%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC324-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 18:01:31 EDT 2024

% Result   : Unsatisfiable 2.59s 2.85s
% Output   : Proof 2.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SWC324-1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n015.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun May 26 15:36:09 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.36/0.54  %----Proving TF0_NAR, FOF, or CNF
% 0.36/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.59/2.85  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.jGTRvrnBHK/cvc5---1.0.5_12144.smt2
% 2.59/2.85  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.jGTRvrnBHK/cvc5---1.0.5_12144.smt2
% 2.73/2.92  (assume a0 (tptp.equalelemsP tptp.nil))
% 2.73/2.92  (assume a1 (tptp.duplicatefreeP tptp.nil))
% 2.73/2.92  (assume a2 (tptp.strictorderedP tptp.nil))
% 2.73/2.92  (assume a3 (tptp.totalorderedP tptp.nil))
% 2.73/2.92  (assume a4 (tptp.strictorderP tptp.nil))
% 2.73/2.92  (assume a5 (tptp.totalorderP tptp.nil))
% 2.73/2.92  (assume a6 (tptp.cyclefreeP tptp.nil))
% 2.73/2.92  (assume a7 (tptp.ssList tptp.nil))
% 2.73/2.92  (assume a8 (tptp.ssItem tptp.skac3))
% 2.73/2.92  (assume a9 (tptp.ssItem tptp.skac2))
% 2.73/2.92  (assume a10 (not (tptp.singletonP tptp.nil)))
% 2.73/2.92  (assume a11 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))))
% 2.73/2.92  (assume a12 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))))
% 2.73/2.92  (assume a13 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf81 U))))
% 2.73/2.92  (assume a14 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf80 U))))
% 2.73/2.92  (assume a15 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf79 U))))
% 2.73/2.92  (assume a16 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf78 U))))
% 2.73/2.92  (assume a17 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf77 U))))
% 2.73/2.92  (assume a18 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf76 U))))
% 2.73/2.92  (assume a19 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf75 U))))
% 2.73/2.92  (assume a20 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf74 U))))
% 2.73/2.92  (assume a21 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf73 U))))
% 2.73/2.92  (assume a22 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf72 U))))
% 2.73/2.92  (assume a23 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf71 U))))
% 2.73/2.92  (assume a24 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf70 U))))
% 2.73/2.92  (assume a25 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf69 U))))
% 2.73/2.92  (assume a26 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf68 U))))
% 2.73/2.92  (assume a27 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf67 U))))
% 2.73/2.92  (assume a28 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf66 U))))
% 2.73/2.92  (assume a29 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf65 U))))
% 2.73/2.92  (assume a30 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf64 U))))
% 2.73/2.92  (assume a31 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf63 U))))
% 2.73/2.92  (assume a32 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf62 U))))
% 2.73/2.92  (assume a33 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf61 U))))
% 2.73/2.92  (assume a34 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf60 U))))
% 2.73/2.92  (assume a35 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf59 U))))
% 2.73/2.92  (assume a36 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf58 U))))
% 2.73/2.92  (assume a37 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf57 U))))
% 2.73/2.92  (assume a38 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf56 U))))
% 2.73/2.92  (assume a39 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf55 U))))
% 2.73/2.92  (assume a40 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf54 U))))
% 2.73/2.92  (assume a41 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf53 U))))
% 2.73/2.92  (assume a42 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf52 U))))
% 2.73/2.92  (assume a43 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf51 U))))
% 2.73/2.92  (assume a44 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf50 U))))
% 2.73/2.92  (assume a45 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf49 U))))
% 2.73/2.92  (assume a46 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf44 U))))
% 2.73/2.92  (assume a47 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf48 U V))))
% 2.73/2.92  (assume a48 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf47 U V))))
% 2.73/2.92  (assume a49 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf46 U V))))
% 2.73/2.92  (assume a50 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf45 U V))))
% 2.73/2.92  (assume a51 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf43 U V))))
% 2.73/2.92  (assume a52 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf42 U V))))
% 2.73/2.92  (assume a53 (not (= tptp.skac3 tptp.skac2)))
% 2.73/2.92  (assume a54 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.geq U U))))
% 2.73/2.92  (assume a55 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U tptp.nil))))
% 2.73/2.92  (assume a56 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))
% 2.73/2.92  (assume a57 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.rearsegP U tptp.nil))))
% 2.73/2.92  (assume a58 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.rearsegP U U))))
% 2.73/2.92  (assume a59 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U tptp.nil))))
% 2.73/2.92  (assume a60 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U U))))
% 2.73/2.92  (assume a61 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.leq U U))))
% 2.73/2.92  (assume a62 (forall ((U $$unsorted)) (or (not (tptp.lt U U)) (not (tptp.ssItem U)))))
% 2.73/2.92  (assume a63 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.equalelemsP (tptp.cons U tptp.nil)))))
% 2.73/2.92  (assume a64 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))))
% 2.73/2.92  (assume a65 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U tptp.nil)))))
% 2.73/2.92  (assume a66 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U tptp.nil)))))
% 2.73/2.92  (assume a67 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.strictorderP (tptp.cons U tptp.nil)))))
% 2.73/2.92  (assume a68 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.totalorderP (tptp.cons U tptp.nil)))))
% 2.73/2.92  (assume a69 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.cyclefreeP (tptp.cons U tptp.nil)))))
% 2.73/2.92  (assume a70 (forall ((U $$unsorted)) (or (not (tptp.memberP tptp.nil U)) (not (tptp.ssItem U)))))
% 2.73/2.92  (assume a71 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (tptp.duplicatefreeP U) (tptp.ssItem V))))
% 2.73/2.92  (assume a72 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app U tptp.nil) U))))
% 2.73/2.92  (assume a73 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U))))
% 2.73/2.92  (assume a74 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssList (tptp.tl U)) (= tptp.nil U))))
% 2.73/2.92  (assume a75 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))))
% 2.73/2.92  (assume a76 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssList (tptp.tl U)) (= tptp.nil U))))
% 2.73/2.92  (assume a77 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))))
% 2.73/2.92  (assume a78 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.segmentP tptp.nil U))))
% 2.73/2.92  (assume a79 (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 2.73/2.92  (assume a80 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.rearsegP tptp.nil U))))
% 2.73/2.92  (assume a81 (forall ((U $$unsorted)) (or (not (tptp.rearsegP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 2.73/2.92  (assume a82 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.frontsegP tptp.nil U))))
% 2.73/2.92  (assume a83 (forall ((U $$unsorted)) (or (not (tptp.frontsegP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 2.73/2.92  (assume a84 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))))
% 2.73/2.92  (assume a85 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))))
% 2.73/2.92  (assume a86 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (tptp.leq (tptp.skaf50 U) (tptp.skaf49 U)))))
% 2.73/2.92  (assume a87 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (tptp.leq (tptp.skaf49 U) (tptp.skaf50 U)))))
% 2.73/2.92  (assume a88 (forall ((U $$unsorted)) (or (not (= (tptp.skaf79 U) (tptp.skaf78 U))) (not (tptp.ssList U)) (tptp.equalelemsP U))))
% 2.73/2.92  (assume a89 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf69 U) (tptp.skaf70 U))) (not (tptp.ssList U)) (tptp.strictorderedP U))))
% 2.73/2.92  (assume a90 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf64 U) (tptp.skaf65 U))) (not (tptp.ssList U)) (tptp.totalorderedP U))))
% 2.73/2.92  (assume a91 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf60 U) (tptp.skaf59 U))) (not (tptp.ssList U)) (tptp.strictorderP U))))
% 2.73/2.92  (assume a92 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf59 U) (tptp.skaf60 U))) (not (tptp.ssList U)) (tptp.strictorderP U))))
% 2.73/2.92  (assume a93 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf55 U) (tptp.skaf54 U))) (not (tptp.ssList U)) (tptp.totalorderP U))))
% 2.73/2.92  (assume a94 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf54 U) (tptp.skaf55 U))) (not (tptp.ssList U)) (tptp.totalorderP U))))
% 2.73/2.92  (assume a95 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.tl (tptp.cons U V)) V))))
% 2.73/2.92  (assume a96 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.hd (tptp.cons U V)) U))))
% 2.73/2.92  (assume a97 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))
% 2.73/2.92  (assume a98 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) V)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))
% 2.73/2.92  (assume a99 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= V U))))
% 2.73/2.92  (assume a100 (forall ((U $$unsorted)) (or (not (tptp.singletonP U)) (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf44 U) tptp.nil) U))))
% 2.73/2.92  (assume a101 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem V)) (tptp.neq V U) (= V U))))
% 2.73/2.92  (assume a102 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq U V))))
% 2.73/2.92  (assume a103 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= tptp.nil U))))
% 2.73/2.92  (assume a104 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt V U))))
% 2.73/2.92  (assume a105 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (tptp.gt V U))))
% 2.73/2.92  (assume a106 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq V U))))
% 2.73/2.92  (assume a107 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (tptp.geq V U))))
% 2.73/2.92  (assume a108 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U))))
% 2.73/2.92  (assume a109 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.gt V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)))))
% 2.73/2.92  (assume a110 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.lt U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)))))
% 2.73/2.92  (assume a111 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.strictorderedP (tptp.cons V U)))))
% 2.73/2.92  (assume a112 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.totalorderedP (tptp.cons V U)))))
% 2.73/2.92  (assume a113 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.lt V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)))))
% 2.73/2.92  (assume a114 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssList V)) (not (tptp.ssList U)))))
% 2.73/2.92  (assume a115 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U tptp.nil) V)) (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.singletonP V))))
% 2.73/2.92  (assume a116 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)))))
% 2.73/2.92  (assume a117 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))))
% 2.73/2.92  (assume a118 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))))
% 2.73/2.92  (assume a119 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))))
% 2.73/2.92  (assume a120 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))))
% 2.73/2.92  (assume a121 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))))
% 2.73/2.92  (assume a122 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.hd (tptp.app V U)) (tptp.hd V)))))
% 2.73/2.92  (assume a123 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP V) (= tptp.nil V))))
% 2.73/2.92  (assume a124 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP V) (= tptp.nil V))))
% 2.73/2.92  (assume a125 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))))
% 2.73/2.92  (assume a126 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 2.73/2.92  (assume a127 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.rearsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 2.73/2.92  (assume a128 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 2.73/2.92  (assume a129 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))))
% 2.73/2.92  (assume a130 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app (tptp.skaf46 U V) V) U))))
% 2.73/2.92  (assume a131 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app V (tptp.skaf45 U V)) U))))
% 2.73/2.92  (assume a132 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.tl (tptp.app V U)) (tptp.app (tptp.tl V) U)))))
% 2.73/2.92  (assume a133 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.lt U (tptp.hd V)) (= tptp.nil V))))
% 2.73/2.92  (assume a134 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.leq U (tptp.hd V)) (= tptp.nil V))))
% 2.73/2.92  (assume a135 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.rearsegP (tptp.app W U) V))))
% 2.73/2.92  (assume a136 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP (tptp.app U W) V))))
% 2.73/2.92  (assume a137 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= U V)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.memberP (tptp.cons V W) U))))
% 2.73/2.92  (assume a138 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons W U) V))))
% 2.73/2.92  (assume a139 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.memberP (tptp.app U W) V))))
% 2.73/2.92  (assume a140 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.app W U) V))))
% 2.73/2.92  (assume a141 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.equalelemsP U) (= (tptp.app (tptp.skaf80 U) (tptp.cons (tptp.skaf78 U) (tptp.cons (tptp.skaf79 U) (tptp.skaf81 U)))) U))))
% 2.73/2.92  (assume a142 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (tptp.rearsegP W V))))
% 2.73/2.92  (assume a143 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (tptp.frontsegP W U))))
% 2.73/2.92  (assume a144 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app U V) tptp.nil))))
% 2.73/2.92  (assume a145 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.gt V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.gt U W))))
% 2.73/2.92  (assume a146 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.lt V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U W))))
% 2.73/2.92  (assume a147 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.geq U W))))
% 2.73/2.92  (assume a148 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (= (tptp.app (tptp.app W V) U) (tptp.app W (tptp.app V U))))))
% 2.73/2.92  (assume a149 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) (tptp.app U W))) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (= V W))))
% 2.73/2.92  (assume a150 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) (tptp.app W V))) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (= U W))))
% 2.73/2.92  (assume a151 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.segmentP U W))))
% 2.73/2.92  (assume a152 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.rearsegP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.rearsegP U W))))
% 2.73/2.92  (assume a153 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP U W))))
% 2.73/2.92  (assume a154 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.lt V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U W))))
% 2.73/2.92  (assume a155 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq U W))))
% 2.73/2.92  (assume a156 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (= (tptp.cons U (tptp.app V W)) (tptp.app (tptp.cons U V) W)))))
% 2.73/2.92  (assume a157 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP (tptp.app U V) W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (tptp.memberP V W) (tptp.memberP U W))))
% 2.73/2.92  (assume a158 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U (tptp.hd V))) (not (tptp.totalorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U V)) (= tptp.nil V))))
% 2.73/2.92  (assume a159 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U (tptp.hd V))) (not (tptp.strictorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U V)) (= tptp.nil V))))
% 2.73/2.92  (assume a160 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP (tptp.cons U V) W)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (not (tptp.ssItem W)) (tptp.memberP V W) (= W U))))
% 2.73/2.92  (assume a161 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.duplicatefreeP U) (= (tptp.app (tptp.app (tptp.skaf75 U) (tptp.cons (tptp.skaf74 U) (tptp.skaf76 U))) (tptp.cons (tptp.skaf74 U) (tptp.skaf77 U))) U))))
% 2.73/2.92  (assume a162 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.strictorderedP U) (= (tptp.app (tptp.app (tptp.skaf71 U) (tptp.cons (tptp.skaf69 U) (tptp.skaf72 U))) (tptp.cons (tptp.skaf70 U) (tptp.skaf73 U))) U))))
% 2.73/2.92  (assume a163 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderedP U) (= (tptp.app (tptp.app (tptp.skaf66 U) (tptp.cons (tptp.skaf64 U) (tptp.skaf67 U))) (tptp.cons (tptp.skaf65 U) (tptp.skaf68 U))) U))))
% 2.73/2.92  (assume a164 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.strictorderP U) (= (tptp.app (tptp.app (tptp.skaf61 U) (tptp.cons (tptp.skaf59 U) (tptp.skaf62 U))) (tptp.cons (tptp.skaf60 U) (tptp.skaf63 U))) U))))
% 2.73/2.92  (assume a165 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderP U) (= (tptp.app (tptp.app (tptp.skaf56 U) (tptp.cons (tptp.skaf54 U) (tptp.skaf57 U))) (tptp.cons (tptp.skaf55 U) (tptp.skaf58 U))) U))))
% 2.73/2.92  (assume a166 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (= (tptp.app (tptp.app (tptp.skaf51 U) (tptp.cons (tptp.skaf49 U) (tptp.skaf52 U))) (tptp.cons (tptp.skaf50 U) (tptp.skaf53 U))) U))))
% 2.73/2.92  (assume a167 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app (tptp.app (tptp.skaf47 U V) V) (tptp.skaf48 V U)) U))))
% 2.73/2.92  (assume a168 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssItem V)) (not (tptp.ssList U)) (= (tptp.app (tptp.skaf42 U V) (tptp.cons V (tptp.skaf43 V U))) U))))
% 2.73/2.92  (assume a169 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.cons U V) (tptp.cons W X))) (not (tptp.ssItem W)) (not (tptp.ssItem U)) (not (tptp.ssList X)) (not (tptp.ssList V)) (= U W))))
% 2.73/2.92  (assume a170 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.cons U V) (tptp.cons W X))) (not (tptp.ssItem W)) (not (tptp.ssItem U)) (not (tptp.ssList X)) (not (tptp.ssList V)) (= X V))))
% 2.73/2.92  (assume a171 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.ssList W)) (not (tptp.ssList X)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.segmentP (tptp.app (tptp.app X U) W) V))))
% 2.73/2.92  (assume a172 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))))
% 2.73/2.92  (assume a173 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.frontsegP (tptp.cons U V) (tptp.cons W X))) (not (tptp.ssList X)) (not (tptp.ssList V)) (not (tptp.ssItem W)) (not (tptp.ssItem U)) (tptp.frontsegP V X))))
% 2.73/2.92  (assume a174 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app U (tptp.cons V W)) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (not (tptp.ssList X)) (tptp.memberP X V))))
% 2.73/2.92  (assume a175 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.frontsegP (tptp.cons U V) (tptp.cons W X))) (not (tptp.ssList X)) (not (tptp.ssList V)) (not (tptp.ssItem W)) (not (tptp.ssItem U)) (= U W))))
% 2.73/2.92  (assume a176 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.tl U) (tptp.tl V))) (not (= (tptp.hd U) (tptp.hd V))) (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= U V) (= tptp.nil U))))
% 2.73/2.92  (assume a177 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.frontsegP U V)) (not (= W X)) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem W)) (tptp.frontsegP (tptp.cons W U) (tptp.cons X V)))))
% 2.73/2.92  (assume a178 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons V X)) Y)) (not (tptp.ssList X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (not (tptp.duplicatefreeP Y)) (not (tptp.ssList Y)))))
% 2.73/2.92  (assume a179 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.app U (tptp.cons V (tptp.cons W X))) Y)) (not (tptp.ssList X)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.equalelemsP Y)) (not (tptp.ssList Y)) (= V W))))
% 2.73/2.92  (assume a180 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons X Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem V)) (not (tptp.strictorderedP Z)) (not (tptp.ssList Z)) (tptp.lt V X))))
% 2.73/2.92  (assume a181 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons X Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem V)) (not (tptp.totalorderedP Z)) (not (tptp.ssList Z)) (tptp.leq V X))))
% 2.73/2.92  (assume a182 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons X Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem V)) (not (tptp.strictorderP Z)) (not (tptp.ssList Z)) (tptp.lt V X) (tptp.lt X V))))
% 2.73/2.92  (assume a183 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons X Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem V)) (not (tptp.totalorderP Z)) (not (tptp.ssList Z)) (tptp.leq V X) (tptp.leq X V))))
% 2.73/2.92  (assume a184 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V U)) (not (= (tptp.app (tptp.app W (tptp.cons U X)) (tptp.cons V Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList X)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (not (tptp.cyclefreeP Z)) (not (tptp.ssList Z)))))
% 2.73/2.92  (assume a185 (tptp.ssList tptp.sk1))
% 2.73/2.92  (assume a186 (tptp.ssList tptp.sk2))
% 2.73/2.92  (assume a187 (tptp.ssList tptp.sk3))
% 2.73/2.92  (assume a188 (tptp.ssList tptp.sk4))
% 2.73/2.92  (assume a189 (= tptp.sk2 tptp.sk4))
% 2.73/2.92  (assume a190 (= tptp.sk1 tptp.sk3))
% 2.73/2.92  (assume a191 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= (tptp.app A B) tptp.sk2)) (not (= (tptp.app B A) tptp.sk1)))))
% 2.73/2.92  (assume a192 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= (tptp.app B (tptp.cons A tptp.nil)) tptp.sk3) (not (= (tptp.app (tptp.cons A tptp.nil) B) tptp.sk4)))))
% 2.73/2.92  (assume a193 (or (= tptp.nil tptp.sk3) (not (= tptp.nil tptp.sk4))))
% 2.73/2.92  (step t1 (cl (not (= (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule equiv_pos2)
% 2.73/2.92  (step t2 (cl (= (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk1 tptp.sk3)))) :rule refl)
% 2.73/2.92  (step t3 (cl (= (not (= tptp.nil tptp.sk3)) (not (= tptp.nil tptp.sk3)))) :rule refl)
% 2.73/2.92  (step t4 (cl (= (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))))) :rule refl)
% 2.73/2.92  (step t5 (cl (= (= (= (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) true) (= (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule equiv_simplify)
% 2.73/2.92  (step t6 (cl (not (= (= (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) true)) (= (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule equiv1 :premises (t5))
% 2.73/2.92  (step t7 (cl (= (= (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))))) :rule all_simplify)
% 2.73/2.92  (step t8 (cl (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule refl)
% 2.73/2.92  (step t9 (cl (= (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule all_simplify)
% 2.73/2.92  (step t10 (cl (= (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule cong :premises (t8 t9))
% 2.73/2.92  (step t11 (cl (= (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) true)) :rule all_simplify)
% 2.73/2.92  (step t12 (cl (= (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) true)) :rule trans :premises (t10 t11))
% 2.73/2.92  (step t13 (cl (= (= (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) true)) :rule trans :premises (t7 t12))
% 2.73/2.92  (step t14 (cl (= (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule resolution :premises (t6 t13))
% 2.73/2.92  (step t15 (cl (= (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule cong :premises (t2 t3 t4 t14))
% 2.73/2.92  (step t16 (cl (not (= (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))))) (not (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule equiv_pos2)
% 2.73/2.92  (step t17 (cl (= (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule refl)
% 2.73/2.92  (step t18 (cl (= (= (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))))) :rule equiv_simplify)
% 2.73/2.92  (step t19 (cl (= (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) (not (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))))) :rule equiv2 :premises (t18))
% 2.73/2.92  (step t20 (cl (not (not (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule not_not)
% 2.73/2.92  (step t21 (cl (= (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule resolution :premises (t19 t20))
% 2.73/2.92  (step t22 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t23)
% 2.73/2.92  (assume t23.a0 (= tptp.nil (tptp.app tptp.nil tptp.nil)))
% 2.73/2.92  (assume t23.a1 (= tptp.nil tptp.sk3))
% 2.73/2.92  (assume t23.a2 (= tptp.sk1 tptp.sk3))
% 2.73/2.92  (assume t23.a3 (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))
% 2.73/2.92  (step t23.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 2.73/2.92  (step t23.t2 (cl (= (= false true) false)) :rule all_simplify)
% 2.73/2.92  (step t23.t3 (cl (= (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) false) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule equiv_simplify)
% 2.73/2.92  (step t23.t4 (cl (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) false) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule equiv2 :premises (t23.t3))
% 2.73/2.92  (step t23.t5 (cl (not (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) :rule not_not)
% 2.73/2.92  (step t23.t6 (cl (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) false) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) :rule resolution :premises (t23.t4 t23.t5))
% 2.73/2.92  (step t23.t7 (cl (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) false)) :rule resolution :premises (t23.t6 t23.a3))
% 2.73/2.92  (step t23.t8 (cl (= false (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule symm :premises (t23.t7))
% 2.73/2.92  (step t23.t9 (cl (= (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) true) (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule equiv_simplify)
% 2.73/2.92  (step t23.t10 (cl (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) true) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule equiv2 :premises (t23.t9))
% 2.73/2.92  (step t23.t11 (cl (= tptp.sk3 tptp.sk1)) :rule symm :premises (t23.a2))
% 2.73/2.92  (step t23.t12 (cl (= tptp.sk1 tptp.sk3)) :rule symm :premises (t23.t11))
% 2.73/2.92  (step t23.t13 (cl (= tptp.sk3 tptp.nil)) :rule symm :premises (t23.a1))
% 2.73/2.92  (step t23.t14 (cl (= tptp.sk1 tptp.nil)) :rule trans :premises (t23.t12 t23.t13))
% 2.73/2.92  (step t23.t15 (cl (= (tptp.app tptp.nil tptp.nil) tptp.nil)) :rule symm :premises (t23.a0))
% 2.73/2.92  (step t23.t16 (cl (= tptp.nil (tptp.app tptp.nil tptp.nil))) :rule symm :premises (t23.t15))
% 2.73/2.92  (step t23.t17 (cl (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) :rule trans :premises (t23.t14 t23.t16))
% 2.73/2.92  (step t23.t18 (cl (= (= tptp.sk1 (tptp.app tptp.nil tptp.nil)) true)) :rule resolution :premises (t23.t10 t23.t17))
% 2.73/2.92  (step t23.t19 (cl (= false true)) :rule trans :premises (t23.t8 t23.t18))
% 2.73/2.92  (step t23.t20 (cl false) :rule resolution :premises (t23.t1 t23.t2 t23.t19))
% 2.73/2.92  (step t23 (cl (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (= tptp.nil tptp.sk3)) (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) :rule subproof :discharge (t23.a0 t23.a1 t23.a2 t23.a3))
% 2.73/2.92  (step t24 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (= tptp.nil (tptp.app tptp.nil tptp.nil))) :rule and_pos)
% 2.73/2.92  (step t25 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (= tptp.nil tptp.sk3)) :rule and_pos)
% 2.73/2.92  (step t26 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (= tptp.sk1 tptp.sk3)) :rule and_pos)
% 2.73/2.92  (step t27 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule and_pos)
% 2.73/2.92  (step t28 (cl false (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule resolution :premises (t23 t24 t25 t26 t27))
% 2.73/2.92  (step t29 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) false) :rule reordering :premises (t28))
% 2.73/2.92  (step t30 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) false) :rule contraction :premises (t29))
% 2.73/2.92  (step t31 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) false) :rule resolution :premises (t22 t30))
% 2.73/2.92  (step t32 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) (not false)) :rule implies_neg2)
% 2.73/2.92  (step t33 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false)) :rule resolution :premises (t31 t32))
% 2.73/2.92  (step t34 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false)) :rule contraction :premises (t33))
% 2.73/2.92  (step t35 (cl (= (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))))) :rule implies_simplify)
% 2.73/2.92  (step t36 (cl (not (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false)) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule equiv1 :premises (t35))
% 2.73/2.92  (step t37 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule resolution :premises (t34 t36))
% 2.73/2.92  (step t38 (cl (= (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false)) :rule resolution :premises (t21 t37))
% 2.73/2.92  (step t39 (cl (= (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false))) :rule cong :premises (t17 t38))
% 2.73/2.92  (step t40 (cl (= (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) false) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))))) :rule all_simplify)
% 2.73/2.92  (step t41 (cl (= (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))))) :rule trans :premises (t39 t40))
% 2.73/2.92  (step t42 (cl (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t43)
% 2.73/2.92  (assume t43.a0 (= tptp.sk1 tptp.sk3))
% 2.73/2.92  (assume t43.a1 (= tptp.nil tptp.sk3))
% 2.73/2.92  (assume t43.a2 (= tptp.nil (tptp.app tptp.nil tptp.nil)))
% 2.73/2.92  (assume t43.a3 (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))
% 2.73/2.92  (step t43.t1 (cl (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (= tptp.nil tptp.sk3)) (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule and_neg)
% 2.73/2.92  (step t43.t2 (cl (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule resolution :premises (t43.t1 t43.a2 t43.a1 t43.a0 t43.a3))
% 2.73/2.92  (step t43 (cl (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule subproof :discharge (t43.a0 t43.a1 t43.a2 t43.a3))
% 2.73/2.92  (step t44 (cl (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (= tptp.sk1 tptp.sk3)) :rule and_pos)
% 2.73/2.92  (step t45 (cl (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (= tptp.nil tptp.sk3)) :rule and_pos)
% 2.73/2.92  (step t46 (cl (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (= tptp.nil (tptp.app tptp.nil tptp.nil))) :rule and_pos)
% 2.73/2.92  (step t47 (cl (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule and_pos)
% 2.73/2.92  (step t48 (cl (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule resolution :premises (t43 t44 t45 t46 t47))
% 2.73/2.92  (step t49 (cl (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule reordering :premises (t48))
% 2.73/2.92  (step t50 (cl (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule contraction :premises (t49))
% 2.73/2.92  (step t51 (cl (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule resolution :premises (t42 t50))
% 2.73/2.92  (step t52 (cl (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule implies_neg2)
% 2.73/2.92  (step t53 (cl (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule resolution :premises (t51 t52))
% 2.73/2.92  (step t54 (cl (=> (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk3) (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule contraction :premises (t53))
% 2.73/2.92  (step t55 (cl (not (and (= tptp.sk1 tptp.sk3) (= tptp.nil tptp.sk3) (= tptp.nil (tptp.app tptp.nil tptp.nil)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule resolution :premises (t16 t41 t54))
% 2.73/2.92  (step t56 (cl (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule not_and :premises (t55))
% 2.73/2.92  (step t57 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (not (= tptp.sk1 tptp.sk3)))) :rule or_neg)
% 2.73/2.92  (step t58 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (not (= tptp.nil tptp.sk3)))) :rule or_neg)
% 2.73/2.92  (step t59 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (not (= tptp.nil (tptp.app tptp.nil tptp.nil))))) :rule or_neg)
% 2.73/2.92  (step t60 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule or_neg)
% 2.73/2.92  (step t61 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule resolution :premises (t56 t57 t58 t59 t60))
% 2.73/2.92  (step t62 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule contraction :premises (t61))
% 2.73/2.92  (step t63 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule resolution :premises (t1 t15 t62))
% 2.73/2.92  (step t64 (cl (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) :rule or :premises (t63))
% 2.73/2.92  (step t65 (cl (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.nil tptp.sk3)) (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) :rule reordering :premises (t64))
% 2.73/2.92  (step t66 (cl (= tptp.nil tptp.sk3) (not (= tptp.nil tptp.sk4))) :rule or :premises (a193))
% 2.73/2.92  (step t67 (cl (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.nil tptp.sk2))) :rule and_neg)
% 2.73/2.92  (step t68 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t69)
% 2.73/2.92  (assume t69.a0 (= tptp.sk2 tptp.sk4))
% 2.73/2.92  (assume t69.a1 (= tptp.nil tptp.sk2))
% 2.73/2.92  (step t69.t1 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t69.t2)
% 2.73/2.92  (assume t69.t2.a0 (= tptp.sk2 tptp.sk4))
% 2.73/2.92  (assume t69.t2.a1 (= tptp.nil tptp.sk2))
% 2.73/2.92  (step t69.t2.t1 (cl (= tptp.sk2 tptp.nil)) :rule symm :premises (t69.t2.a1))
% 2.73/2.92  (step t69.t2.t2 (cl (= tptp.nil tptp.sk2)) :rule symm :premises (t69.t2.t1))
% 2.73/2.92  (step t69.t2.t3 (cl (= tptp.sk4 tptp.sk2)) :rule symm :premises (t69.t2.a0))
% 2.73/2.92  (step t69.t2.t4 (cl (= tptp.sk2 tptp.sk4)) :rule symm :premises (t69.t2.t3))
% 2.73/2.92  (step t69.t2.t5 (cl (= tptp.nil tptp.sk4)) :rule trans :premises (t69.t2.t2 t69.t2.t4))
% 2.73/2.92  (step t69.t2 (cl (not (= tptp.sk2 tptp.sk4)) (not (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) :rule subproof :discharge (t69.t2.a0 t69.t2.a1))
% 2.73/2.92  (step t69.t3 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 2.73/2.92  (step t69.t4 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk2)) :rule and_pos)
% 2.73/2.92  (step t69.t5 (cl (= tptp.nil tptp.sk4) (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)))) :rule resolution :premises (t69.t2 t69.t3 t69.t4))
% 2.73/2.92  (step t69.t6 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk4)) :rule reordering :premises (t69.t5))
% 2.73/2.92  (step t69.t7 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk4)) :rule contraction :premises (t69.t6))
% 2.73/2.92  (step t69.t8 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) (= tptp.nil tptp.sk4)) :rule resolution :premises (t69.t1 t69.t7))
% 2.73/2.92  (step t69.t9 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) (not (= tptp.nil tptp.sk4))) :rule implies_neg2)
% 2.73/2.92  (step t69.t10 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4))) :rule resolution :premises (t69.t8 t69.t9))
% 2.73/2.92  (step t69.t11 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4))) :rule contraction :premises (t69.t10))
% 2.73/2.92  (step t69.t12 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk4)) :rule implies :premises (t69.t11))
% 2.73/2.92  (step t69.t13 (cl (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.nil tptp.sk2))) :rule and_neg)
% 2.73/2.92  (step t69.t14 (cl (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) :rule resolution :premises (t69.t13 t69.a0 t69.a1))
% 2.73/2.92  (step t69.t15 (cl (= tptp.nil tptp.sk4)) :rule resolution :premises (t69.t12 t69.t14))
% 2.73/2.92  (step t69 (cl (not (= tptp.sk2 tptp.sk4)) (not (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) :rule subproof :discharge (t69.a0 t69.a1))
% 2.73/2.92  (step t70 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 2.73/2.92  (step t71 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk2)) :rule and_pos)
% 2.73/2.92  (step t72 (cl (= tptp.nil tptp.sk4) (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)))) :rule resolution :premises (t69 t70 t71))
% 2.73/2.92  (step t73 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk4)) :rule reordering :premises (t72))
% 2.73/2.92  (step t74 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk4)) :rule contraction :premises (t73))
% 2.73/2.92  (step t75 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) (= tptp.nil tptp.sk4)) :rule resolution :premises (t68 t74))
% 2.73/2.92  (step t76 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) (not (= tptp.nil tptp.sk4))) :rule implies_neg2)
% 2.73/2.92  (step t77 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4))) :rule resolution :premises (t75 t76))
% 2.73/2.92  (step t78 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4))) :rule contraction :premises (t77))
% 2.73/2.92  (step t79 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk4)) :rule implies :premises (t78))
% 2.73/2.92  (step t80 (cl (not (= tptp.sk2 tptp.sk4)) (not (= tptp.nil tptp.sk2)) (= tptp.nil tptp.sk4)) :rule resolution :premises (t67 t79))
% 2.73/2.92  (step t81 (cl (= tptp.nil tptp.sk4) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.nil tptp.sk2))) :rule reordering :premises (t80))
% 2.73/2.92  (step t82 (cl (not (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2)) :rule or_pos)
% 2.73/2.92  (step t83 (cl (not (tptp.ssList tptp.sk2)) (= tptp.nil tptp.sk2) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (not (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2)))) :rule reordering :premises (t82))
% 2.73/2.92  (step t84 (cl (not (= (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (or (not (= tptp.sk1 tptp.sk3)) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))))) (not (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (or (not (= tptp.sk1 tptp.sk3)) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule equiv_pos2)
% 2.73/2.92  (step t85 (cl (= (= (= (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) true) (= (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule equiv_simplify)
% 2.73/2.92  (step t86 (cl (not (= (= (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) true)) (= (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule equiv1 :premises (t85))
% 2.73/2.92  (step t87 (cl (= (= (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))))) :rule all_simplify)
% 2.73/2.92  (step t88 (cl (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule refl)
% 2.73/2.92  (step t89 (cl (= (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule all_simplify)
% 2.73/2.92  (step t90 (cl (= (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule cong :premises (t88 t89))
% 2.73/2.92  (step t91 (cl (= (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) true)) :rule all_simplify)
% 2.73/2.92  (step t92 (cl (= (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) true)) :rule trans :premises (t90 t91))
% 2.73/2.92  (step t93 (cl (= (= (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) true)) :rule trans :premises (t87 t92))
% 2.73/2.92  (step t94 (cl (= (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule resolution :premises (t86 t93))
% 2.73/2.92  (step t95 (cl (= (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule refl)
% 2.73/2.92  (step t96 (cl (= (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (or (not (= tptp.sk1 tptp.sk3)) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))))) :rule cong :premises (t2 t94 t95))
% 2.73/2.92  (step t97 (cl (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule and_neg)
% 2.73/2.92  (step t98 (cl (=> (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t99)
% 2.73/2.92  (assume t99.a0 (= tptp.sk1 tptp.sk3))
% 2.73/2.92  (assume t99.a1 (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))
% 2.73/2.92  (step t99.t1 (cl (=> (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3)) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t99.t2)
% 2.73/2.92  (assume t99.t2.a0 (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))
% 2.73/2.92  (assume t99.t2.a1 (= tptp.sk1 tptp.sk3))
% 2.73/2.92  (step t99.t2.t1 (cl (= (= (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) false) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule equiv_simplify)
% 2.73/2.92  (step t99.t2.t2 (cl (not (= (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) false)) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule equiv1 :premises (t99.t2.t1))
% 2.73/2.92  (step t99.t2.t3 (cl (= tptp.sk3 tptp.sk1)) :rule symm :premises (t99.t2.a1))
% 2.73/2.92  (step t99.t2.t4 (cl (= (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)) (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) :rule refl)
% 2.73/2.92  (step t99.t2.t5 (cl (= (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule cong :premises (t99.t2.t3 t99.t2.t4))
% 2.73/2.92  (step t99.t2.t6 (cl (= (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) false) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule equiv_simplify)
% 2.73/2.92  (step t99.t2.t7 (cl (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) false) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule equiv2 :premises (t99.t2.t6))
% 2.73/2.92  (step t99.t2.t8 (cl (not (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) :rule not_not)
% 2.73/2.92  (step t99.t2.t9 (cl (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) false) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) :rule resolution :premises (t99.t2.t7 t99.t2.t8))
% 2.73/2.92  (step t99.t2.t10 (cl (= (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) false)) :rule resolution :premises (t99.t2.t9 t99.t2.a0))
% 2.73/2.92  (step t99.t2.t11 (cl (= (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) false)) :rule trans :premises (t99.t2.t5 t99.t2.t10))
% 2.73/2.92  (step t99.t2.t12 (cl (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule resolution :premises (t99.t2.t2 t99.t2.t11))
% 2.73/2.92  (step t99.t2 (cl (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule subproof :discharge (t99.t2.a0 t99.t2.a1))
% 2.73/2.92  (step t99.t3 (cl (not (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule and_pos)
% 2.73/2.92  (step t99.t4 (cl (not (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3))) (= tptp.sk1 tptp.sk3)) :rule and_pos)
% 2.73/2.92  (step t99.t5 (cl (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (not (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3))) (not (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3)))) :rule resolution :premises (t99.t2 t99.t3 t99.t4))
% 2.73/2.92  (step t99.t6 (cl (not (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3))) (not (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule reordering :premises (t99.t5))
% 2.73/2.92  (step t99.t7 (cl (not (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule contraction :premises (t99.t6))
% 2.73/2.92  (step t99.t8 (cl (=> (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3)) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule resolution :premises (t99.t1 t99.t7))
% 2.73/2.92  (step t99.t9 (cl (=> (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3)) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule implies_neg2)
% 2.73/2.92  (step t99.t10 (cl (=> (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3)) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (=> (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3)) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule resolution :premises (t99.t8 t99.t9))
% 2.73/2.92  (step t99.t11 (cl (=> (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3)) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule contraction :premises (t99.t10))
% 2.73/2.92  (step t99.t12 (cl (not (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule implies :premises (t99.t11))
% 2.73/2.92  (step t99.t13 (cl (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk1 tptp.sk3))) :rule and_neg)
% 2.73/2.92  (step t99.t14 (cl (and (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (= tptp.sk1 tptp.sk3))) :rule resolution :premises (t99.t13 t99.a1 t99.a0))
% 2.73/2.92  (step t99.t15 (cl (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule resolution :premises (t99.t12 t99.t14))
% 2.73/2.92  (step t99 (cl (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule subproof :discharge (t99.a0 t99.a1))
% 2.73/2.92  (step t100 (cl (not (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (= tptp.sk1 tptp.sk3)) :rule and_pos)
% 2.73/2.92  (step t101 (cl (not (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule and_pos)
% 2.73/2.92  (step t102 (cl (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (not (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (not (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))))) :rule resolution :premises (t99 t100 t101))
% 2.73/2.92  (step t103 (cl (not (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (not (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule reordering :premises (t102))
% 2.73/2.92  (step t104 (cl (not (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule contraction :premises (t103))
% 2.73/2.92  (step t105 (cl (=> (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule resolution :premises (t98 t104))
% 2.73/2.92  (step t106 (cl (=> (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule implies_neg2)
% 2.73/2.92  (step t107 (cl (=> (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (=> (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule resolution :premises (t105 t106))
% 2.73/2.92  (step t108 (cl (=> (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule contraction :premises (t107))
% 2.73/2.92  (step t109 (cl (not (and (= tptp.sk1 tptp.sk3) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule implies :premises (t108))
% 2.73/2.92  (step t110 (cl (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule resolution :premises (t97 t109))
% 2.73/2.92  (step t111 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (not (= tptp.sk1 tptp.sk3)))) :rule or_neg)
% 2.73/2.92  (step t112 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))))) :rule or_neg)
% 2.73/2.92  (step t113 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule or_neg)
% 2.73/2.92  (step t114 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule resolution :premises (t110 t111 t112 t113))
% 2.73/2.92  (step t115 (cl (or (not (= tptp.sk1 tptp.sk3)) (not (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule contraction :premises (t114))
% 2.73/2.92  (step t116 (cl (or (not (= tptp.sk1 tptp.sk3)) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule resolution :premises (t84 t96 t115))
% 2.73/2.92  (step t117 (cl (not (= tptp.sk1 tptp.sk3)) (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule or :premises (t116))
% 2.73/2.92  (step t118 (cl (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule or_pos)
% 2.73/2.92  (step t119 (cl (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))))) :rule reordering :premises (t118))
% 2.73/2.92  (step t120 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B)))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t121)
% 2.73/2.92  (assume t121.a0 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))))
% 2.73/2.92  (step t121.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))))) :rule forall_inst :args ((:= A (tptp.skaf83 tptp.sk2)) (:= B (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (step t121.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule or :premises (t121.t1))
% 2.73/2.92  (step t121.t3 (cl (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule resolution :premises (t121.t2 t121.a0))
% 2.73/2.92  (step t121 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule subproof :discharge (t121.a0))
% 2.73/2.92  (step t122 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule resolution :premises (t120 t121))
% 2.73/2.92  (step t123 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))))) :rule implies_neg2)
% 2.73/2.92  (step t124 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))))) :rule resolution :premises (t122 t123))
% 2.73/2.92  (step t125 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))))) :rule contraction :premises (t124))
% 2.73/2.92  (step t126 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule implies :premises (t125))
% 2.73/2.92  (step t127 (cl (not (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= (tptp.app B (tptp.cons A tptp.nil)) tptp.sk3) (not (= (tptp.app (tptp.cons A tptp.nil) B) tptp.sk4)))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))))) (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= (tptp.app B (tptp.cons A tptp.nil)) tptp.sk3) (not (= (tptp.app (tptp.cons A tptp.nil) B) tptp.sk4))))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B)))))) :rule equiv_pos2)
% 2.73/2.92  (anchor :step t128 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 2.73/2.92  (step t128.t1 (cl (= A A)) :rule refl)
% 2.73/2.92  (step t128.t2 (cl (= B B)) :rule refl)
% 2.73/2.92  (step t128.t3 (cl (= (not (tptp.ssItem A)) (not (tptp.ssItem A)))) :rule refl)
% 2.73/2.92  (step t128.t4 (cl (= (not (tptp.ssList B)) (not (tptp.ssList B)))) :rule refl)
% 2.73/2.92  (step t128.t5 (cl (= (= (tptp.app B (tptp.cons A tptp.nil)) tptp.sk3) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))))) :rule all_simplify)
% 2.73/2.92  (step t128.t6 (cl (= (= (tptp.app (tptp.cons A tptp.nil) B) tptp.sk4) (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B)))) :rule all_simplify)
% 2.73/2.92  (step t128.t7 (cl (= (not (= (tptp.app (tptp.cons A tptp.nil) B) tptp.sk4)) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))) :rule cong :premises (t128.t6))
% 2.73/2.92  (step t128.t8 (cl (= (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= (tptp.app B (tptp.cons A tptp.nil)) tptp.sk3) (not (= (tptp.app (tptp.cons A tptp.nil) B) tptp.sk4))) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B)))))) :rule cong :premises (t128.t3 t128.t4 t128.t5 t128.t7))
% 2.73/2.92  (step t128 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= (tptp.app B (tptp.cons A tptp.nil)) tptp.sk3) (not (= (tptp.app (tptp.cons A tptp.nil) B) tptp.sk4)))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B))))))) :rule bind)
% 2.73/2.92  (step t129 (cl (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (= tptp.sk3 (tptp.app B (tptp.cons A tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons A tptp.nil) B)))))) :rule resolution :premises (t127 t128 a192))
% 2.73/2.92  (step t130 (cl (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= tptp.sk3 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule resolution :premises (t126 t129))
% 2.73/2.92  (step t131 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk2))) (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t132)
% 2.73/2.92  (assume t132.a0 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))))
% 2.73/2.92  (step t132.t1 (cl (or (not (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) (tptp.ssList (tptp.skaf82 tptp.sk2)))) :rule forall_inst :args ((:= U tptp.sk2)))
% 2.73/2.92  (step t132.t2 (cl (not (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) (tptp.ssList (tptp.skaf82 tptp.sk2))) :rule or :premises (t132.t1))
% 2.73/2.92  (step t132.t3 (cl (tptp.ssList (tptp.skaf82 tptp.sk2))) :rule resolution :premises (t132.t2 t132.a0))
% 2.73/2.92  (step t132 (cl (not (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) (tptp.ssList (tptp.skaf82 tptp.sk2))) :rule subproof :discharge (t132.a0))
% 2.73/2.92  (step t133 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk2))) (tptp.ssList (tptp.skaf82 tptp.sk2))) :rule resolution :premises (t131 t132))
% 2.73/2.92  (step t134 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2)))) :rule implies_neg2)
% 2.73/2.92  (step t135 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk2))) (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t133 t134))
% 2.73/2.92  (step t136 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk2)))) :rule contraction :premises (t135))
% 2.73/2.92  (step t137 (cl (not (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) (tptp.ssList (tptp.skaf82 tptp.sk2))) :rule implies :premises (t136))
% 2.73/2.92  (step t138 (cl (tptp.ssList (tptp.skaf82 tptp.sk2))) :rule resolution :premises (t137 a12))
% 2.73/2.92  (step t139 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk2))) (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t140)
% 2.73/2.92  (assume t140.a0 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))))
% 2.73/2.92  (step t140.t1 (cl (or (not (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) (tptp.ssItem (tptp.skaf83 tptp.sk2)))) :rule forall_inst :args ((:= U tptp.sk2)))
% 2.73/2.92  (step t140.t2 (cl (not (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) (tptp.ssItem (tptp.skaf83 tptp.sk2))) :rule or :premises (t140.t1))
% 2.73/2.92  (step t140.t3 (cl (tptp.ssItem (tptp.skaf83 tptp.sk2))) :rule resolution :premises (t140.t2 t140.a0))
% 2.73/2.92  (step t140 (cl (not (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) (tptp.ssItem (tptp.skaf83 tptp.sk2))) :rule subproof :discharge (t140.a0))
% 2.73/2.92  (step t141 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk2))) (tptp.ssItem (tptp.skaf83 tptp.sk2))) :rule resolution :premises (t139 t140))
% 2.73/2.92  (step t142 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssItem (tptp.skaf83 tptp.sk2)))) :rule implies_neg2)
% 2.73/2.92  (step t143 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk2))) (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk2)))) :rule resolution :premises (t141 t142))
% 2.73/2.92  (step t144 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk2)))) :rule contraction :premises (t143))
% 2.73/2.92  (step t145 (cl (not (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) (tptp.ssItem (tptp.skaf83 tptp.sk2))) :rule implies :premises (t144))
% 2.73/2.92  (step t146 (cl (tptp.ssItem (tptp.skaf83 tptp.sk2))) :rule resolution :premises (t145 a11))
% 2.73/2.92  (step t147 (cl (not (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule or_pos)
% 2.73/2.92  (step t148 (cl (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (not (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))))) :rule reordering :premises (t147))
% 2.73/2.92  (step t149 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t150)
% 2.73/2.92  (assume t150.a0 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))))
% 2.73/2.92  (step t150.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))))) :rule forall_inst :args ((:= A (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)) (:= B (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (step t150.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule or :premises (t150.t1))
% 2.73/2.92  (step t150.t3 (cl (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule resolution :premises (t150.t2 t150.a0))
% 2.73/2.92  (step t150 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule subproof :discharge (t150.a0))
% 2.73/2.92  (step t151 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule resolution :premises (t149 t150))
% 2.73/2.92  (step t152 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (not (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))))) :rule implies_neg2)
% 2.73/2.92  (step t153 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))))) :rule resolution :premises (t151 t152))
% 2.73/2.92  (step t154 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))))) :rule contraction :premises (t153))
% 2.73/2.92  (step t155 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule implies :premises (t154))
% 2.73/2.92  (step t156 (cl (not (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= (tptp.app A B) tptp.sk2)) (not (= (tptp.app B A) tptp.sk1)))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))))) (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= (tptp.app A B) tptp.sk2)) (not (= (tptp.app B A) tptp.sk1))))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) :rule equiv_pos2)
% 2.73/2.92  (anchor :step t157 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 2.73/2.92  (step t157.t1 (cl (= A A)) :rule refl)
% 2.73/2.92  (step t157.t2 (cl (= B B)) :rule refl)
% 2.73/2.92  (step t157.t3 (cl (= (not (tptp.ssList A)) (not (tptp.ssList A)))) :rule refl)
% 2.73/2.92  (step t157.t4 (cl (= (not (tptp.ssList B)) (not (tptp.ssList B)))) :rule refl)
% 2.73/2.92  (step t157.t5 (cl (= (= (tptp.app A B) tptp.sk2) (= tptp.sk2 (tptp.app A B)))) :rule all_simplify)
% 2.73/2.92  (step t157.t6 (cl (= (not (= (tptp.app A B) tptp.sk2)) (not (= tptp.sk2 (tptp.app A B))))) :rule cong :premises (t157.t5))
% 2.73/2.92  (step t157.t7 (cl (= (= (tptp.app B A) tptp.sk1) (= tptp.sk1 (tptp.app B A)))) :rule all_simplify)
% 2.73/2.92  (step t157.t8 (cl (= (not (= (tptp.app B A) tptp.sk1)) (not (= tptp.sk1 (tptp.app B A))))) :rule cong :premises (t157.t7))
% 2.73/2.92  (step t157.t9 (cl (= (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= (tptp.app A B) tptp.sk2)) (not (= (tptp.app B A) tptp.sk1))) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) :rule cong :premises (t157.t3 t157.t4 t157.t6 t157.t8))
% 2.73/2.92  (step t157 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= (tptp.app A B) tptp.sk2)) (not (= (tptp.app B A) tptp.sk1)))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))))) :rule bind)
% 2.73/2.92  (step t158 (cl (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) :rule resolution :premises (t156 t157 a191))
% 2.73/2.92  (step t159 (cl (or (not (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk1 (tptp.app (tptp.skaf82 tptp.sk2) (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))))) :rule resolution :premises (t155 t158))
% 2.73/2.92  (step t160 (cl (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) :rule or_pos)
% 2.73/2.92  (step t161 (cl (not (tptp.ssList tptp.nil)) (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)) (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule reordering :premises (t160))
% 2.73/2.92  (step t162 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t163)
% 2.73/2.92  (assume t163.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))))
% 2.73/2.92  (step t163.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule forall_inst :args ((:= U (tptp.skaf83 tptp.sk2)) (:= V tptp.nil)))
% 2.73/2.92  (step t163.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) :rule or :premises (t163.t1))
% 2.73/2.92  (step t163.t3 (cl (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) :rule resolution :premises (t163.t2 t163.a0))
% 2.73/2.92  (step t163 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) :rule subproof :discharge (t163.a0))
% 2.73/2.92  (step t164 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) :rule resolution :premises (t162 t163))
% 2.73/2.92  (step t165 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule implies_neg2)
% 2.73/2.92  (step t166 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule resolution :premises (t164 t165))
% 2.73/2.92  (step t167 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))))) :rule contraction :premises (t166))
% 2.73/2.92  (step t168 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) :rule implies :premises (t167))
% 2.73/2.92  (step t169 (cl (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil)))) :rule resolution :premises (t168 a85))
% 2.73/2.92  (step t170 (cl (tptp.ssList (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil))) :rule resolution :premises (t161 a7 t146 t169))
% 2.73/2.92  (step t171 (cl (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule and_neg)
% 2.73/2.92  (step t172 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t173)
% 2.73/2.92  (assume t173.a0 (= tptp.sk2 tptp.sk4))
% 2.73/2.92  (assume t173.a1 (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (assume t173.a2 (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (step t173.t1 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4)) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t173.t2)
% 2.73/2.92  (assume t173.t2.a0 (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (assume t173.t2.a1 (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (assume t173.t2.a2 (= tptp.sk2 tptp.sk4))
% 2.73/2.92  (step t173.t2.t1 (cl (= tptp.sk4 tptp.sk2)) :rule symm :premises (t173.t2.a2))
% 2.73/2.92  (step t173.t2.t2 (cl (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) tptp.sk2)) :rule symm :premises (t173.t2.a1))
% 2.73/2.92  (step t173.t2.t3 (cl (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) :rule symm :premises (t173.t2.t2))
% 2.73/2.92  (step t173.t2.t4 (cl (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) :rule symm :premises (t173.t2.a0))
% 2.73/2.92  (step t173.t2.t5 (cl (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule symm :premises (t173.t2.t4))
% 2.73/2.92  (step t173.t2.t6 (cl (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule trans :premises (t173.t2.t1 t173.t2.t3 t173.t2.t5))
% 2.73/2.92  (step t173.t2 (cl (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 tptp.sk4)) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule subproof :discharge (t173.t2.a0 t173.t2.a1 t173.t2.a2))
% 2.73/2.92  (step t173.t3 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule and_pos)
% 2.73/2.92  (step t173.t4 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) :rule and_pos)
% 2.73/2.92  (step t173.t5 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 2.73/2.92  (step t173.t6 (cl (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4)))) :rule resolution :premises (t173.t2 t173.t3 t173.t4 t173.t5))
% 2.73/2.92  (step t173.t7 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule reordering :premises (t173.t6))
% 2.73/2.92  (step t173.t8 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule contraction :premises (t173.t7))
% 2.73/2.92  (step t173.t9 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4)) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t173.t1 t173.t8))
% 2.73/2.92  (step t173.t10 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4)) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule implies_neg2)
% 2.73/2.92  (step t173.t11 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4)) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4)) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule resolution :premises (t173.t9 t173.t10))
% 2.73/2.92  (step t173.t12 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4)) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule contraction :premises (t173.t11))
% 2.73/2.92  (step t173.t13 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule implies :premises (t173.t12))
% 2.73/2.92  (step t173.t14 (cl (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4)) (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 tptp.sk4))) :rule and_neg)
% 2.73/2.92  (step t173.t15 (cl (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 tptp.sk4))) :rule resolution :premises (t173.t14 t173.a2 t173.a1 t173.a0))
% 2.73/2.92  (step t173.t16 (cl (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t173.t13 t173.t15))
% 2.73/2.92  (step t173 (cl (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule subproof :discharge (t173.a0 t173.a1 t173.a2))
% 2.73/2.92  (step t174 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 2.73/2.92  (step t175 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) :rule and_pos)
% 2.73/2.92  (step t176 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule and_pos)
% 2.73/2.92  (step t177 (cl (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule resolution :premises (t173 t174 t175 t176))
% 2.73/2.92  (step t178 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule reordering :premises (t177))
% 2.73/2.92  (step t179 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule contraction :premises (t178))
% 2.73/2.92  (step t180 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t172 t179))
% 2.73/2.92  (step t181 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule implies_neg2)
% 2.73/2.92  (step t182 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule resolution :premises (t180 t181))
% 2.73/2.92  (step t183 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule contraction :premises (t182))
% 2.73/2.92  (step t184 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule implies :premises (t183))
% 2.73/2.92  (step t185 (cl (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk4 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t171 t184))
% 2.73/2.92  (step t186 (cl (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule or_pos)
% 2.73/2.92  (step t187 (cl (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule reordering :premises (t186))
% 2.73/2.92  (step t188 (cl (not (= (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))))) (not (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule equiv_pos2)
% 2.73/2.92  (step t189 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))))) :rule refl)
% 2.73/2.92  (step t190 (cl (= (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssItem (tptp.skaf83 tptp.sk2))))) :rule refl)
% 2.73/2.92  (step t191 (cl (= (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))))) :rule refl)
% 2.73/2.92  (step t192 (cl (= (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule all_simplify)
% 2.73/2.92  (step t193 (cl (= (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule cong :premises (t190 t191 t192))
% 2.73/2.92  (step t194 (cl (= (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))))) :rule cong :premises (t189 t193))
% 2.73/2.92  (step t195 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t196)
% 2.73/2.92  (assume t196.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))))
% 2.73/2.92  (step t196.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))))) :rule forall_inst :args ((:= U (tptp.skaf83 tptp.sk2)) (:= V (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (step t196.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) :rule or :premises (t196.t1))
% 2.73/2.92  (step t196.t3 (cl (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) :rule resolution :premises (t196.t2 t196.a0))
% 2.73/2.92  (step t196 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) :rule subproof :discharge (t196.a0))
% 2.73/2.92  (step t197 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) :rule resolution :premises (t195 t196))
% 2.73/2.92  (step t198 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))))) :rule implies_neg2)
% 2.73/2.92  (step t199 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))))) :rule resolution :premises (t197 t198))
% 2.73/2.92  (step t200 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))))) :rule contraction :premises (t199))
% 2.73/2.92  (step t201 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule resolution :premises (t188 t194 t200))
% 2.73/2.92  (step t202 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule implies :premises (t201))
% 2.73/2.92  (step t203 (cl (or (not (tptp.ssItem (tptp.skaf83 tptp.sk2))) (not (tptp.ssList (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule resolution :premises (t202 a119))
% 2.73/2.92  (step t204 (cl (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t187 t146 t138 t203))
% 2.73/2.92  (step t205 (cl (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule and_neg)
% 2.73/2.92  (step t206 (cl (=> (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t207)
% 2.73/2.92  (assume t207.a0 (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (assume t207.a1 (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (step t207.t1 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t207.t2)
% 2.73/2.92  (assume t207.t2.a0 (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (assume t207.t2.a1 (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))
% 2.73/2.92  (step t207.t2.t1 (cl (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) tptp.sk2)) :rule symm :premises (t207.t2.a1))
% 2.73/2.92  (step t207.t2.t2 (cl (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) :rule symm :premises (t207.t2.t1))
% 2.73/2.92  (step t207.t2.t3 (cl (= (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)) (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) :rule symm :premises (t207.t2.a0))
% 2.73/2.92  (step t207.t2.t4 (cl (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule symm :premises (t207.t2.t3))
% 2.73/2.92  (step t207.t2.t5 (cl (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule trans :premises (t207.t2.t2 t207.t2.t4))
% 2.73/2.92  (step t207.t2 (cl (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule subproof :discharge (t207.t2.a0 t207.t2.a1))
% 2.73/2.92  (step t207.t3 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule and_pos)
% 2.73/2.92  (step t207.t4 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) :rule and_pos)
% 2.73/2.92  (step t207.t5 (cl (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))))) :rule resolution :premises (t207.t2 t207.t3 t207.t4))
% 2.73/2.92  (step t207.t6 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule reordering :premises (t207.t5))
% 2.73/2.92  (step t207.t7 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule contraction :premises (t207.t6))
% 2.73/2.92  (step t207.t8 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t207.t1 t207.t7))
% 2.73/2.92  (step t207.t9 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule implies_neg2)
% 2.73/2.92  (step t207.t10 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule resolution :premises (t207.t8 t207.t9))
% 2.73/2.92  (step t207.t11 (cl (=> (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule contraction :premises (t207.t10))
% 2.73/2.92  (step t207.t12 (cl (not (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule implies :premises (t207.t11))
% 2.73/2.92  (step t207.t13 (cl (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) :rule and_neg)
% 2.73/2.92  (step t207.t14 (cl (and (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) :rule resolution :premises (t207.t13 t207.a1 t207.a0))
% 2.73/2.92  (step t207.t15 (cl (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t207.t12 t207.t14))
% 2.73/2.92  (step t207 (cl (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule subproof :discharge (t207.a0 t207.a1))
% 2.73/2.92  (step t208 (cl (not (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) :rule and_pos)
% 2.73/2.92  (step t209 (cl (not (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule and_pos)
% 2.73/2.92  (step t210 (cl (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))) (not (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (not (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))))) :rule resolution :premises (t207 t208 t209))
% 2.73/2.92  (step t211 (cl (not (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (not (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule reordering :premises (t210))
% 2.73/2.92  (step t212 (cl (not (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule contraction :premises (t211))
% 2.73/2.92  (step t213 (cl (=> (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t206 t212))
% 2.73/2.92  (step t214 (cl (=> (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule implies_neg2)
% 2.73/2.92  (step t215 (cl (=> (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (=> (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule resolution :premises (t213 t214))
% 2.73/2.92  (step t216 (cl (=> (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) :rule contraction :premises (t215))
% 2.73/2.92  (step t217 (cl (not (and (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2))))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule implies :premises (t216))
% 2.73/2.92  (step t218 (cl (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)) (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) (= tptp.sk2 (tptp.app (tptp.cons (tptp.skaf83 tptp.sk2) tptp.nil) (tptp.skaf82 tptp.sk2)))) :rule resolution :premises (t205 t217))
% 2.73/2.92  (step t219 (cl (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2)))) (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) :rule resolution :premises (t117 a190 t119 t130 t138 t146 t148 t159 t170 t138 t185 t204 a189 t218 t204))
% 2.73/2.92  (step t220 (cl (not (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))))) :rule contraction :premises (t219))
% 2.73/2.92  (step t221 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t222)
% 2.73/2.92  (assume t222.a0 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))))
% 2.73/2.92  (step t222.t1 (cl (or (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2)))) :rule forall_inst :args ((:= U tptp.sk2)))
% 2.73/2.92  (step t222.t2 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) :rule or :premises (t222.t1))
% 2.73/2.92  (step t222.t3 (cl (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) :rule resolution :premises (t222.t2 t222.a0))
% 2.73/2.92  (step t222 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) :rule subproof :discharge (t222.a0))
% 2.73/2.92  (step t223 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) :rule resolution :premises (t221 t222))
% 2.73/2.92  (step t224 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) (not (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2)))) :rule implies_neg2)
% 2.73/2.92  (step t225 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2)))) :rule resolution :premises (t223 t224))
% 2.73/2.92  (step t226 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2)))) :rule contraction :premises (t225))
% 2.73/2.92  (step t227 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)))) (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) :rule implies :premises (t226))
% 2.73/2.92  (step t228 (cl (not (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))))) (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)))) :rule equiv_pos2)
% 2.73/2.92  (anchor :step t229 :args ((U $$unsorted) (:= U U)))
% 2.73/2.92  (step t229.t1 (cl (= U U)) :rule refl)
% 2.73/2.92  (step t229.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 2.73/2.92  (step t229.t3 (cl (= (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))))) :rule all_simplify)
% 2.73/2.92  (step t229.t4 (cl (= (= tptp.nil U) (= tptp.nil U))) :rule refl)
% 2.73/2.92  (step t229.t5 (cl (= (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)))) :rule cong :premises (t229.t2 t229.t3 t229.t4))
% 2.73/2.92  (step t229 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))))) :rule bind)
% 2.73/2.92  (step t230 (cl (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)))) :rule resolution :premises (t228 t229 a108))
% 2.73/2.92  (step t231 (cl (or (not (tptp.ssList tptp.sk2)) (= tptp.sk2 (tptp.cons (tptp.skaf83 tptp.sk2) (tptp.skaf82 tptp.sk2))) (= tptp.nil tptp.sk2))) :rule resolution :premises (t227 t230))
% 2.73/2.92  (step t232 (cl (= tptp.nil tptp.sk2)) :rule resolution :premises (t83 a186 t220 t231))
% 2.73/2.92  (step t233 (cl (= tptp.nil tptp.sk4)) :rule resolution :premises (t81 a189 t232))
% 2.73/2.92  (step t234 (cl (= tptp.nil tptp.sk3)) :rule resolution :premises (t66 t233))
% 2.73/2.92  (step t235 (cl (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule or_pos)
% 2.73/2.92  (step t236 (cl (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule contraction :premises (t235))
% 2.73/2.92  (step t237 (cl (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))) (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule reordering :premises (t236))
% 2.73/2.92  (step t238 (cl (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (= tptp.nil tptp.sk2))) :rule and_neg)
% 2.73/2.92  (step t239 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t240)
% 2.73/2.92  (assume t240.a0 (= tptp.nil (tptp.app tptp.nil tptp.nil)))
% 2.73/2.92  (assume t240.a1 (= tptp.nil tptp.sk2))
% 2.73/2.92  (step t240.t1 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t240.t2)
% 2.73/2.92  (assume t240.t2.a0 (= tptp.nil (tptp.app tptp.nil tptp.nil)))
% 2.73/2.92  (assume t240.t2.a1 (= tptp.nil tptp.sk2))
% 2.73/2.92  (step t240.t2.t1 (cl (= tptp.sk2 tptp.nil)) :rule symm :premises (t240.t2.a1))
% 2.73/2.92  (step t240.t2.t2 (cl (= (tptp.app tptp.nil tptp.nil) tptp.nil)) :rule symm :premises (t240.t2.a0))
% 2.73/2.92  (step t240.t2.t3 (cl (= tptp.nil (tptp.app tptp.nil tptp.nil))) :rule symm :premises (t240.t2.t2))
% 2.73/2.92  (step t240.t2.t4 (cl (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule trans :premises (t240.t2.t1 t240.t2.t3))
% 2.73/2.92  (step t240.t2 (cl (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule subproof :discharge (t240.t2.a0 t240.t2.a1))
% 2.73/2.92  (step t240.t3 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.nil (tptp.app tptp.nil tptp.nil))) :rule and_pos)
% 2.73/2.92  (step t240.t4 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk2)) :rule and_pos)
% 2.73/2.92  (step t240.t5 (cl (= tptp.sk2 (tptp.app tptp.nil tptp.nil)) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)))) :rule resolution :premises (t240.t2 t240.t3 t240.t4))
% 2.73/2.92  (step t240.t6 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule reordering :premises (t240.t5))
% 2.73/2.92  (step t240.t7 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule contraction :premises (t240.t6))
% 2.73/2.92  (step t240.t8 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule resolution :premises (t240.t1 t240.t7))
% 2.73/2.92  (step t240.t9 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil)))) :rule implies_neg2)
% 2.73/2.92  (step t240.t10 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil)))) :rule resolution :premises (t240.t8 t240.t9))
% 2.73/2.92  (step t240.t11 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil)))) :rule contraction :premises (t240.t10))
% 2.73/2.92  (step t240.t12 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule implies :premises (t240.t11))
% 2.73/2.92  (step t240.t13 (cl (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (= tptp.nil tptp.sk2))) :rule and_neg)
% 2.73/2.92  (step t240.t14 (cl (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) :rule resolution :premises (t240.t13 t240.a0 t240.a1))
% 2.73/2.92  (step t240.t15 (cl (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule resolution :premises (t240.t12 t240.t14))
% 2.73/2.92  (step t240 (cl (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule subproof :discharge (t240.a0 t240.a1))
% 2.73/2.92  (step t241 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.nil (tptp.app tptp.nil tptp.nil))) :rule and_pos)
% 2.73/2.92  (step t242 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.nil tptp.sk2)) :rule and_pos)
% 2.73/2.92  (step t243 (cl (= tptp.sk2 (tptp.app tptp.nil tptp.nil)) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)))) :rule resolution :premises (t240 t241 t242))
% 2.73/2.92  (step t244 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule reordering :premises (t243))
% 2.73/2.92  (step t245 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule contraction :premises (t244))
% 2.73/2.92  (step t246 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule resolution :premises (t239 t245))
% 2.73/2.92  (step t247 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil)))) :rule implies_neg2)
% 2.73/2.92  (step t248 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil)))) :rule resolution :premises (t246 t247))
% 2.73/2.92  (step t249 (cl (=> (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil)))) :rule contraction :premises (t248))
% 2.73/2.92  (step t250 (cl (not (and (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil tptp.sk2))) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule implies :premises (t249))
% 2.73/2.92  (step t251 (cl (not (= tptp.nil (tptp.app tptp.nil tptp.nil))) (not (= tptp.nil tptp.sk2)) (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule resolution :premises (t238 t250))
% 2.73/2.92  (step t252 (cl (not (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app U V) tptp.nil))) (or (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))))) (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app U V) tptp.nil)))) (or (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil)))) :rule equiv_pos2)
% 2.73/2.92  (anchor :step t253 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 2.73/2.92  (step t253.t1 (cl (= U U)) :rule refl)
% 2.73/2.92  (step t253.t2 (cl (= V V)) :rule refl)
% 2.73/2.92  (step t253.t3 (cl (= (not (= tptp.nil U)) (not (= tptp.nil U)))) :rule refl)
% 2.73/2.92  (step t253.t4 (cl (= (not (= tptp.nil V)) (not (= tptp.nil V)))) :rule refl)
% 2.73/2.92  (step t253.t5 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 2.73/2.92  (step t253.t6 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 2.73/2.92  (step t253.t7 (cl (= (= (tptp.app U V) tptp.nil) (= tptp.nil (tptp.app U V)))) :rule all_simplify)
% 2.73/2.92  (step t253.t8 (cl (= (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app U V) tptp.nil)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil (tptp.app U V))))) :rule cong :premises (t253.t3 t253.t4 t253.t5 t253.t6 t253.t7))
% 2.73/2.92  (step t253 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app U V) tptp.nil))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil (tptp.app U V)))))) :rule bind)
% 2.73/2.92  (step t254 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil (tptp.app U V)))) (or (not (= tptp.nil tptp.nil)) (not (= tptp.nil tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))))) :rule all_simplify)
% 2.73/2.92  (step t255 (cl (= (= tptp.nil tptp.nil) true)) :rule all_simplify)
% 2.73/2.92  (step t256 (cl (= (not (= tptp.nil tptp.nil)) (not true))) :rule cong :premises (t255))
% 2.73/2.92  (step t257 (cl (= (not true) false)) :rule all_simplify)
% 2.73/2.92  (step t258 (cl (= (not (= tptp.nil tptp.nil)) false)) :rule trans :premises (t256 t257))
% 2.73/2.92  (step t259 (cl (= (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)))) :rule refl)
% 2.73/2.92  (step t260 (cl (= (= tptp.nil (tptp.app tptp.nil tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil)))) :rule refl)
% 2.73/2.92  (step t261 (cl (= (or (not (= tptp.nil tptp.nil)) (not (= tptp.nil tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))) (or false false (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))))) :rule cong :premises (t258 t258 t259 t259 t260))
% 2.73/2.92  (step t262 (cl (= (or false false (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))) (or (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))))) :rule all_simplify)
% 2.73/2.92  (step t263 (cl (= (or (not (= tptp.nil tptp.nil)) (not (= tptp.nil tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))) (or (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))))) :rule trans :premises (t261 t262))
% 2.73/2.92  (step t264 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil (tptp.app U V)))) (or (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))))) :rule trans :premises (t254 t263))
% 2.73/2.92  (step t265 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app U V) tptp.nil))) (or (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))))) :rule trans :premises (t253 t264))
% 2.73/2.92  (step t266 (cl (or (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil)))) :rule resolution :premises (t252 t265 a144))
% 2.73/2.92  (step t267 (cl (not (tptp.ssList tptp.nil)) (= tptp.nil (tptp.app tptp.nil tptp.nil))) :rule or :premises (t266))
% 2.73/2.92  (step t268 (cl (= tptp.nil (tptp.app tptp.nil tptp.nil))) :rule resolution :premises (t267 a7))
% 2.73/2.92  (step t269 (cl (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) :rule resolution :premises (t251 t268 t232))
% 2.73/2.92  (step t270 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) :rule implies_neg1)
% 2.73/2.92  (anchor :step t271)
% 2.73/2.92  (assume t271.a0 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))))
% 2.73/2.92  (step t271.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule forall_inst :args ((:= A tptp.nil) (:= B tptp.nil)))
% 2.73/2.92  (step t271.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule or :premises (t271.t1))
% 2.73/2.92  (step t271.t3 (cl (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule resolution :premises (t271.t2 t271.a0))
% 2.73/2.92  (step t271 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule subproof :discharge (t271.a0))
% 2.73/2.92  (step t272 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule resolution :premises (t270 t271))
% 2.73/2.92  (step t273 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule implies_neg2)
% 2.73/2.92  (step t274 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule resolution :premises (t272 t273))
% 2.73/2.92  (step t275 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))))) :rule contraction :premises (t274))
% 2.73/2.92  (step t276 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.ssList B)) (not (= tptp.sk2 (tptp.app A B))) (not (= tptp.sk1 (tptp.app B A)))))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule implies :premises (t275))
% 2.73/2.92  (step t277 (cl (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (= tptp.sk2 (tptp.app tptp.nil tptp.nil))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil))))) :rule resolution :premises (t276 t158))
% 2.73/2.92  (step t278 (cl (not (= tptp.sk1 (tptp.app tptp.nil tptp.nil)))) :rule resolution :premises (t237 a7 t269 t277))
% 2.73/2.92  (step t279 (cl) :rule resolution :premises (t65 t234 t278 a190 t268))
% 2.73/2.92  
% 2.73/2.93  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.jGTRvrnBHK/cvc5---1.0.5_12144.smt2
% 2.73/2.94  % cvc5---1.0.5 exiting
% 2.73/2.94  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------