tcf(c_80250,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))))
    | ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_15971,c_80146]) ).

tcf(c_80251,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_15972,c_80146]) ).

tcf(c_80252,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_15976,c_80146]) ).

tcf(c_80253,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_15982,c_80146]) ).

tcf(c_80254,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4))))))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_15983,c_80146]) ).

tcf(c_80255,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk4))))
    | ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk4,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk4,sk4))) ),
    inference(superposition,[status(thm)],[c_34550,c_80146]) ).

tcf(c_80256,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4))))))
    | ( app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4)))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17012,c_80146]) ).

tcf(c_80257,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4))))))
    | ( app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4)))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17013,c_80146]) ).

tcf(c_80258,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),app(sk4,sk4)))))
    | ( app(sk3,cons(hd(sk3),app(sk4,sk4))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),app(sk4,sk4))))
    | ~ ssList(app(sk3,cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17032,c_80146]) ).

tcf(c_80259,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),app(sk4,sk4)))))
    | ( app(sk4,cons(hd(sk3),app(sk4,sk4))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),app(sk4,sk4))))
    | ~ ssList(app(sk4,cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17033,c_80146]) ).

tcf(c_80260,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),nil))))
    | ( app(sk4,cons(hd(sk3),nil)) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),nil)))
    | ~ ssList(app(sk4,cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_17289,c_80146]) ).

tcf(c_80261,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk3),app(sk4,sk4)))))
    | ( cons(hd(sk4),cons(hd(sk3),app(sk4,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),app(sk4,sk4))))
    | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17298,c_80146]) ).

tcf(c_80262,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk3),app(sk4,sk4)))))
    | ( cons(hd(sk3),cons(hd(sk3),app(sk4,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk4))))
    | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk4,sk4)))) ),
    inference(superposition,[status(thm)],[c_17299,c_80146]) ).

tcf(c_80263,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,tl(sk3))))
    | ( app(sk3,tl(sk3)) = nil )
    | ~ totalorderedP(app(sk3,tl(sk3)))
    | ~ ssList(app(sk3,tl(sk3))) ),
    inference(superposition,[status(thm)],[c_17619,c_80146]) ).

tcf(c_80264,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,tl(sk4))))
    | ( app(sk3,tl(sk4)) = nil )
    | ~ totalorderedP(app(sk3,tl(sk4)))
    | ~ ssList(app(sk3,tl(sk4))) ),
    inference(superposition,[status(thm)],[c_17373,c_80146]) ).

tcf(c_80265,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_17388,c_80146]) ).

tcf(c_80266,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_17387,c_80146]) ).

tcf(c_80267,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_17386,c_80146]) ).

tcf(c_80268,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))))
    | ( app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17385,c_80146]) ).

tcf(c_80269,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))))
    | ( app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))
    | ~ ssList(app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_17384,c_80146]) ).

tcf(c_80270,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk4))))
    | ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,sk4)))
    | ~ ssList(cons(hd(sk3),app(sk3,sk4))) ),
    inference(superposition,[status(thm)],[c_34151,c_80146]) ).

tcf(c_80271,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4))))))
    | ( app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4)))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_17770,c_80146]) ).

tcf(c_80272,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4))))))
    | ( app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4)))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_17771,c_80146]) ).

tcf(c_80273,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),app(sk3,sk4)))))
    | ( app(sk3,cons(hd(sk3),app(sk3,sk4))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),app(sk3,sk4))))
    | ~ ssList(app(sk3,cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17790,c_80146]) ).

tcf(c_80274,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),app(sk3,sk4)))))
    | ( app(sk4,cons(hd(sk3),app(sk3,sk4))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),app(sk3,sk4))))
    | ~ ssList(app(sk4,cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17791,c_80146]) ).

tcf(c_80275,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk3),app(sk3,sk4)))))
    | ( cons(hd(sk4),cons(hd(sk3),app(sk3,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),app(sk3,sk4))))
    | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17980,c_80146]) ).

tcf(c_80276,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk3),app(sk3,sk4)))))
    | ( cons(hd(sk3),cons(hd(sk3),app(sk3,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk4))))
    | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_17981,c_80146]) ).

tcf(c_80277,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk3),sk3)))))
    | ( app(sk3,app(sk3,cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_18187,c_80146]) ).

tcf(c_80278,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk3),sk4)))))
    | ( app(sk3,app(sk3,cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),sk4))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_18189,c_80146]) ).

tcf(c_80279,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_18191,c_80146]) ).

tcf(c_80280,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_18195,c_80146]) ).

tcf(c_80281,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18201,c_80146]) ).

tcf(c_80282,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))))
    | ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18202,c_80146]) ).

tcf(c_80283,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))))
    | ( app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18205,c_80146]) ).

tcf(c_80284,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))))
    | ( app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18206,c_80146]) ).

tcf(c_80285,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk3),sk3)))))
    | ( app(sk3,app(sk4,cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_18499,c_80146]) ).

tcf(c_80286,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_18500,c_80146]) ).

tcf(c_80287,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk3),sk4)))))
    | ( app(sk3,app(sk4,cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),sk4))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_18501,c_80146]) ).

tcf(c_80288,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))
    | ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_18502,c_80146]) ).

tcf(c_80289,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_18503,c_80146]) ).

tcf(c_80290,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_18507,c_80146]) ).

tcf(c_80291,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18513,c_80146]) ).

tcf(c_80292,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4))))))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18514,c_80146]) ).

tcf(c_80293,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4))))))
    | ( app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4)))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_18517,c_80146]) ).

tcf(c_80294,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4))))))
    | ( app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4)))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_18518,c_80146]) ).

tcf(c_80295,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk3))))
    | ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk4,sk3)))
    | ~ ssList(cons(hd(sk3),app(sk4,sk3))) ),
    inference(superposition,[status(thm)],[c_34492,c_80146]) ).

tcf(c_80296,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3))))))
    | ( app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3)))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19240,c_80146]) ).

tcf(c_80297,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))))
    | ( app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19241,c_80146]) ).

tcf(c_80298,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3))))))
    | ( app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3)))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19245,c_80146]) ).

tcf(c_80299,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3))))))
    | ( app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3)))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_19246,c_80146]) ).

tcf(c_80300,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),app(sk4,sk3)))))
    | ( app(sk3,cons(hd(sk3),app(sk4,sk3))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),app(sk4,sk3))))
    | ~ ssList(app(sk3,cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19265,c_80146]) ).

tcf(c_80301,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),app(sk4,sk3)))))
    | ( app(sk4,cons(hd(sk3),app(sk4,sk3))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),app(sk4,sk3))))
    | ~ ssList(app(sk4,cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19266,c_80146]) ).

tcf(c_80302,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),nil))))
    | ( app(sk3,cons(hd(sk4),nil)) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),nil)))
    | ~ ssList(app(sk3,cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_19900,c_80146]) ).

tcf(c_80303,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),nil))))
    | ( app(sk3,cons(hd(sk3),nil)) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),nil)))
    | ~ ssList(app(sk3,cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_19901,c_80146]) ).

tcf(c_80304,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk3),app(sk4,sk3)))))
    | ( cons(hd(sk4),cons(hd(sk3),app(sk4,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),app(sk4,sk3))))
    | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19910,c_80146]) ).

tcf(c_80305,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk3),app(sk4,sk3)))))
    | ( cons(hd(sk3),cons(hd(sk3),app(sk4,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk3))))
    | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk4,sk3)))) ),
    inference(superposition,[status(thm)],[c_19911,c_80146]) ).

tcf(c_80306,plain,
    ( totalorderedP(cons(hd(tl(sk3)),app(tl(sk3),sk3)))
    | ( tl(sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ~ totalorderedP(app(tl(sk3),sk3))
    | ~ ssList(app(tl(sk3),sk3)) ),
    inference(superposition,[status(thm)],[c_67966,c_80146]) ).

tcf(c_80307,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk3))))
    | ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,sk3)))
    | ~ ssList(cons(hd(sk3),app(sk3,sk3))) ),
    inference(superposition,[status(thm)],[c_34103,c_80146]) ).

tcf(c_80308,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3))))))
    | ( app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3)))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20550,c_80146]) ).

tcf(c_80309,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))))
    | ( app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20551,c_80146]) ).

tcf(c_80310,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3))))))
    | ( app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3)))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20555,c_80146]) ).

tcf(c_80311,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3))))))
    | ( app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3)))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_20556,c_80146]) ).

tcf(c_80312,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),app(sk3,sk3)))))
    | ( app(sk3,cons(hd(sk3),app(sk3,sk3))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),app(sk3,sk3))))
    | ~ ssList(app(sk3,cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20575,c_80146]) ).

tcf(c_80313,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),app(sk3,sk3)))))
    | ( app(sk4,cons(hd(sk3),app(sk3,sk3))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),app(sk3,sk3))))
    | ~ ssList(app(sk4,cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20576,c_80146]) ).

tcf(c_80314,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk3),app(sk3,sk3)))))
    | ( cons(hd(sk4),cons(hd(sk3),app(sk3,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),app(sk3,sk3))))
    | ~ ssList(cons(hd(sk4),cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20778,c_80146]) ).

tcf(c_80315,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk3),app(sk3,sk3)))))
    | ( cons(hd(sk3),cons(hd(sk3),app(sk3,sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk3))))
    | ~ ssList(cons(hd(sk3),cons(hd(sk3),app(sk3,sk3)))) ),
    inference(superposition,[status(thm)],[c_20779,c_80146]) ).

tcf(c_80316,plain,
    ( totalorderedP(cons(hd(tl(sk3)),app(tl(sk3),sk4)))
    | ( tl(sk3) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ~ totalorderedP(app(tl(sk3),sk4))
    | ~ ssList(app(tl(sk3),sk4)) ),
    inference(superposition,[status(thm)],[c_67967,c_80146]) ).

tcf(c_80317,plain,
    ( totalorderedP(cons(hd(tl(sk4)),app(tl(sk4),sk3)))
    | ( tl(sk4) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ~ totalorderedP(app(tl(sk4),sk3))
    | ~ ssList(app(tl(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_67647,c_80146]) ).

tcf(c_80318,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),sk3))))
    | ( app(sk3,app(tl(sk4),sk3)) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),sk3)))
    | ~ ssList(app(sk3,app(tl(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_75971,c_80146]) ).

tcf(c_80319,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),sk3))))
    | ( app(sk4,app(tl(sk4),sk3)) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),sk3)))
    | ~ ssList(app(sk4,app(tl(sk4),sk3))) ),
    inference(superposition,[status(thm)],[c_76483,c_80146]) ).

tcf(c_80320,plain,
    ( totalorderedP(cons(hd(tl(sk4)),app(tl(sk4),sk4)))
    | ( tl(sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ~ totalorderedP(app(tl(sk4),sk4))
    | ~ ssList(app(tl(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_67648,c_80146]) ).

tcf(c_80321,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),sk4))))
    | ( app(sk3,app(tl(sk4),sk4)) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),sk4)))
    | ~ ssList(app(sk3,app(tl(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_59252,c_80146]) ).

tcf(c_80322,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),sk4))))
    | ( app(sk4,app(tl(sk4),sk4)) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),sk4)))
    | ~ ssList(app(sk4,app(tl(sk4),sk4))) ),
    inference(superposition,[status(thm)],[c_76484,c_80146]) ).

tcf(c_80323,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))))
    | ( app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3)))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_54862,c_80146]) ).

tcf(c_80324,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))))
    | ( app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3)))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_40734,c_80146]) ).

tcf(c_80325,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))))
    | ( app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4)))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_54864,c_80146]) ).

tcf(c_80326,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))))
    | ( app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4)))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_40736,c_80146]) ).

tcf(c_80327,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38016,c_80146]) ).

tcf(c_80328,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38020,c_80146]) ).

tcf(c_80329,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(sk4))))
    | ( cons(hd(sk3),tl(sk4)) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(sk4)))
    | ~ ssList(cons(hd(sk3),tl(sk4))) ),
    inference(superposition,[status(thm)],[c_32100,c_80146]) ).

tcf(c_80330,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),tl(sk3))))
    | ( cons(hd(sk4),tl(sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk4),tl(sk3)))
    | ~ ssList(cons(hd(sk4),tl(sk3))) ),
    inference(superposition,[status(thm)],[c_32112,c_80146]) ).

tcf(c_80331,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(sk3))))
    | ( cons(hd(sk3),tl(sk3)) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(sk3)))
    | ~ ssList(cons(hd(sk3),tl(sk3))) ),
    inference(superposition,[status(thm)],[c_32113,c_80146]) ).

tcf(c_80332,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))))
    | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_32313,c_80146]) ).

tcf(c_80333,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))))
    | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_32314,c_80146]) ).

tcf(c_80334,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))))
    | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_32315,c_80146]) ).

tcf(c_80335,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))))
    | ( app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_32316,c_80146]) ).

tcf(c_80336,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))))
    | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_32561,c_80146]) ).

tcf(c_80337,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))))
    | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_32562,c_80146]) ).

tcf(c_80338,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))))
    | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_32563,c_80146]) ).

tcf(c_80339,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))))
    | ( app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_32564,c_80146]) ).

tcf(c_80340,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))))
    | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_32970,c_80146]) ).

tcf(c_80341,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))))
    | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_32971,c_80146]) ).

tcf(c_80342,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))))
    | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_32972,c_80146]) ).

tcf(c_80343,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))))
    | ( app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_32973,c_80146]) ).

tcf(c_80344,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),cons(hd(sk3),sk3)))))
    | ( app(sk4,cons(hd(sk4),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_33089,c_80146]) ).

tcf(c_80345,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),cons(hd(sk3),sk3)))))
    | ( app(sk4,cons(hd(sk3),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_33090,c_80146]) ).

tcf(c_80346,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),cons(hd(sk4),sk3)))))
    | ( app(sk4,cons(hd(sk4),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_33113,c_80146]) ).

tcf(c_80347,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),cons(hd(sk4),sk3)))))
    | ( app(sk4,cons(hd(sk3),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_33114,c_80146]) ).

tcf(c_80348,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),cons(hd(sk4),sk4)))))
    | ( app(sk4,cons(hd(sk4),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_33123,c_80146]) ).

tcf(c_80349,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),cons(hd(sk4),sk4)))))
    | ( app(sk4,cons(hd(sk3),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_33124,c_80146]) ).

tcf(c_80350,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,cons(hd(sk3),sk3)))))
    | ( cons(hd(sk4),app(sk3,cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,cons(hd(sk3),sk3))))
    | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35257,c_80146]) ).

tcf(c_80351,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,cons(hd(sk3),sk3)))))
    | ( cons(hd(sk3),app(sk3,cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),sk3))))
    | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35258,c_80146]) ).

tcf(c_80352,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,cons(hd(sk4),sk3)))))
    | ( cons(hd(sk4),app(sk3,cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,cons(hd(sk4),sk3))))
    | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35267,c_80146]) ).

tcf(c_80353,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,cons(hd(sk4),sk3)))))
    | ( cons(hd(sk3),app(sk3,cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),sk3))))
    | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35268,c_80146]) ).

tcf(c_80354,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,cons(hd(sk3),sk4)))))
    | ( cons(hd(sk4),app(sk3,cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,cons(hd(sk3),sk4))))
    | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35281,c_80146]) ).

tcf(c_80355,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,cons(hd(sk3),sk4)))))
    | ( cons(hd(sk3),app(sk3,cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),sk4))))
    | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35282,c_80146]) ).

tcf(c_80356,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,cons(hd(sk4),sk4)))))
    | ( cons(hd(sk4),app(sk3,cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,cons(hd(sk4),sk4))))
    | ~ ssList(cons(hd(sk4),app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35346,c_80146]) ).

tcf(c_80357,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,cons(hd(sk4),sk4)))))
    | ( cons(hd(sk3),app(sk3,cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),sk4))))
    | ~ ssList(cons(hd(sk3),app(sk3,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35347,c_80146]) ).

tcf(c_80358,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,cons(hd(sk3),sk3)))))
    | ( cons(hd(sk4),app(sk4,cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),sk3))))
    | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35356,c_80146]) ).

tcf(c_80359,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,cons(hd(sk3),sk3)))))
    | ( cons(hd(sk3),app(sk4,cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk4,cons(hd(sk3),sk3))))
    | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_35357,c_80146]) ).

tcf(c_80360,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,cons(hd(sk4),sk3)))))
    | ( cons(hd(sk4),app(sk4,cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),sk3))))
    | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35388,c_80146]) ).

tcf(c_80361,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,cons(hd(sk4),sk3)))))
    | ( cons(hd(sk3),app(sk4,cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk4,cons(hd(sk4),sk3))))
    | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_35389,c_80146]) ).

tcf(c_80362,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,cons(hd(sk3),sk4)))))
    | ( cons(hd(sk4),app(sk4,cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),sk4))))
    | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35431,c_80146]) ).

tcf(c_80363,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,cons(hd(sk3),sk4)))))
    | ( cons(hd(sk3),app(sk4,cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk4,cons(hd(sk3),sk4))))
    | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_35432,c_80146]) ).

tcf(c_80364,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,cons(hd(sk4),sk4)))))
    | ( cons(hd(sk4),app(sk4,cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),sk4))))
    | ~ ssList(cons(hd(sk4),app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35441,c_80146]) ).

tcf(c_80365,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,cons(hd(sk4),sk4)))))
    | ( cons(hd(sk3),app(sk4,cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk4,cons(hd(sk4),sk4))))
    | ~ ssList(cons(hd(sk3),app(sk4,cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_35442,c_80146]) ).

tcf(c_80366,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk4),nil))))
    | ( cons(hd(sk4),cons(hd(sk4),nil)) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk4),nil)))
    | ~ ssList(cons(hd(sk4),cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_36033,c_80146]) ).

tcf(c_80367,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk4),nil))))
    | ( cons(hd(sk3),cons(hd(sk4),nil)) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk4),nil)))
    | ~ ssList(cons(hd(sk3),cons(hd(sk4),nil))) ),
    inference(superposition,[status(thm)],[c_36034,c_80146]) ).

tcf(c_80368,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk3),nil))))
    | ( cons(hd(sk4),cons(hd(sk3),nil)) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),nil)))
    | ~ ssList(cons(hd(sk4),cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_36085,c_80146]) ).

tcf(c_80369,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk3),nil))))
    | ( cons(hd(sk3),cons(hd(sk3),nil)) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),nil)))
    | ~ ssList(cons(hd(sk3),cons(hd(sk3),nil))) ),
    inference(superposition,[status(thm)],[c_36086,c_80146]) ).

tcf(c_80370,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))))
    | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_36640,c_80146]) ).

tcf(c_80371,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))))
    | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_36641,c_80146]) ).

tcf(c_80372,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))))
    | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_36642,c_80146]) ).

tcf(c_80373,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))))
    | ( app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_36643,c_80146]) ).

tcf(c_80374,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))))
    | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_36861,c_80146]) ).

tcf(c_80375,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))))
    | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_36862,c_80146]) ).

tcf(c_80376,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))))
    | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_36863,c_80146]) ).

tcf(c_80377,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))))
    | ( app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_36864,c_80146]) ).

tcf(c_80378,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))))
    | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_37184,c_80146]) ).

tcf(c_80379,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))))
    | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_37185,c_80146]) ).

tcf(c_80380,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))))
    | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_37186,c_80146]) ).

tcf(c_80381,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))))
    | ( app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_37187,c_80146]) ).

tcf(c_80382,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),cons(hd(sk3),sk3)))))
    | ( app(sk3,cons(hd(sk4),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_37318,c_80146]) ).

tcf(c_80383,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),cons(hd(sk3),sk3)))))
    | ( app(sk3,cons(hd(sk3),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_37319,c_80146]) ).

tcf(c_80384,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),cons(hd(sk4),sk3)))))
    | ( app(sk3,cons(hd(sk4),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_37366,c_80146]) ).

tcf(c_80385,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),cons(hd(sk4),sk3)))))
    | ( app(sk3,cons(hd(sk3),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_37367,c_80146]) ).

tcf(c_80386,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),cons(hd(sk4),sk4)))))
    | ( app(sk3,cons(hd(sk4),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_37376,c_80146]) ).

tcf(c_80387,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),cons(hd(sk4),sk4)))))
    | ( app(sk3,cons(hd(sk3),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_37377,c_80146]) ).

tcf(c_80388,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(sk3)))))
    | ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(sk3))))
    | ~ ssList(app(sk4,app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_37579,c_80146]) ).

tcf(c_80389,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(sk4)))))
    | ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(sk4))))
    | ~ ssList(app(sk4,app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_37428,c_80146]) ).

tcf(c_80390,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))))
    | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))))
    | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37446,c_80146]) ).

tcf(c_80391,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))))
    | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))))
    | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37445,c_80146]) ).

tcf(c_80392,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))))
    | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))))
    | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37444,c_80146]) ).

tcf(c_80393,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))))
    | ( app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))))
    | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37443,c_80146]) ).

tcf(c_80394,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))))
    | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))))
    | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37442,c_80146]) ).

tcf(c_80395,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))))
    | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))))
    | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37441,c_80146]) ).

tcf(c_80396,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))))
    | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))))
    | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_37440,c_80146]) ).

tcf(c_80397,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))))
    | ( app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))))
    | ~ ssList(app(sk4,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_37439,c_80146]) ).

tcf(c_80398,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3)))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_38008,c_80146]) ).

tcf(c_80399,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4)))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_38010,c_80146]) ).

tcf(c_80400,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38026,c_80146]) ).

tcf(c_80401,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38027,c_80146]) ).

tcf(c_80402,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38031,c_80146]) ).

tcf(c_80403,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38032,c_80146]) ).

tcf(c_80404,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_38033,c_80146]) ).

tcf(c_80405,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))))
    | ( app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38034,c_80146]) ).

tcf(c_80406,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3))))))
    | ( app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3)))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_38639,c_80146]) ).

tcf(c_80407,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))))
    | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3)))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_38640,c_80146]) ).

tcf(c_80408,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4))))))
    | ( app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4)))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_38641,c_80146]) ).

tcf(c_80409,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))))
    | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4)))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_38642,c_80146]) ).

tcf(c_80410,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))))
    | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38647,c_80146]) ).

tcf(c_80411,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))))
    | ( app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_38651,c_80146]) ).

tcf(c_80412,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3))))))
    | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3)))))
    | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_39658,c_80146]) ).

tcf(c_80413,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3))))))
    | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3)))))
    | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_39659,c_80146]) ).

tcf(c_80414,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4))))))
    | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4)))))
    | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_39668,c_80146]) ).

tcf(c_80415,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4))))))
    | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4)))))
    | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_39669,c_80146]) ).

tcf(c_80416,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk4),nil)))))
    | ( app(sk4,app(sk3,cons(hd(sk4),nil))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),nil))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_39919,c_80146]) ).

tcf(c_80417,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk3),nil)))))
    | ( app(sk4,app(sk3,cons(hd(sk3),nil))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),nil))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_39920,c_80146]) ).

tcf(c_80418,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(sk3)))))
    | ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(sk3))))
    | ~ ssList(app(sk4,app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_40142,c_80146]) ).

tcf(c_80419,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(sk4)))))
    | ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(sk4))))
    | ~ ssList(app(sk4,app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_39968,c_80146]) ).

tcf(c_80420,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))))
    | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))))
    | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39986,c_80146]) ).

tcf(c_80421,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))))
    | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))))
    | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39985,c_80146]) ).

tcf(c_80422,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))))
    | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))))
    | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39984,c_80146]) ).

tcf(c_80423,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))))
    | ( app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))))
    | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39983,c_80146]) ).

tcf(c_80424,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))))
    | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))))
    | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39982,c_80146]) ).

tcf(c_80425,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))))
    | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))))
    | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39981,c_80146]) ).

tcf(c_80426,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))))
    | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))))
    | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_39980,c_80146]) ).

tcf(c_80427,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))))
    | ( app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))))
    | ~ ssList(app(sk4,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_39979,c_80146]) ).

tcf(c_80428,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3))))))
    | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3)))))
    | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_40283,c_80146]) ).

tcf(c_80429,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3))))))
    | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3)))))
    | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_40284,c_80146]) ).

tcf(c_80430,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4))))))
    | ( cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4)))))
    | ~ ssList(cons(hd(sk4),tl(cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40331,c_80146]) ).

tcf(c_80431,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4))))))
    | ( cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4)))))
    | ~ ssList(cons(hd(sk3),tl(cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40332,c_80146]) ).

tcf(c_80432,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4))))))
    | ( cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(cons(hd(sk4),tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40341,c_80146]) ).

tcf(c_80433,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4))))))
    | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_40342,c_80146]) ).

tcf(c_80434,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4))))))
    | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_40352,c_80146]) ).

tcf(c_80435,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3))))))
    | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_40362,c_80146]) ).

tcf(c_80436,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3))))))
    | ( cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(cons(hd(sk3),tl(cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_40373,c_80146]) ).

tcf(c_80437,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3))))))
    | ( app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3)))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_40733,c_80146]) ).

tcf(c_80438,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4))))))
    | ( app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4)))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_40735,c_80146]) ).

tcf(c_80439,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3))))))
    | ( app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3)))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_41214,c_80146]) ).

tcf(c_80440,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))))
    | ( app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3)))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_41215,c_80146]) ).

tcf(c_80441,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4))))))
    | ( app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4)))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_41216,c_80146]) ).

tcf(c_80442,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))))
    | ( app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4)))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_41217,c_80146]) ).

tcf(c_80443,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))))
    | ( app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3)))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_42678,c_80146]) ).

tcf(c_80444,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),nil)))))
    | ( app(sk4,app(sk4,cons(hd(sk4),nil))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),nil))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_43033,c_80146]) ).

tcf(c_80445,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk3),nil)))))
    | ( app(sk4,app(sk4,cons(hd(sk3),nil))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),nil))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_43034,c_80146]) ).

tcf(c_80446,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3))))))
    | ( cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3)))))
    | ~ ssList(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_43045,c_80146]) ).

tcf(c_80447,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3))))))
    | ( cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))
    | ~ ssList(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_43046,c_80146]) ).

tcf(c_80448,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))))
    | ( app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4)))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_43510,c_80146]) ).

tcf(c_80449,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4))))))
    | ( cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4)))))
    | ~ ssList(cons(hd(sk4),app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_44133,c_80146]) ).

tcf(c_80450,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4))))))
    | ( cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))
    | ~ ssList(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_44134,c_80146]) ).

tcf(c_80451,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))))
    | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))))
    | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_44197,c_80146]) ).

tcf(c_80452,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))))
    | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))))
    | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_44196,c_80146]) ).

tcf(c_80453,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))))
    | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))))
    | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_44195,c_80146]) ).

tcf(c_80454,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))))
    | ( app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))))
    | ~ ssList(app(sk4,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_44194,c_80146]) ).

tcf(c_80455,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(sk3)))))
    | ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(sk3))))
    | ~ ssList(app(sk3,app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_48789,c_80146]) ).

tcf(c_80456,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(sk4)))))
    | ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(sk4))))
    | ~ ssList(app(sk3,app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_48433,c_80146]) ).

tcf(c_80457,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))))
    | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3))))))
    | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48451,c_80146]) ).

tcf(c_80458,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))))
    | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3))))))
    | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48450,c_80146]) ).

tcf(c_80459,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))))
    | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4))))))
    | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48449,c_80146]) ).

tcf(c_80460,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))))
    | ( app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4))))))
    | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48448,c_80146]) ).

tcf(c_80461,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))))
    | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4))))))
    | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48447,c_80146]) ).

tcf(c_80462,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))))
    | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3))))))
    | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48446,c_80146]) ).

tcf(c_80463,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))))
    | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4))))))
    | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_48445,c_80146]) ).

tcf(c_80464,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))))
    | ( app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3))))))
    | ~ ssList(app(sk3,app(sk3,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_48444,c_80146]) ).

tcf(c_80465,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3))))))
    | ( app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3)))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_49216,c_80146]) ).

tcf(c_80466,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4))))))
    | ( app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4)))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_49218,c_80146]) ).

tcf(c_80467,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3))))))
    | ( app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3)))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_49549,c_80146]) ).

tcf(c_80468,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4))))))
    | ( app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4)))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_49551,c_80146]) ).

tcf(c_80469,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))))
    | ( app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3)))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk3))))) ),
    inference(superposition,[status(thm)],[c_50181,c_80146]) ).

tcf(c_80470,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))))
    | ( app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4)))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk4),sk4))))) ),
    inference(superposition,[status(thm)],[c_51250,c_80146]) ).

tcf(c_80471,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk4),nil)))))
    | ( app(sk3,app(sk3,cons(hd(sk4),nil))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk4),nil))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_52391,c_80146]) ).

tcf(c_80472,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk3),nil)))))
    | ( app(sk3,app(sk3,cons(hd(sk3),nil))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),nil))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_52392,c_80146]) ).

tcf(c_80473,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(sk3)))))
    | ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(sk3))))
    | ~ ssList(app(sk3,app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_53652,c_80146]) ).

tcf(c_80474,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(sk4)))))
    | ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(sk4))))
    | ~ ssList(app(sk3,app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_53363,c_80146]) ).

tcf(c_80475,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))))
    | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))))
    | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53381,c_80146]) ).

tcf(c_80476,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))))
    | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))))
    | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53380,c_80146]) ).

tcf(c_80477,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))))
    | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))))
    | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53379,c_80146]) ).

tcf(c_80478,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))))
    | ( app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))))
    | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk4),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53378,c_80146]) ).

tcf(c_80479,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))))
    | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))))
    | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53377,c_80146]) ).

tcf(c_80480,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))))
    | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))))
    | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53376,c_80146]) ).

tcf(c_80481,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))))
    | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))))
    | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_53375,c_80146]) ).

tcf(c_80482,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))))
    | ( app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))))
    | ~ ssList(app(sk3,app(sk4,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_53374,c_80146]) ).

tcf(c_80483,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3))))))
    | ( app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3)))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_54861,c_80146]) ).

tcf(c_80484,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4))))))
    | ( app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4)))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_54863,c_80146]) ).

tcf(c_80485,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3))))))
    | ( app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3)))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk3))))) ),
    inference(superposition,[status(thm)],[c_55172,c_80146]) ).

tcf(c_80486,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4))))))
    | ( app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4)))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk3),sk4))))) ),
    inference(superposition,[status(thm)],[c_55174,c_80146]) ).

tcf(c_80487,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),nil)))))
    | ( app(sk3,app(sk4,cons(hd(sk4),nil))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),nil))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk4),nil)))) ),
    inference(superposition,[status(thm)],[c_56252,c_80146]) ).

tcf(c_80488,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk3),nil)))))
    | ( app(sk3,app(sk4,cons(hd(sk3),nil))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),nil))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),nil)))) ),
    inference(superposition,[status(thm)],[c_56253,c_80146]) ).

tcf(c_80489,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))))
    | ( app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_56394,c_80146]) ).

tcf(c_80490,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))))
    | ( app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_56395,c_80146]) ).

tcf(c_80491,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))))
    | ( app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_56397,c_80146]) ).

tcf(c_80492,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))))
    | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4))))))
    | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk4)))))) ),
    inference(superposition,[status(thm)],[c_56759,c_80146]) ).

tcf(c_80493,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))))
    | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3))))))
    | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk4,sk3)))))) ),
    inference(superposition,[status(thm)],[c_56758,c_80146]) ).

tcf(c_80494,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))))
    | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4))))))
    | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk4)))))) ),
    inference(superposition,[status(thm)],[c_56757,c_80146]) ).

tcf(c_80495,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))))
    | ( app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3))))))
    | ~ ssList(app(sk3,app(nil,tl(cons(hd(sk3),app(sk3,sk3)))))) ),
    inference(superposition,[status(thm)],[c_56756,c_80146]) ).

tcf(c_80496,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk4),cons(hd(sk3),sk4)))))
    | ( app(sk4,cons(hd(sk4),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk4),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk4,cons(hd(sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_57992,c_80146]) ).

tcf(c_80497,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),cons(hd(sk3),sk4)))))
    | ( app(sk4,cons(hd(sk3),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk4,cons(hd(sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_57993,c_80146]) ).

tcf(c_80498,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))))
    | ( app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_58477,c_80146]) ).

tcf(c_80499,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))))
    | ( app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_58478,c_80146]) ).

tcf(c_80500,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))))
    | ( app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_58480,c_80146]) ).

tcf(c_80501,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk4),cons(hd(sk3),sk4)))))
    | ( app(sk3,cons(hd(sk4),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk4),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk3,cons(hd(sk4),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_58633,c_80146]) ).

tcf(c_80502,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),cons(hd(sk3),sk4)))))
    | ( app(sk3,cons(hd(sk3),cons(hd(sk3),sk4))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),cons(hd(sk3),sk4))))
    | ~ ssList(app(sk3,cons(hd(sk3),cons(hd(sk3),sk4)))) ),
    inference(superposition,[status(thm)],[c_58634,c_80146]) ).

tcf(c_80503,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk3),sk4),tl(sk4)))))
    | ( app(sk3,app(cons(hd(sk3),sk4),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk4),tl(sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk3),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62780,c_80146]) ).

tcf(c_80504,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk3),sk4),tl(sk4)))))
    | ( app(sk4,app(cons(hd(sk3),sk4),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk4),tl(sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk3),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62786,c_80146]) ).

tcf(c_80505,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,tl(sk4))))))
    | ( app(sk3,app(sk4,app(sk4,tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,tl(sk4)))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62789,c_80146]) ).

tcf(c_80506,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,tl(sk4))))))
    | ( app(sk3,app(sk4,app(sk3,tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,tl(sk4)))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62790,c_80146]) ).

tcf(c_80507,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,tl(sk4))))))
    | ( app(sk3,app(sk3,app(sk4,tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,tl(sk4)))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62794,c_80146]) ).

tcf(c_80508,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,tl(sk4))))))
    | ( app(sk3,app(sk3,app(sk3,tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,tl(sk4)))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62795,c_80146]) ).

tcf(c_80509,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,tl(sk4))))))
    | ( app(sk4,app(sk4,app(sk4,tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,tl(sk4)))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62807,c_80146]) ).

tcf(c_80510,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,tl(sk4))))))
    | ( app(sk4,app(sk4,app(sk3,tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,tl(sk4)))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62808,c_80146]) ).

tcf(c_80511,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,tl(sk4))))))
    | ( app(sk4,app(sk3,app(sk4,tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,tl(sk4)))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62812,c_80146]) ).

tcf(c_80512,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,tl(sk4))))))
    | ( app(sk4,app(sk3,app(sk3,tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,tl(sk4)))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_62813,c_80146]) ).

tcf(c_80513,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk4),tl(sk4)))))
    | ( app(sk3,app(cons(hd(sk4),sk4),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk4),tl(sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62815,c_80146]) ).

tcf(c_80514,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk4),sk3),tl(sk4)))))
    | ( app(sk3,app(cons(hd(sk4),sk3),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk4),sk3),tl(sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk4),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62816,c_80146]) ).

tcf(c_80515,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(cons(hd(sk3),sk3),tl(sk4)))))
    | ( app(sk3,app(cons(hd(sk3),sk3),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(cons(hd(sk3),sk3),tl(sk4))))
    | ~ ssList(app(sk3,app(cons(hd(sk3),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62817,c_80146]) ).

tcf(c_80516,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk4),tl(sk4)))))
    | ( app(sk4,app(cons(hd(sk4),sk4),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk4),tl(sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62827,c_80146]) ).

tcf(c_80517,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk4),sk3),tl(sk4)))))
    | ( app(sk4,app(cons(hd(sk4),sk3),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk4),sk3),tl(sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk4),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62828,c_80146]) ).

tcf(c_80518,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(cons(hd(sk3),sk3),tl(sk4)))))
    | ( app(sk4,app(cons(hd(sk3),sk3),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(cons(hd(sk3),sk3),tl(sk4))))
    | ~ ssList(app(sk4,app(cons(hd(sk3),sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_62829,c_80146]) ).

tcf(c_80519,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,tl(sk3))))))
    | ( app(sk3,app(sk4,app(sk4,tl(sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,tl(sk3)))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65099,c_80146]) ).

tcf(c_80520,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,tl(sk3))))))
    | ( app(sk3,app(sk4,app(sk3,tl(sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,tl(sk3)))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65100,c_80146]) ).

tcf(c_80521,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,tl(sk3))))))
    | ( app(sk3,app(sk3,app(sk4,tl(sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,tl(sk3)))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65104,c_80146]) ).

tcf(c_80522,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,tl(sk3))))))
    | ( app(sk3,app(sk3,app(sk3,tl(sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,tl(sk3)))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65105,c_80146]) ).

tcf(c_80523,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,tl(sk3))))))
    | ( app(sk4,app(sk4,app(sk4,tl(sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,tl(sk3)))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65117,c_80146]) ).

tcf(c_80524,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,tl(sk3))))))
    | ( app(sk4,app(sk4,app(sk3,tl(sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,tl(sk3)))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65118,c_80146]) ).

tcf(c_80525,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,tl(sk3))))))
    | ( app(sk4,app(sk3,app(sk4,tl(sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,tl(sk3)))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65122,c_80146]) ).

tcf(c_80526,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,tl(sk3))))))
    | ( app(sk4,app(sk3,app(sk3,tl(sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,tl(sk3)))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,tl(sk3))))) ),
    inference(superposition,[status(thm)],[c_65123,c_80146]) ).

tcf(c_80527,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,tl(sk4)))))
    | ( cons(hd(sk4),app(sk4,tl(sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,tl(sk4))))
    | ~ ssList(cons(hd(sk4),app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_66119,c_80146]) ).

tcf(c_80528,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,tl(sk4)))))
    | ( cons(hd(sk3),app(sk4,tl(sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk4,tl(sk4))))
    | ~ ssList(cons(hd(sk3),app(sk4,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_66120,c_80146]) ).

tcf(c_80529,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,tl(sk4)))))
    | ( cons(hd(sk4),app(sk3,tl(sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,tl(sk4))))
    | ~ ssList(cons(hd(sk4),app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_67533,c_80146]) ).

tcf(c_80530,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,tl(sk4)))))
    | ( cons(hd(sk3),app(sk3,tl(sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,tl(sk4))))
    | ~ ssList(cons(hd(sk3),app(sk3,tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_67534,c_80146]) ).

tcf(c_80531,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,tl(sk3)))))
    | ( cons(hd(sk4),app(sk4,tl(sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk4,tl(sk3))))
    | ~ ssList(cons(hd(sk4),app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68656,c_80146]) ).

tcf(c_80532,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,tl(sk3)))))
    | ( cons(hd(sk3),app(sk4,tl(sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk4,tl(sk3))))
    | ~ ssList(cons(hd(sk3),app(sk4,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68657,c_80146]) ).

tcf(c_80533,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,tl(sk3)))))
    | ( cons(hd(sk4),app(sk3,tl(sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,tl(sk3))))
    | ~ ssList(cons(hd(sk4),app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68680,c_80146]) ).

tcf(c_80534,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,tl(sk3)))))
    | ( cons(hd(sk3),app(sk3,tl(sk3))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,tl(sk3))))
    | ~ ssList(cons(hd(sk3),app(sk3,tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_68681,c_80146]) ).

tcf(c_80535,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4)))))))
    | ( app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4))))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69810,c_80146]) ).

tcf(c_80536,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4)))))))
    | ( app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4))))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69811,c_80146]) ).

tcf(c_80537,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4)))))))
    | ( app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4))))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69815,c_80146]) ).

tcf(c_80538,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4)))))))
    | ( app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4))))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_69816,c_80146]) ).

tcf(c_80539,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4)))))))
    | ( app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4))))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70506,c_80146]) ).

tcf(c_80540,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4)))))))
    | ( app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4))))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70507,c_80146]) ).

tcf(c_80541,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4)))))))
    | ( app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4))))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70511,c_80146]) ).

tcf(c_80542,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4)))))))
    | ( app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_70512,c_80146]) ).

tcf(c_80543,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4)))))))
    | ( app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4))))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71450,c_80146]) ).

tcf(c_80544,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4)))))))
    | ( app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4))))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71451,c_80146]) ).

tcf(c_80545,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4)))))))
    | ( app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4))))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71455,c_80146]) ).

tcf(c_80546,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4)))))))
    | ( app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4))))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_71456,c_80146]) ).

tcf(c_80547,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3)))))))
    | ( app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3))))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72821,c_80146]) ).

tcf(c_80548,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3)))))))
    | ( app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3))))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72822,c_80146]) ).

tcf(c_80549,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3)))))))
    | ( app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3))))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72826,c_80146]) ).

tcf(c_80550,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3)))))))
    | ( app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3))))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_72827,c_80146]) ).

tcf(c_80551,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3)))))))
    | ( app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3))))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73439,c_80146]) ).

tcf(c_80552,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3)))))))
    | ( app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3))))))
    | ~ ssList(app(sk3,app(sk3,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73440,c_80146]) ).

tcf(c_80553,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3)))))))
    | ( app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3))))))
    | ~ ssList(app(sk4,app(sk4,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73444,c_80146]) ).

tcf(c_80554,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3)))))))
    | ( app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3))))))
    | ~ ssList(app(sk4,app(sk3,app(sk3,app(sk4,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73445,c_80146]) ).

tcf(c_80555,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3)))))))
    | ( app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3))))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73973,c_80146]) ).

tcf(c_80556,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3)))))))
    | ( app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3))))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73974,c_80146]) ).

tcf(c_80557,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3)))))))
    | ( app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3))))))
    | ~ ssList(app(sk4,app(sk4,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73978,c_80146]) ).

tcf(c_80558,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3)))))))
    | ( app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3))))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3))))))
    | ~ ssList(app(sk4,app(sk3,app(sk4,app(sk3,tl(sk3)))))) ),
    inference(superposition,[status(thm)],[c_73979,c_80146]) ).

tcf(c_80559,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),tl(sk4)))))
    | ( app(sk3,app(tl(sk4),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),tl(sk4))))
    | ~ ssList(app(sk3,app(tl(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_75977,c_80146]) ).

tcf(c_80560,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk3),sk3)))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_75978,c_80146]) ).

tcf(c_80561,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk4),sk3)))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_75979,c_80146]) ).

tcf(c_80562,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk4),sk4)))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_75981,c_80146]) ).

tcf(c_80563,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),tl(sk3)))))
    | ( app(sk3,app(tl(sk4),tl(sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),tl(sk3))))
    | ~ ssList(app(sk3,app(tl(sk4),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_75982,c_80146]) ).

tcf(c_80564,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_75987,c_80146]) ).

tcf(c_80565,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_75991,c_80146]) ).

tcf(c_80566,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_75997,c_80146]) ).

tcf(c_80567,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_75998,c_80146]) ).

tcf(c_80568,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_76002,c_80146]) ).

tcf(c_80569,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_76003,c_80146]) ).

tcf(c_80570,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_76004,c_80146]) ).

tcf(c_80571,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))))
    | ( app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))))
    | ~ ssList(app(sk3,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_76005,c_80146]) ).

tcf(c_80572,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),tl(sk4)))))
    | ( app(sk4,app(tl(sk4),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),tl(sk4))))
    | ~ ssList(app(sk4,app(tl(sk4),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_76489,c_80146]) ).

tcf(c_80573,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk3),sk3)))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_76490,c_80146]) ).

tcf(c_80574,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk4),sk3)))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_76491,c_80146]) ).

tcf(c_80575,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk4),sk4)))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_76493,c_80146]) ).

tcf(c_80576,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),tl(sk3)))))
    | ( app(sk4,app(tl(sk4),tl(sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),tl(sk3))))
    | ~ ssList(app(sk4,app(tl(sk4),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_76494,c_80146]) ).

tcf(c_80577,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3)))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_76499,c_80146]) ).

tcf(c_80578,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3)))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_76503,c_80146]) ).

tcf(c_80579,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4)))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_76509,c_80146]) ).

tcf(c_80580,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4)))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk4),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_76510,c_80146]) ).

tcf(c_80581,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4)))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk4))))) ),
    inference(superposition,[status(thm)],[c_76514,c_80146]) ).

tcf(c_80582,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3)))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk4,sk3))))) ),
    inference(superposition,[status(thm)],[c_76515,c_80146]) ).

tcf(c_80583,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4)))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk4))))) ),
    inference(superposition,[status(thm)],[c_76516,c_80146]) ).

tcf(c_80584,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))))
    | ( app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3)))))
    | ~ ssList(app(sk4,app(tl(sk4),cons(hd(sk3),app(sk3,sk3))))) ),
    inference(superposition,[status(thm)],[c_76517,c_80146]) ).

tcf(c_80585,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,cons(hd(sk3),tl(sk4)))))
    | ( app(sk3,cons(hd(sk3),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,cons(hd(sk3),tl(sk4))))
    | ~ ssList(app(sk3,cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_78856,c_80146]) ).

tcf(c_80586,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,cons(hd(sk3),tl(sk4)))))
    | ( app(sk4,cons(hd(sk3),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,cons(hd(sk3),tl(sk4))))
    | ~ ssList(app(sk4,cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_79675,c_80146]) ).

tcf(c_80587,plain,
    ! [X0: $i] :
      ( leq(hd(X0),hd(X0))
      | ( X0 = nil )
      | ~ totalorderedP(X0)
      | ~ ssList(X0)
      | ~ ssItem(hd(X0)) ),
    inference(superposition,[status(thm)],[c_80146,c_281]) ).

tcf(c_80634,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),sk4)))
    | ~ totalorderedP(cons(hd(sk4),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80159,c_4281,c_4223]) ).

tcf(c_80637,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),sk4)))
    | ( cons(hd(sk3),sk4) = nil )
    | ~ totalorderedP(cons(hd(sk3),sk4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80158,c_12796]) ).

tcf(c_80641,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),sk3)))
    | ~ totalorderedP(cons(hd(sk4),sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80157,c_4430,c_4358]) ).

tcf(c_80644,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),sk3)))
    | ( cons(hd(sk3),sk3) = nil )
    | ~ totalorderedP(cons(hd(sk3),sk3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80156,c_13784]) ).

tcf(c_80712,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(sk4)))))
    | ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80474,c_70418]) ).

tcf(c_80716,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,tl(sk3)))))
    | ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80473,c_73351]) ).

tcf(c_80728,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(sk4)))))
    | ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80419,c_69722]) ).

tcf(c_80732,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,tl(sk3)))))
    | ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80418,c_72733]) ).

tcf(c_80736,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(sk4)))))
    | ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80389,c_71362]) ).

tcf(c_80740,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,tl(sk3)))))
    | ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,tl(sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80388,c_73885]) ).

tcf(c_80760,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk3))))
    | ~ totalorderedP(cons(hd(sk3),app(sk3,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80307,c_20706,c_20483]) ).

tcf(c_80771,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk3))))
    | ~ totalorderedP(cons(hd(sk3),app(sk4,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80295,c_19513,c_19123]) ).

tcf(c_80774,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,sk4))))
    | ~ totalorderedP(cons(hd(sk3),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80270,c_17701,c_17697]) ).

tcf(c_80781,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk4,sk4))))
    | ~ totalorderedP(cons(hd(sk3),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80255,c_16926,c_16922]) ).

tcf(c_80796,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk4))))
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80209,c_10611,c_10606]) ).

tcf(c_80799,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk4))))
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk4))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80206,c_10190,c_10188]) ).

tcf(c_80810,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk4,sk3))))
    | ~ totalorderedP(cons(hd(sk4),app(sk4,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80182,c_7545,c_7540]) ).

tcf(c_80813,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,sk3))))
    | ~ totalorderedP(cons(hd(sk4),app(sk3,sk3))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80170,c_5891,c_5886]) ).

tcf(c_81112,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80288,c_44126,c_43441]) ).

tcf(c_81119,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80286,c_43038,c_42609]) ).

tcf(c_81150,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),sk4)))))
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80250,c_51895,c_51167]) ).

tcf(c_81157,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),sk3)))))
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80248,c_50642,c_50099]) ).

tcf(c_81808,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80291,c_61722]) ).

tcf(c_81812,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80290,c_46613]) ).

tcf(c_81816,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80289,c_44714]) ).

tcf(c_81864,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80253,c_59405]) ).

tcf(c_81868,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80252,c_53971]) ).

tcf(c_81872,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))
    | ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80251,c_52696]) ).

tcf(c_81880,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))
    | ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_80245,c_64396]) ).

tcf(c_84227,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( app(tl(sk4),tl(tl(X0))) = tl(app(sk4,tl(tl(X0)))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_5592]) ).

tcf(c_84228,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( app(tl(sk4),tl(app(X1,X0))) = tl(app(sk4,tl(app(X1,X0)))) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_5592]) ).

tcf(c_84229,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( app(tl(sk4),tl(cons(X1,X0))) = tl(app(sk4,tl(cons(X1,X0)))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_5592]) ).

tcf(c_84230,plain,
    ( ( tl(sk4) = nil )
    | ( app(tl(sk4),tl(tl(sk4))) = tl(app(sk4,tl(tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_62750,c_5592]) ).

tcf(c_84231,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk3),sk3))) = tl(app(sk4,tl(cons(hd(sk3),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_13784,c_5592]) ).

tcf(c_84232,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk4),sk3))) = tl(app(sk4,tl(cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_4358,c_5592]) ).

tcf(c_84233,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk3),sk4))) = tl(app(sk4,tl(cons(hd(sk3),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_12796,c_5592]) ).

tcf(c_84234,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk4),sk4))) = tl(app(sk4,tl(cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_4223,c_5592]) ).

tcf(c_84235,plain,
    ( ( tl(sk3) = nil )
    | ( app(tl(sk4),tl(tl(sk3))) = tl(app(sk4,tl(tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_65060,c_5592]) ).

tcf(c_84236,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( app(tl(sk4),tl(app(tl(sk3),sk3))) = tl(app(sk4,tl(app(tl(sk3),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_5592]) ).

tcf(c_84237,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( app(tl(sk4),tl(app(tl(sk3),sk4))) = tl(app(sk4,tl(app(tl(sk3),sk4)))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_5592]) ).

tcf(c_84238,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( app(tl(sk4),tl(app(tl(sk4),sk3))) = tl(app(sk4,tl(app(tl(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_5592]) ).

tcf(c_84239,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( app(tl(sk4),tl(app(tl(sk4),sk4))) = tl(app(sk4,tl(app(tl(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_22091,c_5592]) ).

tcf(c_84240,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk4),app(sk3,sk3)))) = tl(app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_5592]) ).

tcf(c_84241,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk3,sk3)))) = tl(app(sk4,tl(app(sk3,app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_5592]) ).

tcf(c_84242,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk3,sk4)))) = tl(app(sk4,tl(app(sk3,app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_5592]) ).

tcf(c_84243,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk3,sk3)))) = tl(app(sk4,tl(app(sk4,app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_5592]) ).

tcf(c_84244,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk4),app(sk4,sk3)))) = tl(app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_5592]) ).

tcf(c_84245,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk3,sk4)))) = tl(app(sk4,tl(app(sk4,app(sk3,sk4))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_5592]) ).

tcf(c_84246,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk4,sk3)))) = tl(app(sk4,tl(app(sk3,app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_5592]) ).

tcf(c_84247,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk4,sk4)))) = tl(app(sk4,tl(app(sk3,app(sk4,sk4))))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_5592]) ).

tcf(c_84248,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk4,sk3)))) = tl(app(sk4,tl(app(sk4,app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_5592]) ).

tcf(c_84249,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk4,sk4)))) = tl(app(sk4,tl(app(sk4,app(sk4,sk4))))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_5592]) ).

tcf(c_84250,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk4),app(sk3,sk4)))) = tl(app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_5592]) ).

tcf(c_84251,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk4),app(sk4,sk4)))) = tl(app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_5592]) ).

tcf(c_84252,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk3,cons(hd(sk4),sk3))))) = tl(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_5592]) ).

tcf(c_84253,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk3,cons(hd(sk4),sk4))))) = tl(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_5592]) ).

tcf(c_84254,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_5592]) ).

tcf(c_84255,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk3),app(sk4,sk4)))) = tl(app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_5592]) ).

tcf(c_84256,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk3),app(sk4,sk3)))) = tl(app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_5592]) ).

tcf(c_84257,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk3),app(sk3,sk4)))) = tl(app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_5592]) ).

tcf(c_84258,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk3),app(sk3,sk3)))) = tl(app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_5592]) ).

tcf(c_84259,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),sk3))))) = tl(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),sk3)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_5592]) ).

tcf(c_84260,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),sk4))))) = tl(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),sk4)))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_5592]) ).

tcf(c_84261,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_5592]) ).

tcf(c_84262,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_5592]) ).

tcf(c_84263,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_5592]) ).

tcf(c_84264,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_5592]) ).

tcf(c_84265,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_5592]) ).

tcf(c_84266,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_5592]) ).

tcf(c_84267,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk4,tl(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_5592]) ).

tcf(c_84268,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_5592]) ).

tcf(c_84269,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_5592]) ).

tcf(c_84270,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_5592]) ).

tcf(c_84271,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_5592]) ).

tcf(c_84272,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk4,tl(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_5592]) ).

tcf(c_84273,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))))) = tl(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_5592]) ).

tcf(c_84274,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))))) = tl(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_5592]) ).

tcf(c_84275,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))))) = tl(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_5592]) ).

tcf(c_84276,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk3,tl(sk4))))) = tl(app(sk4,tl(app(sk4,app(sk3,tl(sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_5592]) ).

tcf(c_84277,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk3,tl(sk3))))) = tl(app(sk4,tl(app(sk4,app(sk3,tl(sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_5592]) ).

tcf(c_84278,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk4,tl(sk4))))) = tl(app(sk4,tl(app(sk4,app(sk4,tl(sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_5592]) ).

tcf(c_84279,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( app(tl(sk4),tl(app(sk4,app(sk4,tl(sk3))))) = tl(app(sk4,tl(app(sk4,app(sk4,tl(sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_5592]) ).

tcf(c_84280,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk3,tl(sk4))))) = tl(app(sk4,tl(app(sk3,app(sk3,tl(sk4)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_5592]) ).

tcf(c_84281,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk3,tl(sk3))))) = tl(app(sk4,tl(app(sk3,app(sk3,tl(sk3)))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_5592]) ).

tcf(c_84282,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk4,tl(sk4))))) = tl(app(sk4,tl(app(sk3,app(sk4,tl(sk4)))))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_5592]) ).

tcf(c_84283,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( app(tl(sk4),tl(app(sk3,app(sk4,tl(sk3))))) = tl(app(sk4,tl(app(sk3,app(sk4,tl(sk3)))))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_5592]) ).

tcf(c_84316,plain,
    app(tl(sk4),tl(cons(hd(sk3),app(sk3,sk3)))) = tl(app(sk4,tl(cons(hd(sk3),app(sk3,sk3))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84258,c_20706]) ).

tcf(c_84317,plain,
    app(tl(sk4),tl(cons(hd(sk3),app(sk3,sk4)))) = tl(app(sk4,tl(cons(hd(sk3),app(sk3,sk4))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84257,c_17701]) ).

tcf(c_84318,plain,
    app(tl(sk4),tl(cons(hd(sk3),app(sk4,sk3)))) = tl(app(sk4,tl(cons(hd(sk3),app(sk4,sk3))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84256,c_19513]) ).

tcf(c_84319,plain,
    app(tl(sk4),tl(cons(hd(sk3),app(sk4,sk4)))) = tl(app(sk4,tl(cons(hd(sk3),app(sk4,sk4))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84255,c_16926]) ).

tcf(c_84320,plain,
    app(tl(sk4),tl(cons(hd(sk4),app(sk4,sk4)))) = tl(app(sk4,tl(cons(hd(sk4),app(sk4,sk4))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84251,c_10611]) ).

tcf(c_84321,plain,
    app(tl(sk4),tl(cons(hd(sk4),app(sk3,sk4)))) = tl(app(sk4,tl(cons(hd(sk4),app(sk3,sk4))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84250,c_10190]) ).

tcf(c_84322,plain,
    app(tl(sk4),tl(cons(hd(sk4),app(sk4,sk3)))) = tl(app(sk4,tl(cons(hd(sk4),app(sk4,sk3))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84244,c_7545]) ).

tcf(c_84323,plain,
    app(tl(sk4),tl(cons(hd(sk4),app(sk3,sk3)))) = tl(app(sk4,tl(cons(hd(sk4),app(sk3,sk3))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84240,c_5891]) ).

tcf(c_84369,plain,
    app(tl(sk4),tl(app(sk3,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk4)))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84264,c_44126]) ).

tcf(c_84370,plain,
    app(tl(sk4),tl(app(sk3,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk4,tl(app(sk3,app(sk4,cons(hd(sk4),sk3)))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84263,c_43038]) ).

tcf(c_84371,plain,
    app(tl(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),sk4))))) = tl(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk4)))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84262,c_51895]) ).

tcf(c_84372,plain,
    app(tl(sk4),tl(app(sk4,app(sk4,cons(hd(sk4),sk3))))) = tl(app(sk4,tl(app(sk4,app(sk4,cons(hd(sk4),sk3)))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_84261,c_50642]) ).

tcf(c_84832,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = nil )
      | ( hd(cons(hd(tl(X0)),cons(hd(sk4),sk4))) = hd(tl(X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_5646]) ).

tcf(c_84833,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,X0) = nil )
      | ( hd(cons(hd(app(X1,X0)),cons(hd(sk4),sk4))) = hd(app(X1,X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_5646]) ).

tcf(c_84834,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,X0) = nil )
      | ( hd(cons(hd(cons(X1,X0)),cons(hd(sk4),sk4))) = hd(cons(X1,X0)) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_5646]) ).

tcf(c_84835,plain,
    ( ( tl(sk4) = nil )
    | ( hd(cons(hd(tl(sk4)),cons(hd(sk4),sk4))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_62750,c_5646]) ).

tcf(c_84836,plain,
    ( ( cons(hd(sk3),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk3)),cons(hd(sk4),sk4))) = hd(cons(hd(sk3),sk3)) ) ),
    inference(superposition,[status(thm)],[c_13784,c_5646]) ).

tcf(c_84837,plain,
    ( ( cons(hd(sk4),sk3) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk3)),cons(hd(sk4),sk4))) = hd(cons(hd(sk4),sk3)) ) ),
    inference(superposition,[status(thm)],[c_4358,c_5646]) ).

tcf(c_84838,plain,
    ( ( cons(hd(sk3),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk3),sk4)),cons(hd(sk4),sk4))) = hd(cons(hd(sk3),sk4)) ) ),
    inference(superposition,[status(thm)],[c_12796,c_5646]) ).

tcf(c_84839,plain,
    ( ( cons(hd(sk4),sk4) = nil )
    | ( hd(cons(hd(cons(hd(sk4),sk4)),cons(hd(sk4),sk4))) = hd(cons(hd(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_4223,c_5646]) ).

tcf(c_84840,plain,
    ( ( tl(sk3) = nil )
    | ( hd(cons(hd(tl(sk3)),cons(hd(sk4),sk4))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_65060,c_5646]) ).

tcf(c_84841,plain,
    ( ( app(sk3,sk3) = nil )
    | ( app(tl(sk3),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk3)),cons(hd(sk4),sk4))) = hd(app(tl(sk3),sk3)) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_5646]) ).

tcf(c_84842,plain,
    ( ( app(sk3,sk4) = nil )
    | ( app(tl(sk3),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk3),sk4)),cons(hd(sk4),sk4))) = hd(app(tl(sk3),sk4)) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_5646]) ).

tcf(c_84843,plain,
    ( ( app(sk4,sk3) = nil )
    | ( app(tl(sk4),sk3) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk3)),cons(hd(sk4),sk4))) = hd(app(tl(sk4),sk3)) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_5646]) ).

tcf(c_84844,plain,
    ( ( app(sk4,sk4) = nil )
    | ( app(tl(sk4),sk4) = nil )
    | ( hd(cons(hd(app(tl(sk4),sk4)),cons(hd(sk4),sk4))) = hd(app(tl(sk4),sk4)) ) ),
    inference(superposition,[status(thm)],[c_22091,c_5646]) ).

tcf(c_84845,plain,
    ( ( cons(hd(sk4),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk3))),cons(hd(sk4),sk4))) = hd(cons(hd(sk4),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_5886,c_5646]) ).

tcf(c_84846,plain,
    ( ( app(sk3,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk3))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk3,sk3))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_5646]) ).

tcf(c_84847,plain,
    ( ( app(sk3,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,sk4))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk3,sk4))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_5646]) ).

tcf(c_84848,plain,
    ( ( app(sk4,app(sk3,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk3))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk3,sk3))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_5646]) ).

tcf(c_84849,plain,
    ( ( cons(hd(sk4),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk3))),cons(hd(sk4),sk4))) = hd(cons(hd(sk4),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_7540,c_5646]) ).

tcf(c_84850,plain,
    ( ( app(sk4,app(sk3,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,sk4))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk3,sk4))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_5646]) ).

tcf(c_84851,plain,
    ( ( app(sk3,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk3))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk4,sk3))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_5646]) ).

tcf(c_84852,plain,
    ( ( app(sk3,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,sk4))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk4,sk4))) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_5646]) ).

tcf(c_84853,plain,
    ( ( app(sk4,app(sk4,sk3)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk3))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk4,sk3))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_5646]) ).

tcf(c_84854,plain,
    ( ( app(sk4,app(sk4,sk4)) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,sk4))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk4,sk4))) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_5646]) ).

tcf(c_84855,plain,
    ( ( cons(hd(sk4),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk3,sk4))),cons(hd(sk4),sk4))) = hd(cons(hd(sk4),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10188,c_5646]) ).

tcf(c_84856,plain,
    ( ( cons(hd(sk4),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk4),app(sk4,sk4))),cons(hd(sk4),sk4))) = hd(cons(hd(sk4),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_10606,c_5646]) ).

tcf(c_84857,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_5646]) ).

tcf(c_84858,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_5646]) ).

tcf(c_84859,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_5646]) ).

tcf(c_84860,plain,
    ( ( cons(hd(sk3),app(sk4,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk4))),cons(hd(sk4),sk4))) = hd(cons(hd(sk3),app(sk4,sk4))) ) ),
    inference(superposition,[status(thm)],[c_16922,c_5646]) ).

tcf(c_84861,plain,
    ( ( cons(hd(sk3),app(sk4,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk4,sk3))),cons(hd(sk4),sk4))) = hd(cons(hd(sk3),app(sk4,sk3))) ) ),
    inference(superposition,[status(thm)],[c_19123,c_5646]) ).

tcf(c_84862,plain,
    ( ( cons(hd(sk3),app(sk3,sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk4))),cons(hd(sk4),sk4))) = hd(cons(hd(sk3),app(sk3,sk4))) ) ),
    inference(superposition,[status(thm)],[c_17697,c_5646]) ).

tcf(c_84863,plain,
    ( ( cons(hd(sk3),app(sk3,sk3)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),app(sk3,sk3))),cons(hd(sk4),sk4))) = hd(cons(hd(sk3),app(sk3,sk3))) ) ),
    inference(superposition,[status(thm)],[c_20483,c_5646]) ).

tcf(c_84864,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk3)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_5646]) ).

tcf(c_84865,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),sk4)))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_5646]) ).

tcf(c_84866,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_50099,c_5646]) ).

tcf(c_84867,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_51167,c_5646]) ).

tcf(c_84868,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk3)))) ) ),
    inference(superposition,[status(thm)],[c_42609,c_5646]) ).

tcf(c_84869,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),sk4)))) ) ),
    inference(superposition,[status(thm)],[c_43441,c_5646]) ).

tcf(c_84870,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_5646]) ).

tcf(c_84871,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_5646]) ).

tcf(c_84872,plain,
    ( ( app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_64396,c_5646]) ).

tcf(c_84873,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_52696,c_5646]) ).

tcf(c_84874,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_53971,c_5646]) ).

tcf(c_84875,plain,
    ( ( app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_59405,c_5646]) ).

tcf(c_84876,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_5646]) ).

tcf(c_84877,plain,
    ( ( app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_5646]) ).

tcf(c_84878,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_44714,c_5646]) ).

tcf(c_84879,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))) ) ),
    inference(superposition,[status(thm)],[c_46613,c_5646]) ).

tcf(c_84880,plain,
    ( ( app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4)))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))) ) ),
    inference(superposition,[status(thm)],[c_61722,c_5646]) ).

tcf(c_84881,plain,
    ( ( app(sk4,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk4)))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk3,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_71362,c_5646]) ).

tcf(c_84882,plain,
    ( ( app(sk4,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk3,tl(sk3)))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk3,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73885,c_5646]) ).

tcf(c_84883,plain,
    ( ( app(sk4,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk4)))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_69722,c_5646]) ).

tcf(c_84884,plain,
    ( ( app(sk4,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk4,app(sk4,tl(sk3)))),cons(hd(sk4),sk4))) = hd(app(sk4,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_72733,c_5646]) ).

tcf(c_84885,plain,
    ( ( app(sk3,app(sk3,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk4)))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk3,tl(sk4)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_5646]) ).

tcf(c_84886,plain,
    ( ( app(sk3,app(sk3,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk3,tl(sk3)))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk3,tl(sk3)))) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_5646]) ).

tcf(c_84887,plain,
    ( ( app(sk3,app(sk4,tl(sk4))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk4)))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk4,tl(sk4)))) ) ),
    inference(superposition,[status(thm)],[c_70418,c_5646]) ).

tcf(c_84888,plain,
    ( ( app(sk3,app(sk4,tl(sk3))) = nil )
    | ( hd(cons(hd(app(sk3,app(sk4,tl(sk3)))),cons(hd(sk4),sk4))) = hd(app(sk3,app(sk4,tl(sk3)))) ) ),
    inference(superposition,[status(thm)],[c_73351,c_5646]) ).

tcf(c_85074,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(sk4) = nil )
      | ( cons(hd(tl(sk4)),sk3) = nil )
      | ( cons(hd(tl(sk4)),sk3) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(tl(sk4)),sk3))
      | ( tl(X0) != sk3 )
      | ( hd(cons(hd(tl(sk4)),sk3)) != hd(X0) ) ),
    inference(superposition,[status(thm)],[c_62870,c_273]) ).

tcf(c_85085,plain,
    ( ( cons(hd(sk3),nil) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),tl(sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_63852,c_255]) ).

tcf(c_85086,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),tl(sk4)) != nil ) ),
    inference(superposition,[status(thm)],[c_63852,c_254]) ).

tcf(c_85087,plain,
    ( ssList(cons(hd(sk3),tl(sk4)))
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(superposition,[status(thm)],[c_63852,c_272]) ).

tcf(c_85088,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(cons(hd(sk3),nil),X0) != cons(hd(sk3),tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_63852,c_270]) ).

tcf(c_85089,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(tl(sk4))
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),tl(sk4)) != app(X0,tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_63852,c_269]) ).

tcf(c_85090,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),tl(sk4)) != cons(hd(sk3),sk3) ) ),
    inference(superposition,[status(thm)],[c_63852,c_13743]) ).

tcf(c_85091,plain,
    ( ( tl(sk4) = sk4 )
    | ~ ssList(tl(sk4))
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),tl(sk4)) != cons(hd(sk3),sk4) ) ),
    inference(superposition,[status(thm)],[c_63852,c_12754]) ).

tcf(c_85092,plain,
    ( ssList(cons(hd(sk3),tl(sk4)))
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_85087,c_62750]) ).

tcf(c_85095,plain,
    ( ( tl(sk4) = nil )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),tl(sk4)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_85086,c_62750]) ).

tcf(c_85099,plain,
    ( ( cons(hd(sk3),nil) = nil )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),tl(sk4)) != nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_85085,c_62750]) ).

tcf(c_85103,plain,
    ( ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),tl(sk4)) != cons(hd(sk3),sk4) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_85091,c_3659,c_62750]) ).

tcf(c_85106,plain,
    ( ( tl(sk4) = sk3 )
    | ~ ssList(cons(hd(sk3),nil))
    | ( cons(hd(sk3),tl(sk4)) != cons(hd(sk3),sk3) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_85090,c_62750]) ).

tcf(c_85110,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),nil) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( cons(hd(sk3),tl(sk4)) != app(X0,tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_85089,c_62750]) ).

tcf(c_85115,plain,
    ! [X0: $i] :
      ( ( tl(sk4) = X0 )
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),nil))
      | ( app(cons(hd(sk3),nil),X0) != cons(hd(sk3),tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_85088,c_62750]) ).

tcf(c_85229,plain,
    ssList(cons(hd(sk3),tl(sk4))),
    inference(global_subsumption_just,[status(thm)],[c_85092,c_247,c_246,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_7561,c_20375,c_85092]) ).

tcf(c_85231,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,app(cons(hd(sk3),tl(sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_18773]) ).

tcf(c_85232,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,app(cons(hd(sk3),tl(sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_18497]) ).

tcf(c_85233,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,app(cons(hd(sk3),tl(sk4)),X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_18185]) ).

tcf(c_85234,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,app(cons(hd(sk3),tl(sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_16330]) ).

tcf(c_85235,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,app(cons(hd(sk3),tl(sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_15966]) ).

tcf(c_85236,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,app(cons(hd(sk3),tl(sk4)),X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_15593]) ).

tcf(c_85237,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),tl(sk4)),nil),X0) = app(cons(hd(sk3),tl(sk4)),app(nil,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_4541]) ).

tcf(c_85238,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,app(cons(hd(sk3),tl(sk4)),X0))) = X1 )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3154]) ).

tcf(c_85239,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(cons(hd(sk3),tl(sk4)),X0))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_4037]) ).

tcf(c_85240,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(cons(hd(sk3),tl(sk4)),X0))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3952]) ).

tcf(c_85241,plain,
    ! [X0: $i] :
      ( ( app(nil,app(cons(hd(sk3),tl(sk4)),X0)) = app(cons(hd(sk3),tl(sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3050]) ).

tcf(c_85242,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),tl(sk4)),X0),nil) = app(cons(hd(sk3),tl(sk4)),X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3049]) ).

tcf(c_85243,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),tl(sk4)),sk4),X0) = app(cons(hd(sk3),tl(sk4)),app(sk4,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_4540]) ).

tcf(c_85244,plain,
    ! [X0: $i] :
      ( ( app(app(cons(hd(sk3),tl(sk4)),sk3),X0) = app(cons(hd(sk3),tl(sk4)),app(sk3,X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_4539]) ).

tcf(c_85245,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(X1,cons(hd(sk3),tl(sk4))),X0) = app(X1,app(cons(hd(sk3),tl(sk4)),X0)) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_271]) ).

tcf(c_85246,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(X1,app(X0,cons(hd(sk3),tl(sk4)))) = app(cons(X1,X0),cons(hd(sk3),tl(sk4))) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_266]) ).

tcf(c_85247,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = nil )
      | ( app(tl(cons(hd(sk3),tl(sk4))),X0) = tl(app(cons(hd(sk3),tl(sk4)),X0)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_274]) ).

tcf(c_85248,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = nil )
      | ( hd(app(cons(hd(sk3),tl(sk4)),X0)) = hd(cons(hd(sk3),tl(sk4))) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_283]) ).

tcf(c_85249,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),cons(hd(sk4),sk4))) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_5646]) ).

tcf(c_85250,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(tl(sk4),tl(cons(hd(sk3),tl(sk4)))) = tl(app(sk4,tl(cons(hd(sk3),tl(sk4))))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_5592]) ).

tcf(c_85251,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),tl(sk4))),nil)) = cons(hd(cons(hd(sk3),tl(sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_85229,c_4817]) ).

tcf(c_85252,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(tl(sk3),tl(cons(hd(sk3),tl(sk4)))) = tl(app(sk3,tl(cons(hd(sk3),tl(sk4))))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_4293]) ).

tcf(c_85253,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),tl(sk4))),sk4)) = cons(hd(cons(hd(sk3),tl(sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_4022]) ).

tcf(c_85254,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(nil,cons(hd(cons(hd(sk3),tl(sk4))),sk3)) = cons(hd(cons(hd(sk3),tl(sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_4014]) ).

tcf(c_85255,plain,
    hd(app(sk4,app(tl(sk4),cons(hd(sk3),tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_62761]) ).

tcf(c_85256,plain,
    hd(app(sk3,app(tl(sk4),cons(hd(sk3),tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_62760]) ).

tcf(c_85257,plain,
    app(tl(sk3),app(nil,cons(hd(sk3),tl(sk4)))) = app(tl(sk3),cons(hd(sk3),tl(sk4))),
    inference(superposition,[status(thm)],[c_85229,c_65316]) ).

tcf(c_85258,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),tl(sk4))),nil),nil) = cons(hd(cons(hd(sk3),tl(sk4))),nil) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3653]) ).

tcf(c_85259,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),tl(sk4))),nil),sk4) = cons(hd(cons(hd(sk3),tl(sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3470]) ).

tcf(c_85260,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),tl(sk4))),nil),sk3) = cons(hd(cons(hd(sk3),tl(sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3460]) ).

tcf(c_85261,plain,
    ( ( tl(sk3) = nil )
    | ( hd(app(tl(sk3),cons(hd(sk3),tl(sk4)))) = hd(tl(sk3)) ) ),
    inference(superposition,[status(thm)],[c_85229,c_65079]) ).

tcf(c_85262,plain,
    ( ( tl(sk4) = nil )
    | ( hd(app(tl(sk4),cons(hd(sk3),tl(sk4)))) = hd(tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_85229,c_62769]) ).

tcf(c_85263,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),tl(sk4))),tl(sk3))) = tl(sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_61402]) ).

tcf(c_85264,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),tl(sk4))),tl(sk4))) = tl(sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_61324]) ).

tcf(c_85265,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = nil )
      | ( tl(cons(X0,tl(cons(hd(sk3),tl(sk4))))) = tl(cons(hd(sk3),tl(sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3118]) ).

tcf(c_85266,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),app(sk4,sk4))) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_34548]) ).

tcf(c_85267,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),app(sk4,sk3))) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_34490]) ).

tcf(c_85268,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),app(sk3,sk4))) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_34149]) ).

tcf(c_85269,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),app(sk3,sk3))) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_34101]) ).

tcf(c_85270,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),tl(sk4))),nil))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_19899]) ).

tcf(c_85271,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),tl(sk4))),sk4))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_19024]) ).

tcf(c_85272,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk3,cons(hd(cons(hd(sk3),tl(sk4))),sk3))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_19014]) ).

tcf(c_85273,plain,
    hd(app(sk3,app(cons(hd(sk3),sk4),cons(hd(sk3),tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_17999]) ).

tcf(c_85274,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(nil,cons(X0,cons(hd(sk3),tl(sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_18774]) ).

tcf(c_85275,plain,
    hd(app(sk3,app(nil,app(nil,cons(hd(sk3),tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_57010]) ).

tcf(c_85276,plain,
    hd(app(sk3,app(nil,app(sk4,cons(hd(sk3),tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_57009]) ).

tcf(c_85277,plain,
    hd(app(sk3,app(nil,app(sk3,cons(hd(sk3),tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_57008]) ).

tcf(c_85278,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk3,app(nil,tl(cons(hd(sk3),tl(sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_18772]) ).

tcf(c_85279,plain,
    hd(app(sk4,app(cons(hd(sk3),sk4),cons(hd(sk3),tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_15409]) ).

tcf(c_85280,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk4,cons(X0,cons(hd(sk3),tl(sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_18498]) ).

tcf(c_85281,plain,
    hd(app(sk3,app(sk4,app(nil,cons(hd(sk3),tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_54564]) ).

tcf(c_85282,plain,
    hd(app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_54563]) ).

tcf(c_85283,plain,
    hd(app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_54562]) ).

tcf(c_85284,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk3,app(sk4,tl(cons(hd(sk3),tl(sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_18496]) ).

tcf(c_85285,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,app(sk3,cons(X0,cons(hd(sk3),tl(sk4)))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_18186]) ).

tcf(c_85286,plain,
    hd(app(sk3,app(sk3,app(nil,cons(hd(sk3),tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_48819]) ).

tcf(c_85287,plain,
    hd(app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_48818]) ).

tcf(c_85288,plain,
    hd(app(sk3,app(sk3,app(sk3,cons(hd(sk3),tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_48817]) ).

tcf(c_85289,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk3,app(sk3,tl(cons(hd(sk3),tl(sk4)))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_18184]) ).

tcf(c_85290,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),tl(sk4))),nil))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_17287]) ).

tcf(c_85291,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),tl(sk4))),sk4))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_16680]) ).

tcf(c_85292,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk4,cons(hd(cons(hd(sk3),tl(sk4))),sk3))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_16670]) ).

tcf(c_85293,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(nil,cons(X0,cons(hd(sk3),tl(sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_16331]) ).

tcf(c_85294,plain,
    hd(app(sk4,app(nil,app(nil,cons(hd(sk3),tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_45260]) ).

tcf(c_85295,plain,
    hd(app(sk4,app(nil,app(sk4,cons(hd(sk3),tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_45259]) ).

tcf(c_85296,plain,
    hd(app(sk4,app(nil,app(sk3,cons(hd(sk3),tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_45258]) ).

tcf(c_85297,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk4,app(nil,tl(cons(hd(sk3),tl(sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_16329]) ).

tcf(c_85298,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk4,cons(X0,cons(hd(sk3),tl(sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_15967]) ).

tcf(c_85299,plain,
    hd(app(sk4,app(sk4,app(nil,cons(hd(sk3),tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_40467]) ).

tcf(c_85300,plain,
    hd(app(sk4,app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_40466]) ).

tcf(c_85301,plain,
    hd(app(sk4,app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_40465]) ).

tcf(c_85302,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk4,app(sk4,tl(cons(hd(sk3),tl(sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_15965]) ).

tcf(c_85303,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,app(sk3,cons(X0,cons(hd(sk3),tl(sk4)))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_15594]) ).

tcf(c_85304,plain,
    hd(app(sk4,app(sk3,app(nil,cons(hd(sk3),tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_37606]) ).

tcf(c_85305,plain,
    hd(app(sk4,app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_37605]) ).

tcf(c_85306,plain,
    hd(app(sk4,app(sk3,app(sk3,cons(hd(sk3),tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_37604]) ).

tcf(c_85307,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk4,app(sk3,tl(cons(hd(sk3),tl(sk4)))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_15592]) ).

tcf(c_85308,plain,
    hd(app(sk3,app(cons(hd(sk4),sk4),cons(hd(sk3),tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_18000]) ).

tcf(c_85309,plain,
    hd(app(sk3,app(cons(hd(sk4),sk3),cons(hd(sk3),tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_17998]) ).

tcf(c_85310,plain,
    hd(app(sk3,app(cons(hd(sk3),sk3),cons(hd(sk3),tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_17997]) ).

tcf(c_85311,plain,
    app(sk3,app(nil,cons(hd(sk3),tl(sk4)))) = app(sk3,cons(hd(sk3),tl(sk4))),
    inference(superposition,[status(thm)],[c_85229,c_35790]) ).

tcf(c_85312,plain,
    app(sk4,app(nil,cons(hd(sk3),tl(sk4)))) = app(sk4,cons(hd(sk3),tl(sk4))),
    inference(superposition,[status(thm)],[c_85229,c_35787]) ).

tcf(c_85313,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),tl(sk4)),nil)) = app(cons(X0,cons(hd(sk3),tl(sk4))),nil) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_4463]) ).

tcf(c_85314,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(cons(X1,cons(X0,cons(hd(sk3),tl(sk4))))) = X1 )
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3155]) ).

tcf(c_85315,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(nil,cons(hd(sk3),tl(sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_33403]) ).

tcf(c_85316,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk4,cons(hd(sk3),tl(sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_33402]) ).

tcf(c_85317,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,cons(hd(sk3),tl(sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_33401]) ).

tcf(c_85318,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),tl(sk3))) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_32111]) ).

tcf(c_85319,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),tl(sk4))) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_32098]) ).

tcf(c_85320,plain,
    hd(app(sk4,app(cons(hd(sk4),sk4),cons(hd(sk3),tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_15410]) ).

tcf(c_85321,plain,
    hd(app(sk4,app(cons(hd(sk4),sk3),cons(hd(sk3),tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_15408]) ).

tcf(c_85322,plain,
    hd(app(sk4,app(cons(hd(sk3),sk3),cons(hd(sk3),tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_15407]) ).

tcf(c_85323,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = nil )
      | ( hd(cons(X0,tl(cons(hd(sk3),tl(sk4))))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3153]) ).

tcf(c_85324,plain,
    ! [X0: $i] :
      ( ( hd(app(sk3,cons(X0,cons(hd(sk3),tl(sk4))))) = hd(sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_4038]) ).

tcf(c_85325,plain,
    hd(app(sk3,app(nil,cons(hd(sk3),tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_17993]) ).

tcf(c_85326,plain,
    hd(app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_17992]) ).

tcf(c_85327,plain,
    hd(app(sk3,app(sk3,cons(hd(sk3),tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_17991]) ).

tcf(c_85328,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk3,tl(cons(hd(sk3),tl(sk4))))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_4036]) ).

tcf(c_85329,plain,
    ! [X0: $i] :
      ( ( hd(app(sk4,cons(X0,cons(hd(sk3),tl(sk4))))) = hd(sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3953]) ).

tcf(c_85330,plain,
    hd(app(sk4,app(nil,cons(hd(sk3),tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_15403]) ).

tcf(c_85331,plain,
    hd(app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_15402]) ).

tcf(c_85332,plain,
    hd(app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_15401]) ).

tcf(c_85333,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(app(sk4,tl(cons(hd(sk3),tl(sk4))))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3951]) ).

tcf(c_85334,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),nil)) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3423]) ).

tcf(c_85335,plain,
    app(nil,app(nil,cons(hd(sk3),tl(sk4)))) = app(nil,cons(hd(sk3),tl(sk4))),
    inference(superposition,[status(thm)],[c_85229,c_13452]) ).

tcf(c_85336,plain,
    app(app(nil,cons(hd(sk3),tl(sk4))),nil) = app(nil,cons(hd(sk3),tl(sk4))),
    inference(superposition,[status(thm)],[c_85229,c_12354]) ).

tcf(c_85337,plain,
    app(app(sk4,cons(hd(sk3),tl(sk4))),nil) = app(sk4,cons(hd(sk3),tl(sk4))),
    inference(superposition,[status(thm)],[c_85229,c_12353]) ).

tcf(c_85338,plain,
    app(app(sk3,cons(hd(sk3),tl(sk4))),nil) = app(sk3,cons(hd(sk3),tl(sk4))),
    inference(superposition,[status(thm)],[c_85229,c_12352]) ).

tcf(c_85339,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),tl(sk4))),nil)) = nil ) ),
    inference(superposition,[status(thm)],[c_85229,c_3199]) ).

tcf(c_85340,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(nil,tl(cons(hd(sk3),tl(sk4)))) = tl(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3066]) ).

tcf(c_85341,plain,
    app(nil,app(sk4,cons(hd(sk3),tl(sk4)))) = app(sk4,cons(hd(sk3),tl(sk4))),
    inference(superposition,[status(thm)],[c_85229,c_8061]) ).

tcf(c_85342,plain,
    app(app(sk4,sk4),cons(hd(sk3),tl(sk4))) = app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))),
    inference(superposition,[status(thm)],[c_85229,c_8048]) ).

tcf(c_85343,plain,
    app(nil,app(sk3,cons(hd(sk3),tl(sk4)))) = app(sk3,cons(hd(sk3),tl(sk4))),
    inference(superposition,[status(thm)],[c_85229,c_5745]) ).

tcf(c_85344,plain,
    app(app(sk3,sk4),cons(hd(sk3),tl(sk4))) = app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))),
    inference(superposition,[status(thm)],[c_85229,c_8047]) ).

tcf(c_85345,plain,
    app(app(sk4,sk3),cons(hd(sk3),tl(sk4))) = app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))),
    inference(superposition,[status(thm)],[c_85229,c_5738]) ).

tcf(c_85346,plain,
    app(app(sk3,sk3),cons(hd(sk3),tl(sk4))) = app(sk3,app(sk3,cons(hd(sk3),tl(sk4)))),
    inference(superposition,[status(thm)],[c_85229,c_5737]) ).

tcf(c_85347,plain,
    app(tl(sk4),cons(hd(sk3),tl(sk4))) = tl(app(sk4,cons(hd(sk3),tl(sk4)))),
    inference(superposition,[status(thm)],[c_85229,c_4136]) ).

tcf(c_85348,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),tl(sk4)),sk4)) = app(cons(X0,cons(hd(sk3),tl(sk4))),sk4) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_4462]) ).

tcf(c_85349,plain,
    ! [X0: $i] :
      ( ( cons(X0,app(cons(hd(sk3),tl(sk4)),sk3)) = app(cons(X0,cons(hd(sk3),tl(sk4))),sk3) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_4461]) ).

tcf(c_85350,plain,
    app(tl(sk3),cons(hd(sk3),tl(sk4))) = tl(app(sk3,cons(hd(sk3),tl(sk4)))),
    inference(superposition,[status(thm)],[c_85229,c_4284]) ).

tcf(c_85353,plain,
    ! [X0: $i] :
      ( ( app(nil,cons(X0,cons(hd(sk3),tl(sk4)))) = cons(X0,cons(hd(sk3),tl(sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3019]) ).

tcf(c_85354,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),tl(sk4))),sk4),nil) = cons(hd(cons(hd(sk3),tl(sk4))),sk4) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3452]) ).

tcf(c_85355,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(cons(hd(cons(hd(sk3),tl(sk4))),sk3),nil) = cons(hd(cons(hd(sk3),tl(sk4))),sk3) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3444]) ).

tcf(c_85356,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( app(tl(cons(hd(sk3),tl(sk4))),nil) = tl(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3065]) ).

tcf(c_85357,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),sk4)) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3215]) ).

tcf(c_85358,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( hd(cons(hd(cons(hd(sk3),tl(sk4))),sk3)) = hd(cons(hd(sk3),tl(sk4))) ) ),
    inference(superposition,[status(thm)],[c_85229,c_3207]) ).

tcf(c_85359,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,nil),cons(hd(sk3),tl(sk4))) = cons(X0,cons(hd(sk3),tl(sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_253]) ).

tcf(c_85360,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( cons(hd(cons(hd(sk3),tl(sk4))),tl(cons(hd(sk3),tl(sk4)))) = cons(hd(sk3),tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_85229,c_275]) ).

tcf(c_85361,plain,
    ! [X0: $i] :
      ( ( app(cons(X0,cons(hd(sk3),tl(sk4))),nil) = cons(X0,cons(hd(sk3),tl(sk4))) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_3018]) ).

tcf(c_85362,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),tl(sk4))),sk4)) = sk4 ) ),
    inference(superposition,[status(thm)],[c_85229,c_3191]) ).

tcf(c_85363,plain,
    ( ( cons(hd(sk3),tl(sk4)) = nil )
    | ( tl(cons(hd(cons(hd(sk3),tl(sk4))),sk3)) = sk3 ) ),
    inference(superposition,[status(thm)],[c_85229,c_3183]) ).

tcf(c_85364,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,cons(hd(sk3),tl(sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_284]) ).

tcf(c_85365,plain,
    ! [X0: $i] :
      ( ( tl(cons(X0,cons(hd(sk3),tl(sk4)))) = cons(hd(sk3),tl(sk4)) )
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_85229,c_276]) ).

tcf(c_85366,plain,
    app(cons(hd(sk3),tl(sk4)),nil) = cons(hd(sk3),tl(sk4)),
    inference(superposition,[status(thm)],[c_85229,c_258]) ).

tcf(c_85367,plain,
    app(nil,cons(hd(sk3),tl(sk4))) = cons(hd(sk3),tl(sk4)),
    inference(superposition,[status(thm)],[c_85229,c_257]) ).

tcf(c_85479,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = nil )
      | ( hd(app(cons(hd(sk3),tl(sk4)),X0)) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_85248,c_32100]) ).

tcf(c_85496,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = nil )
      | ( tl(app(cons(hd(sk3),tl(sk4)),X0)) = app(tl(sk4),X0) )
      | ~ ssList(X0) ),
    inference(light_normalisation,[status(thm)],[c_85247,c_61326]) ).

tcf(c_86327,plain,
    hd(app(sk3,app(tl(sk3),sk3))) = hd(sk3),
    inference(superposition,[status(thm)],[c_246,c_65070]) ).

tcf(c_86328,plain,
    hd(app(sk3,app(tl(sk3),sk4))) = hd(sk3),
    inference(superposition,[status(thm)],[c_247,c_65070]) ).

tcf(c_86329,plain,
    hd(app(sk3,app(tl(sk3),nil))) = hd(sk3),
    inference(superposition,[status(thm)],[c_259,c_65070]) ).

tcf(c_86330,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk3,app(tl(sk3),tl(X0)))) = hd(sk3) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_65070]) ).

tcf(c_86331,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(tl(sk3),app(X1,X0)))) = hd(sk3) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_65070]) ).

tcf(c_86332,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk3,app(tl(sk3),cons(X1,X0)))) = hd(sk3) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_65070]) ).

tcf(c_86333,plain,
    hd(app(sk3,app(tl(sk3),tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_62750,c_65070]) ).

tcf(c_86334,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk3),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_13784,c_65070]) ).

tcf(c_86335,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk4),sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4358,c_65070]) ).

tcf(c_86336,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk3),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_12796,c_65070]) ).

tcf(c_86337,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk4),sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_4223,c_65070]) ).

tcf(c_86338,plain,
    hd(app(sk3,app(tl(sk3),tl(sk3)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_65060,c_65070]) ).

tcf(c_86339,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk3,app(tl(sk3),app(tl(sk3),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_65070]) ).

tcf(c_86340,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk3,app(tl(sk3),app(tl(sk3),sk4)))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_65070]) ).

tcf(c_86341,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk3,app(tl(sk3),app(tl(sk4),sk3)))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_65070]) ).

tcf(c_86342,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk3,app(tl(sk3),app(tl(sk4),sk4)))) = hd(sk3) ) ),
    inference(superposition,[status(thm)],[c_22091,c_65070]) ).

tcf(c_86343,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk4),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_5886,c_65070]) ).

tcf(c_86344,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_65070]) ).

tcf(c_86345,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_65070]) ).

tcf(c_86346,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk4,app(sk3,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_65070]) ).

tcf(c_86347,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk4),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_7540,c_65070]) ).

tcf(c_86348,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk4,app(sk3,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_65070]) ).

tcf(c_86349,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_65070]) ).

tcf(c_86350,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_65070]) ).

tcf(c_86351,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk4,app(sk4,sk3))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_65070]) ).

tcf(c_86352,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk4,app(sk4,sk4))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_65070]) ).

tcf(c_86353,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk4),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10188,c_65070]) ).

tcf(c_86354,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk4),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10606,c_65070]) ).

tcf(c_86355,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_65070]) ).

tcf(c_86356,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_65070]) ).

tcf(c_86357,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_65070]) ).

tcf(c_86358,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk3),app(sk4,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_16922,c_65070]) ).

tcf(c_86359,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk3),app(sk4,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_19123,c_65070]) ).

tcf(c_86360,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk3),app(sk3,sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_17697,c_65070]) ).

tcf(c_86361,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk3),app(sk3,sk3))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_20483,c_65070]) ).

tcf(c_86362,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_65070]) ).

tcf(c_86363,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_65070]) ).

tcf(c_86364,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_50099,c_65070]) ).

tcf(c_86365,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_51167,c_65070]) ).

tcf(c_86366,plain,
    hd(app(sk3,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_42609,c_65070]) ).

tcf(c_86367,plain,
    hd(app(sk3,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_43441,c_65070]) ).

tcf(c_86368,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_65070]) ).

tcf(c_86369,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_65070]) ).

tcf(c_86370,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_64396,c_65070]) ).

tcf(c_86371,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_52696,c_65070]) ).

tcf(c_86372,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_53971,c_65070]) ).

tcf(c_86373,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_59405,c_65070]) ).

tcf(c_86374,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_65070]) ).

tcf(c_86375,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_65070]) ).

tcf(c_86376,plain,
    hd(app(sk3,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_44714,c_65070]) ).

tcf(c_86377,plain,
    hd(app(sk3,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_46613,c_65070]) ).

tcf(c_86378,plain,
    hd(app(sk3,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_61722,c_65070]) ).

tcf(c_86379,plain,
    hd(app(sk3,app(tl(sk3),cons(hd(sk3),tl(sk4))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_85229,c_65070]) ).

tcf(c_86380,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk3,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_71362,c_65070]) ).

tcf(c_86381,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk3,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73885,c_65070]) ).

tcf(c_86382,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_69722,c_65070]) ).

tcf(c_86383,plain,
    hd(app(sk3,app(tl(sk3),app(sk4,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_72733,c_65070]) ).

tcf(c_86384,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk3,tl(sk4)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_65070]) ).

tcf(c_86385,plain,
    ( ( hd(app(sk3,app(tl(sk3),app(sk3,app(sk3,tl(sk3)))))) = hd(sk3) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_65070]) ).

tcf(c_86386,plain,
    hd(app(sk3,app(tl(sk3),app(sk3,app(sk4,tl(sk4)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_70418,c_65070]) ).

tcf(c_86387,plain,
    hd(app(sk3,app(tl(sk3),app(sk3,app(sk4,tl(sk3)))))) = hd(sk3),
    inference(superposition,[status(thm)],[c_73351,c_65070]) ).

tcf(c_86656,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk3),sk3))))
    | ( app(sk3,app(tl(sk3),sk3)) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk3),sk3)))
    | ~ ssList(app(sk3,app(tl(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_86327,c_80146]) ).

tcf(c_86658,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk3),sk3))))
      | ( app(sk3,app(tl(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk3),sk3)))
      | ~ ssList(app(sk3,app(tl(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_86327,c_280]) ).

tcf(c_86659,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk3),sk3))))
      | ( app(sk3,app(tl(sk3),sk3)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk3),sk3)))
      | ~ ssList(app(sk3,app(tl(sk3),sk3))) ),
    inference(superposition,[status(thm)],[c_86327,c_279]) ).

tcf(c_86678,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk3),sk4))))
    | ( app(sk3,app(tl(sk3),sk4)) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk3),sk4)))
    | ~ ssList(app(sk3,app(tl(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_86328,c_80146]) ).

tcf(c_86680,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk3),sk4))))
      | ( app(sk3,app(tl(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk3),sk4)))
      | ~ ssList(app(sk3,app(tl(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_86328,c_280]) ).

tcf(c_86681,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk3),sk4))))
      | ( app(sk3,app(tl(sk3),sk4)) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk3),sk4)))
      | ~ ssList(app(sk3,app(tl(sk3),sk4))) ),
    inference(superposition,[status(thm)],[c_86328,c_279]) ).

tcf(c_86738,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),sk4)))
    | ( cons(hd(sk4),sk4) = nil )
    | ~ ssItem(hd(sk4))
    | ~ totalorderedP(cons(hd(sk4),sk4))
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(superposition,[status(thm)],[c_80634,c_281]) ).

tcf(c_86740,plain,
    ( leq(hd(sk4),hd(sk4))
    | ( cons(hd(sk4),sk4) = nil )
    | ~ ssItem(hd(sk4))
    | ~ totalorderedP(cons(hd(sk4),sk4))
    | ~ ssList(cons(hd(sk4),sk4)) ),
    inference(light_normalisation,[status(thm)],[c_86738,c_3537]) ).

tcf(c_86745,plain,
    ( leq(hd(sk4),hd(cons(hd(sk4),sk3)))
    | ( cons(hd(sk4),sk3) = nil )
    | ~ ssItem(hd(sk4))
    | ~ totalorderedP(cons(hd(sk4),sk3))
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(superposition,[status(thm)],[c_80641,c_281]) ).

tcf(c_86747,plain,
    ( leq(hd(sk4),hd(sk4))
    | ( cons(hd(sk4),sk3) = nil )
    | ~ ssItem(hd(sk4))
    | ~ totalorderedP(cons(hd(sk4),sk3))
    | ~ ssList(cons(hd(sk4),sk3)) ),
    inference(light_normalisation,[status(thm)],[c_86745,c_3488]) ).

tcf(c_86748,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))))
    | ( app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))
    | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85326,c_80146]) ).

tcf(c_86750,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85326,c_280]) ).

tcf(c_86751,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))))
      | ( app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))
      | ~ ssList(app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85326,c_279]) ).

tcf(c_86770,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,cons(hd(sk3),tl(sk4))))))
    | ( app(sk3,app(sk3,cons(hd(sk3),tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),tl(sk4)))))
    | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85327,c_80146]) ).

tcf(c_86772,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),tl(sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,cons(hd(sk3),tl(sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85327,c_280]) ).

tcf(c_86773,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,cons(hd(sk3),tl(sk4))))))
      | ( app(sk3,app(sk3,cons(hd(sk3),tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,cons(hd(sk3),tl(sk4)))))
      | ~ ssList(app(sk3,app(sk3,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85327,c_279]) ).

tcf(c_86836,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))))
    | ( app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))
    | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85331,c_80146]) ).

tcf(c_86838,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85331,c_280]) ).

tcf(c_86839,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))))
      | ( app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))
      | ~ ssList(app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85331,c_279]) ).

tcf(c_86858,plain,
    ( totalorderedP(cons(hd(sk4),app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))))
    | ( app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))) = nil )
    | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))
    | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85332,c_80146]) ).

tcf(c_86860,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85332,c_280]) ).

tcf(c_86861,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))))
      | ( app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))
      | ~ ssList(app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))) ),
    inference(superposition,[status(thm)],[c_85332,c_279]) ).

tcf(c_86880,plain,
    cons(hd(sk4),app(sk3,sk3)) != cons(hd(sk4),sk3),
    inference(global_subsumption_just,[status(thm)],[c_10410,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_10410]) ).

tcf(c_86886,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),cons(hd(sk3),tl(sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_85364]) ).

tcf(c_86887,plain,
    hd(cons(hd(sk4),cons(hd(sk3),tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_85364]) ).

tcf(c_86888,plain,
    hd(cons(hd(sk3),cons(hd(sk3),tl(sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_85364]) ).

tcf(c_86900,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),tl(sk4)))
      | ( app(cons(hd(sk3),tl(sk4)),X0) != cons(hd(sk3),tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_85366,c_270]) ).

tcf(c_86901,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),tl(sk4)))
      | ( cons(hd(sk3),tl(sk4)) != app(X0,nil) ) ),
    inference(superposition,[status(thm)],[c_85366,c_269]) ).

tcf(c_86902,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),tl(sk4)) != app(X0,nil) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_86901,c_259,c_85229]) ).

tcf(c_86906,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(cons(hd(sk3),tl(sk4)),X0) != cons(hd(sk3),tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_86900,c_259,c_85229]) ).

tcf(c_86919,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = X0 )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),tl(sk4)))
      | ( cons(hd(sk3),tl(sk4)) != app(nil,X0) ) ),
    inference(superposition,[status(thm)],[c_85367,c_270]) ).

tcf(c_86920,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(cons(hd(sk3),tl(sk4)))
      | ( app(X0,cons(hd(sk3),tl(sk4))) != cons(hd(sk3),tl(sk4)) ) ),
    inference(superposition,[status(thm)],[c_85367,c_269]) ).

tcf(c_86921,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk4))
      | ~ ssList(app(cons(hd(sk3),tl(sk4)),cons(X0,X1)))
      | ~ totalorderedP(app(app(nil,cons(hd(sk3),tl(sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_85367,c_300]) ).

tcf(c_86922,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk4))
      | ~ ssList(app(cons(hd(sk3),tl(sk4)),cons(X0,X1)))
      | ~ strictorderedP(app(app(nil,cons(hd(sk3),tl(sk4))),cons(X0,X1))) ),
    inference(superposition,[status(thm)],[c_85367,c_287]) ).

tcf(c_86923,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ( app(X0,cons(hd(sk3),tl(sk4))) != cons(hd(sk3),tl(sk4)) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_86920,c_259,c_85229]) ).

tcf(c_86927,plain,
    ! [X0: $i] :
      ( ( cons(hd(sk3),tl(sk4)) = X0 )
      | ~ ssList(X0)
      | ( cons(hd(sk3),tl(sk4)) != app(nil,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_86919,c_259,c_85229]) ).

tcf(c_86931,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk4))
      | ~ strictorderedP(app(cons(hd(sk3),tl(sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),tl(sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_86922,c_85367]) ).

tcf(c_86932,plain,
    ! [X0: $i,X1: $i] :
      ( lt(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ strictorderedP(app(cons(hd(sk3),tl(sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),tl(sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_86931,c_259,c_10117,c_62750]) ).

tcf(c_86938,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssList(nil)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssItem(hd(sk3))
      | ~ ssList(tl(sk4))
      | ~ totalorderedP(app(cons(hd(sk3),tl(sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),tl(sk4)),cons(X0,X1))) ),
    inference(light_normalisation,[status(thm)],[c_86921,c_85367]) ).

tcf(c_86939,plain,
    ! [X0: $i,X1: $i] :
      ( leq(hd(sk3),X0)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ totalorderedP(app(cons(hd(sk3),tl(sk4)),cons(X0,X1)))
      | ~ ssList(app(cons(hd(sk3),tl(sk4)),cons(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_86938,c_259,c_10117,c_62750]) ).

tcf(c_87068,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(cons(hd(X0),cons(hd(sk3),tl(sk4)))) = cons(hd(sk3),tl(sk4)) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_85365]) ).

tcf(c_87069,plain,
    tl(cons(hd(sk4),cons(hd(sk3),tl(sk4)))) = cons(hd(sk3),tl(sk4)),
    inference(superposition,[status(thm)],[c_4059,c_85365]) ).

tcf(c_87070,plain,
    tl(cons(hd(sk3),cons(hd(sk3),tl(sk4)))) = cons(hd(sk3),tl(sk4)),
    inference(superposition,[status(thm)],[c_10117,c_85365]) ).

tcf(c_87074,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk3),tl(sk4)))))
    | ( app(sk3,app(tl(sk3),tl(sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk3),tl(sk4))))
    | ~ ssList(app(sk3,app(tl(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_86333,c_80146]) ).

tcf(c_87076,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk3),tl(sk4)))))
      | ( app(sk3,app(tl(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk3),tl(sk4))))
      | ~ ssList(app(sk3,app(tl(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_86333,c_280]) ).

tcf(c_87077,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk3),tl(sk4)))))
      | ( app(sk3,app(tl(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk3),tl(sk4))))
      | ~ ssList(app(sk3,app(tl(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_86333,c_279]) ).

tcf(c_87096,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk3),tl(sk3)))))
    | ( app(sk3,app(tl(sk3),tl(sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk3),tl(sk3))))
    | ~ ssList(app(sk3,app(tl(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_86338,c_80146]) ).

tcf(c_87098,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk3),tl(sk3)))))
      | ( app(sk3,app(tl(sk3),tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk3),tl(sk3))))
      | ~ ssList(app(sk3,app(tl(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_86338,c_280]) ).

tcf(c_87099,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk3),tl(sk3)))))
      | ( app(sk3,app(tl(sk3),tl(sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk3),tl(sk3))))
      | ~ ssList(app(sk3,app(tl(sk3),tl(sk3)))) ),
    inference(superposition,[status(thm)],[c_86338,c_279]) ).

tcf(c_87118,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),cons(hd(sk3),tl(sk4)))))
    | ( cons(hd(sk4),cons(hd(sk3),tl(sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),tl(sk4))))
    | ~ ssList(cons(hd(sk4),cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_86887,c_80146]) ).

tcf(c_87120,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),tl(sk4)))))
      | ( cons(hd(sk4),cons(hd(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),cons(hd(sk3),tl(sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_86887,c_280]) ).

tcf(c_87121,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),cons(hd(sk3),tl(sk4)))))
      | ( cons(hd(sk4),cons(hd(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),cons(hd(sk3),tl(sk4))))
      | ~ ssList(cons(hd(sk4),cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_86887,c_279]) ).

tcf(c_87140,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),cons(hd(sk3),tl(sk4)))))
    | ( cons(hd(sk3),cons(hd(sk3),tl(sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(sk4))))
    | ~ ssList(cons(hd(sk3),cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_86888,c_80146]) ).

tcf(c_87142,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),tl(sk4)))))
      | ( cons(hd(sk3),cons(hd(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),cons(hd(sk3),tl(sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_86888,c_280]) ).

tcf(c_87143,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),cons(hd(sk3),tl(sk4)))))
      | ( cons(hd(sk3),cons(hd(sk3),tl(sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),cons(hd(sk3),tl(sk4))))
      | ~ ssList(cons(hd(sk3),cons(hd(sk3),tl(sk4)))) ),
    inference(superposition,[status(thm)],[c_86888,c_279]) ).

tcf(c_87162,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk3),cons(hd(sk3),sk3)))))
    | ( app(sk3,app(tl(sk3),cons(hd(sk3),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk3),cons(hd(sk3),sk3))))
    | ~ ssList(app(sk3,app(tl(sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_86334,c_80146]) ).

tcf(c_87164,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk3),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(tl(sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(tl(sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_86334,c_280]) ).

tcf(c_87165,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk3),cons(hd(sk3),sk3)))))
      | ( app(sk3,app(tl(sk3),cons(hd(sk3),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk3),cons(hd(sk3),sk3))))
      | ~ ssList(app(sk3,app(tl(sk3),cons(hd(sk3),sk3)))) ),
    inference(superposition,[status(thm)],[c_86334,c_279]) ).

tcf(c_87184,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk3),cons(hd(sk4),sk3)))))
    | ( app(sk3,app(tl(sk3),cons(hd(sk4),sk3))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk3),cons(hd(sk4),sk3))))
    | ~ ssList(app(sk3,app(tl(sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_86335,c_80146]) ).

tcf(c_87186,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk3),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(tl(sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(tl(sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_86335,c_280]) ).

tcf(c_87187,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk3),cons(hd(sk4),sk3)))))
      | ( app(sk3,app(tl(sk3),cons(hd(sk4),sk3))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk3),cons(hd(sk4),sk3))))
      | ~ ssList(app(sk3,app(tl(sk3),cons(hd(sk4),sk3)))) ),
    inference(superposition,[status(thm)],[c_86335,c_279]) ).

tcf(c_87235,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(tl(sk3),cons(hd(sk4),sk4)))))
    | ( app(sk3,app(tl(sk3),cons(hd(sk4),sk4))) = nil )
    | ~ totalorderedP(app(sk3,app(tl(sk3),cons(hd(sk4),sk4))))
    | ~ ssList(app(sk3,app(tl(sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_86337,c_80146]) ).

tcf(c_87237,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(tl(sk3),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(tl(sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(tl(sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(tl(sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_86337,c_280]) ).

tcf(c_87238,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(tl(sk3),cons(hd(sk4),sk4)))))
      | ( app(sk3,app(tl(sk3),cons(hd(sk4),sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(tl(sk3),cons(hd(sk4),sk4))))
      | ~ ssList(app(sk3,app(tl(sk3),cons(hd(sk4),sk4)))) ),
    inference(superposition,[status(thm)],[c_86337,c_279]) ).

tcf(c_87277,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))))
    | ( app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))))
    | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_85282,c_80146]) ).

tcf(c_87279,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_85282,c_280]) ).

tcf(c_87280,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk4,cons(hd(sk3),tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_85282,c_279]) ).

tcf(c_87299,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))))
    | ( app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))))
    | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_85283,c_80146]) ).

tcf(c_87301,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_85283,c_280]) ).

tcf(c_87302,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))))
      | ( app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4))))))
      | ~ ssList(app(sk3,app(sk4,app(sk3,cons(hd(sk3),tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_85283,c_279]) ).

tcf(c_87321,plain,
    ( totalorderedP(cons(hd(sk3),app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))))
    | ( app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))) = nil )
    | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))))
    | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_85287,c_80146]) ).

tcf(c_87323,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_85287,c_280]) ).

tcf(c_87324,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))))
      | ( app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4))))))
      | ~ ssList(app(sk3,app(sk3,app(sk4,cons(hd(sk3),tl(sk4)))))) ),
    inference(superposition,[status(thm)],[c_85287,c_279]) ).

tcf(c_87343,plain,
    cons(hd(sk4),app(sk4,sk3)) != cons(hd(sk4),sk4),
    inference(global_subsumption_just,[status(thm)],[c_10445,c_247,c_259,c_1242,c_3427,c_3439,c_3582,c_3703,c_3715,c_10445]) ).

tcf(c_87345,plain,
    ! [X0: $i] :
      ( ( hd(cons(X0,app(sk3,app(sk3,sk4)))) = X0 )
      | ~ ssItem(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_7006,c_65569]) ).

tcf(c_87351,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(cons(hd(X0),app(sk3,app(sk3,sk4)))) = hd(X0) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_286,c_87345]) ).

tcf(c_87352,plain,
    hd(cons(hd(sk4),app(sk3,app(sk3,sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4059,c_87345]) ).

tcf(c_87353,plain,
    hd(cons(hd(sk3),app(sk3,app(sk3,sk4)))) = hd(sk3),
    inference(superposition,[status(thm)],[c_10117,c_87345]) ).

tcf(c_87357,plain,
    ( totalorderedP(cons(hd(sk4),cons(hd(sk4),app(sk3,app(sk3,sk4)))))
    | ( cons(hd(sk4),app(sk3,app(sk3,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk4),app(sk3,app(sk3,sk4))))
    | ~ ssList(cons(hd(sk4),app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_87352,c_80146]) ).

tcf(c_87359,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk4),app(sk3,app(sk3,sk4)))))
      | ( cons(hd(sk4),app(sk3,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk4))
      | ~ totalorderedP(cons(hd(sk4),app(sk3,app(sk3,sk4))))
      | ~ ssList(cons(hd(sk4),app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_87352,c_280]) ).

tcf(c_87360,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk4),app(sk3,app(sk3,sk4)))))
      | ( cons(hd(sk4),app(sk3,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk4))
      | ~ strictorderedP(cons(hd(sk4),app(sk3,app(sk3,sk4))))
      | ~ ssList(cons(hd(sk4),app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_87352,c_279]) ).

tcf(c_87379,plain,
    ( totalorderedP(cons(hd(sk3),cons(hd(sk3),app(sk3,app(sk3,sk4)))))
    | ( cons(hd(sk3),app(sk3,app(sk3,sk4))) = nil )
    | ~ totalorderedP(cons(hd(sk3),app(sk3,app(sk3,sk4))))
    | ~ ssList(cons(hd(sk3),app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_87353,c_80146]) ).

tcf(c_87381,plain,
    ! [X0: $i] :
      ( totalorderedP(cons(X0,cons(hd(sk3),app(sk3,app(sk3,sk4)))))
      | ( cons(hd(sk3),app(sk3,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ leq(X0,hd(sk3))
      | ~ totalorderedP(cons(hd(sk3),app(sk3,app(sk3,sk4))))
      | ~ ssList(cons(hd(sk3),app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_87353,c_280]) ).

tcf(c_87382,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,cons(hd(sk3),app(sk3,app(sk3,sk4)))))
      | ( cons(hd(sk3),app(sk3,app(sk3,sk4))) = nil )
      | ~ ssItem(X0)
      | ~ lt(X0,hd(sk3))
      | ~ strictorderedP(cons(hd(sk3),app(sk3,app(sk3,sk4))))
      | ~ ssList(cons(hd(sk3),app(sk3,app(sk3,sk4)))) ),
    inference(superposition,[status(thm)],[c_87353,c_279]) ).

tcf(c_87423,plain,
    hd(app(sk4,app(tl(sk3),sk3))) = hd(sk4),
    inference(superposition,[status(thm)],[c_246,c_65071]) ).

tcf(c_87424,plain,
    hd(app(sk4,app(tl(sk3),sk4))) = hd(sk4),
    inference(superposition,[status(thm)],[c_247,c_65071]) ).

tcf(c_87425,plain,
    hd(app(sk4,app(tl(sk3),nil))) = hd(sk4),
    inference(superposition,[status(thm)],[c_259,c_65071]) ).

tcf(c_87426,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(app(sk4,app(tl(sk3),tl(X0)))) = hd(sk4) )
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_278,c_65071]) ).

tcf(c_87427,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(tl(sk3),app(X1,X0)))) = hd(sk4) )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_272,c_65071]) ).

tcf(c_87428,plain,
    ! [X0: $i,X1: $i] :
      ( ( hd(app(sk4,app(tl(sk3),cons(X1,X0)))) = hd(sk4) )
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(superposition,[status(thm)],[c_268,c_65071]) ).

tcf(c_87429,plain,
    hd(app(sk4,app(tl(sk3),tl(sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_62750,c_65071]) ).

tcf(c_87430,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk3),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_13784,c_65071]) ).

tcf(c_87431,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk4),sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4358,c_65071]) ).

tcf(c_87432,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk3),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_12796,c_65071]) ).

tcf(c_87433,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk4),sk4)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_4223,c_65071]) ).

tcf(c_87434,plain,
    hd(app(sk4,app(tl(sk3),tl(sk3)))) = hd(sk4),
    inference(superposition,[status(thm)],[c_65060,c_65071]) ).

tcf(c_87435,plain,
    ( ( app(sk3,sk3) = nil )
    | ( hd(app(sk4,app(tl(sk3),app(tl(sk3),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_4309,c_65071]) ).

tcf(c_87436,plain,
    ( ( app(sk3,sk4) = nil )
    | ( hd(app(sk4,app(tl(sk3),app(tl(sk3),sk4)))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_4313,c_65071]) ).

tcf(c_87437,plain,
    ( ( app(sk4,sk3) = nil )
    | ( hd(app(sk4,app(tl(sk3),app(tl(sk4),sk3)))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_5634,c_65071]) ).

tcf(c_87438,plain,
    ( ( app(sk4,sk4) = nil )
    | ( hd(app(sk4,app(tl(sk3),app(tl(sk4),sk4)))) = hd(sk4) ) ),
    inference(superposition,[status(thm)],[c_22091,c_65071]) ).

tcf(c_87439,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk4),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_5886,c_65071]) ).

tcf(c_87440,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6586,c_65071]) ).

tcf(c_87441,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_6934,c_65071]) ).

tcf(c_87442,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk4,app(sk3,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7243,c_65071]) ).

tcf(c_87443,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk4),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_7540,c_65071]) ).

tcf(c_87444,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk4,app(sk3,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_7754,c_65071]) ).

tcf(c_87445,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8252,c_65071]) ).

tcf(c_87446,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk4)) ),
    inference(superposition,[status(thm)],[c_8538,c_65071]) ).

tcf(c_87447,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk4,app(sk4,sk3))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9229,c_65071]) ).

tcf(c_87448,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk4,app(sk4,sk4))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk4)) ),
    inference(superposition,[status(thm)],[c_9513,c_65071]) ).

tcf(c_87449,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk4),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10188,c_65071]) ).

tcf(c_87450,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk4),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_10606,c_65071]) ).

tcf(c_87451,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_11248,c_65071]) ).

tcf(c_87452,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_12015,c_65071]) ).

tcf(c_87453,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_13113,c_65071]) ).

tcf(c_87454,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk3),app(sk4,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_16922,c_65071]) ).

tcf(c_87455,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk3),app(sk4,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_19123,c_65071]) ).

tcf(c_87456,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk3),app(sk3,sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_17697,c_65071]) ).

tcf(c_87457,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk3),app(sk3,sk3))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_20483,c_65071]) ).

tcf(c_87458,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_22967,c_65071]) ).

tcf(c_87459,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_23820,c_65071]) ).

tcf(c_87460,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_50099,c_65071]) ).

tcf(c_87461,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_51167,c_65071]) ).

tcf(c_87462,plain,
    hd(app(sk4,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_42609,c_65071]) ).

tcf(c_87463,plain,
    hd(app(sk4,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_43441,c_65071]) ).

tcf(c_87464,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_28923,c_65071]) ).

tcf(c_87465,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk4,sk3)) ),
    inference(superposition,[status(thm)],[c_29288,c_65071]) ).

tcf(c_87466,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_64396,c_65071]) ).

tcf(c_87467,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_52696,c_65071]) ).

tcf(c_87468,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_53971,c_65071]) ).

tcf(c_87469,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_59405,c_65071]) ).

tcf(c_87470,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_29715,c_65071]) ).

tcf(c_87471,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk3,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_66135,c_65071]) ).

tcf(c_87472,plain,
    hd(app(sk4,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_44714,c_65071]) ).

tcf(c_87473,plain,
    hd(app(sk4,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk4,sk3))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_46613,c_65071]) ).

tcf(c_87474,plain,
    hd(app(sk4,app(tl(sk3),app(sk3,app(sk4,cons(hd(sk4),app(sk3,sk4))))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_61722,c_65071]) ).

tcf(c_87475,plain,
    hd(app(sk4,app(tl(sk3),cons(hd(sk3),tl(sk4))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_85229,c_65071]) ).

tcf(c_87476,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk3,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_71362,c_65071]) ).

tcf(c_87477,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk3,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73885,c_65071]) ).

tcf(c_87478,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_69722,c_65071]) ).

tcf(c_87479,plain,
    hd(app(sk4,app(tl(sk3),app(sk4,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_72733,c_65071]) ).

tcf(c_87480,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk3,tl(sk4)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69515,c_65071]) ).

tcf(c_87481,plain,
    ( ( hd(app(sk4,app(tl(sk3),app(sk3,app(sk3,tl(sk3)))))) = hd(sk4) )
    | ~ ssList(app(sk3,sk3)) ),
    inference(superposition,[status(thm)],[c_69689,c_65071]) ).

tcf(c_87482,plain,
    hd(app(sk4,app(tl(sk3),app(sk3,app(sk4,tl(sk4)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_70418,c_65071]) ).

tcf(c_87483,plain,
    hd(app(sk4,app(tl(sk3),app(sk3,app(sk4,tl(sk3)))))) = hd(sk4),
    inference(superposition,[status(thm)],[c_73351,c_65071]) ).

tcf(c_88342,plain,
    $false,
    inference(smt_impl_just,[status(thm)],[c_87483,c_87482,c_87481,c_87480,c_87479,c_87478,c_87477,c_87476,c_87475,c_87474,c_87473,c_87472,c_87471,c_87470,c_87469,c_87468,c_87467,c_87466,c_87465,c_87464,c_87463,c_87462,c_87461,c_87460,c_87459,c_87458,c_87457,c_87456,c_87455,c_87454,c_87453,c_87452,c_87451,c_87450,c_87449,c_87448,c_87447,c_87446,c_87445,c_87444,c_87443,c_87442,c_87441,c_87440,c_87439,c_87438,c_87437,c_87436,c_87435,c_87434,c_87433,c_87432,c_87431,c_87430,c_87429,c_87428,c_87427,c_87426,c_87425,c_87424,c_87423,c_87382,c_87381,c_87379,c_87360,c_87359,c_87357,c_87353,c_87352,c_87351,c_87343,c_87324,c_87323,c_87321,c_87302,c_87301,c_87299,c_87280,c_87279,c_87277,c_87238,c_87237,c_87235,c_87187,c_87186,c_87184,c_87165,c_87164,c_87162,c_87143,c_87142,c_87140,c_87121,c_87120,c_87118,c_87099,c_87098,c_87096,c_87077,c_87076,c_87074,c_87070,c_87069,c_87068,c_86939,c_86938,c_86932,c_86931,c_86927,c_86923,c_86922,c_86921,c_86920,c_86919,c_86906,c_86902,c_86901,c_86900,c_86888,c_86887,c_86886,c_86880,c_86861,c_86860,c_86858,c_86839,c_86838,c_86836,c_86773,c_86772,c_86770,c_86751,c_86750,c_86748,c_86747,c_86745,c_86740,c_86738,c_86681,c_86680,c_86678,c_86659,c_86658,c_86656,c_86387,c_86386,c_86385,c_86384,c_86383,c_86382,c_86381,c_86380,c_86379,c_86378,c_86377,c_86376,c_86375,c_86374,c_86373,c_86372,c_86371,c_86370,c_86369,c_86368,c_86367,c_86366,c_86365,c_86364,c_86363,c_86362,c_86361,c_86360,c_86359,c_86358,c_86357,c_86356,c_86355,c_86354,c_86353,c_86352,c_86351,c_86350,c_86349,c_86348,c_86347,c_86346,c_86345,c_86344,c_86343,c_86342,c_86341,c_86340,c_86339,c_86338,c_86337,c_86336,c_86335,c_86334,c_86333,c_86332,c_86331,c_86330,c_86329,c_86328,c_86327,c_85496,c_85479,c_85367,c_85366,c_85365,c_85364,c_85363,c_85362,c_85361,c_85360,c_85359,c_85358,c_85357,c_85356,c_85355,c_85354,c_85353,c_85350,c_85349,c_85348,c_85347,c_85346,c_85345,c_85344,c_85343,c_85342,c_85341,c_85340,c_85339,c_85338,c_85337,c_85336,c_85335,c_85334,c_85333,c_85332,c_85331,c_85330,c_85329,c_85328,c_85327,c_85326,c_85325,c_85324,c_85323,c_85322,c_85321,c_85320,c_85319,c_85318,c_85317,c_85316,c_85315,c_85314,c_85313,c_85312,c_85311,c_85310,c_85309,c_85308,c_85307,c_85306,c_85305,c_85304,c_85303,c_85302,c_85301,c_85300,c_85299,c_85298,c_85297,c_85296,c_85295,c_85294,c_85293,c_85292,c_85291,c_85290,c_85289,c_85288,c_85287,c_85286,c_85285,c_85284,c_85283,c_85282,c_85281,c_85280,c_85279,c_85278,c_85277,c_85276,c_85275,c_85274,c_85273,c_85272,c_85271,c_85270,c_85269,c_85268,c_85267,c_85266,c_85265,c_85264,c_85263,c_85262,c_85261,c_85260,c_85259,c_85258,c_85257,c_85256,c_85255,c_85254,c_85253,c_85252,c_85251,c_85250,c_85249,c_85248,c_85247,c_85246,c_85245,c_85244,c_85243,c_85242,c_85241,c_85240,c_85239,c_85238,c_85237,c_85236,c_85235,c_85234,c_85233,c_85232,c_85231,c_85229,c_85115,c_85110,c_85106,c_85103,c_85099,c_85095,c_85092,c_85091,c_85090,c_85087,c_85086,c_85085,c_85089,c_85088,c_85074,c_84888,c_84887,c_84886,c_84885,c_84884,c_84883,c_84882,c_84881,c_84880,c_84879,c_84878,c_84877,c_84876,c_84875,c_84874,c_84873,c_84872,c_84871,c_84870,c_84869,c_84868,c_84867,c_84866,c_84865,c_84864,c_84863,c_84862,c_84861,c_84860,c_84859,c_84858,c_84857,c_84856,c_84855,c_84854,c_84853,c_84852,c_84851,c_84850,c_84849,c_84848,c_84847,c_84846,c_84845,c_84844,c_84843,c_84842,c_84841,c_84840,c_84839,c_84838,c_84837,c_84836,c_84835,c_84834,c_84833,c_84832,c_84372,c_84371,c_84370,c_84369,c_84323,c_84322,c_84321,c_84320,c_84319,c_84318,c_84317,c_84316,c_84283,c_84282,c_84281,c_84280,c_84279,c_84278,c_84277,c_84276,c_84275,c_84274,c_84273,c_84272,c_84271,c_84270,c_84269,c_84268,c_84267,c_84266,c_84265,c_84264,c_84263,c_84262,c_84261,c_84260,c_84259,c_84258,c_84257,c_84256,c_84255,c_84254,c_84253,c_84252,c_84251,c_84250,c_84249,c_84248,c_84247,c_84246,c_84245,c_84244,c_84243,c_84242,c_84241,c_84240,c_84239,c_84238,c_84237,c_84236,c_84235,c_84234,c_84233,c_84232,c_84231,c_84230,c_84229,c_84228,c_84227,c_81880,c_81872,c_81868,c_81864,c_81816,c_81812,c_81808,c_81157,c_81150,c_81119,c_81112,c_80813,c_80810,c_80799,c_80796,c_80781,c_80774,c_80771,c_80760,c_80740,c_80736,c_80732,c_80728,c_80716,c_80712,c_80644,c_80641,c_80637,c_80634,c_80586,c_80585,c_80584,c_80583,c_80582,c_80581,c_80580,c_80579,c_80578,c_80577,c_80576,c_80575,c_80574,c_80573,c_80572,c_80571,c_80570,c_80569,c_80568,c_80567,c_80566,c_80565,c_80564,c_80563,c_80562,c_80561,c_80560,c_80559,c_80558,c_80557,c_80556,c_80555,c_80554,c_80553,c_80552,c_80551,c_80550,c_80549,c_80548,c_80547,c_80546,c_80545,c_80544,c_80543,c_80542,c_80541,c_80540,c_80539,c_80538,c_80537,c_80536,c_80535,c_80534,c_80533,c_80532,c_80531,c_80530,c_80529,c_80528,c_80527,c_80526,c_80525,c_80524,c_80523,c_80522,c_80521,c_80520,c_80519,c_80518,c_80517,c_80516,c_80515,c_80514,c_80513,c_80512,c_80511,c_80510,c_80509,c_80508,c_80507,c_80506,c_80505,c_80504,c_80503,c_80502,c_80501,c_80500,c_80499,c_80498,c_80497,c_80496,c_80495,c_80494,c_80493,c_80492,c_80491,c_80490,c_80489,c_80488,c_80487,c_80486,c_80485,c_80484,c_80483,c_80482,c_80481,c_80480,c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).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWC418-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37  % Computer : n001.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Thu Sep 24 18:15:08 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41  Running first-order theorem proving
% 0.10/0.41  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42  
% 0.10/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42  
% 0.10/0.42  % Detected problem language: tptp
% 0.10/0.43  % Proving...
% 60.53/10.43  % SZS status Started for theBenchmark.p
% 60.53/10.43  % SZS status Unsatisfiable for theBenchmark.p
% 60.53/10.43  
% 60.53/10.43  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 60.53/10.43  
% 60.53/10.43  % ------  iProver source info
% 60.53/10.43  
% 60.53/10.43  % git: date: 2026-07-19 20:42:38 +0200
% 60.53/10.43  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 60.53/10.43  % git: non_committed_changes: false
% 60.53/10.43  
% 60.53/10.43  % ------ Parsing...% successful
% 60.53/10.43  
% 60.53/10.43  
% 60.53/10.43  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 60.53/10.43  
% 60.53/10.43  % ------ 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 % 
% 60.53/10.43  
% 60.53/10.43  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 60.53/10.43  
% 60.53/10.43  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 60.53/10.43  % ------ Proving...
% 60.53/10.43  % ------ Problem Properties 
% 60.53/10.43  
% 60.53/10.43  % 
% 60.53/10.43  % clauses                               51
% 60.53/10.43  % conjectures                           3
% 60.53/10.43  % EPR                                   15
% 60.53/10.43  % Horn                                  38
% 60.53/10.43  % unary                                 7
% 60.53/10.43  % binary                                6
% 60.53/10.43  % lits                                  195
% 60.53/10.43  % lits eq                               47
% 60.53/10.43  % fd_pure                               0
% 60.53/10.43  % fd_pseudo                             0
% 60.53/10.43  % fd_cond                               12
% 60.53/10.43  % fd_pseudo_cond                        7
% 60.53/10.43  % AC symbols                            0
% 60.53/10.43  
% 60.53/10.43  % ------ Schedule dynamic 5 is on 
% 60.53/10.43  
% 60.53/10.43  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 60.53/10.43  
% 60.53/10.43  
% 60.53/10.43  % ------ 
% 60.53/10.43  % Current options:
% 60.53/10.43  % ------ 
% 60.53/10.43  
% 60.53/10.43  
% 60.53/10.43  % 
% 60.53/10.43  
% 60.53/10.43  % ------ Proving...
% 60.53/10.43  % 
% 60.53/10.43  
% 60.53/10.43  % SZS status Unsatisfiable for theBenchmark.p
% 60.53/10.43  
% 60.53/10.43  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 70.22/10.57  
% 70.22/10.57  
%------------------------------------------------------------------------------