TSTP Solution File: SWC065-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC065-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n012.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 18:00:10 EDT 2024
% Result : Unsatisfiable 20.85s 21.05s
% Output : Proof 20.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWC065-1 : TPTP v8.2.0. Released v2.4.0.
% 0.04/0.15 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 26 16:16:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.21/0.53 %----Proving TF0_NAR, FOF, or CNF
% 0.38/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.57/10.78 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.60/15.80 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.63/20.83 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 20.85/21.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.zFPkPDXVLc/cvc5---1.0.5_18497.smt2
% 20.85/21.05 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.zFPkPDXVLc/cvc5---1.0.5_18497.smt2
% 20.87/21.08 (assume a0 (tptp.equalelemsP tptp.nil))
% 20.87/21.08 (assume a1 (tptp.duplicatefreeP tptp.nil))
% 20.87/21.08 (assume a2 (tptp.strictorderedP tptp.nil))
% 20.87/21.08 (assume a3 (tptp.totalorderedP tptp.nil))
% 20.87/21.08 (assume a4 (tptp.strictorderP tptp.nil))
% 20.87/21.08 (assume a5 (tptp.totalorderP tptp.nil))
% 20.87/21.08 (assume a6 (tptp.cyclefreeP tptp.nil))
% 20.87/21.08 (assume a7 (tptp.ssList tptp.nil))
% 20.87/21.08 (assume a8 (tptp.ssItem tptp.skac3))
% 20.87/21.08 (assume a9 (tptp.ssItem tptp.skac2))
% 20.87/21.08 (assume a10 (not (tptp.singletonP tptp.nil)))
% 20.87/21.08 (assume a11 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))))
% 20.87/21.08 (assume a12 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))))
% 20.87/21.08 (assume a13 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf81 U))))
% 20.87/21.08 (assume a14 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf80 U))))
% 20.87/21.08 (assume a15 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf79 U))))
% 20.87/21.08 (assume a16 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf78 U))))
% 20.87/21.08 (assume a17 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf77 U))))
% 20.87/21.08 (assume a18 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf76 U))))
% 20.87/21.08 (assume a19 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf75 U))))
% 20.87/21.08 (assume a20 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf74 U))))
% 20.87/21.08 (assume a21 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf73 U))))
% 20.87/21.08 (assume a22 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf72 U))))
% 20.87/21.08 (assume a23 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf71 U))))
% 20.87/21.08 (assume a24 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf70 U))))
% 20.87/21.08 (assume a25 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf69 U))))
% 20.87/21.08 (assume a26 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf68 U))))
% 20.87/21.08 (assume a27 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf67 U))))
% 20.87/21.08 (assume a28 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf66 U))))
% 20.87/21.08 (assume a29 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf65 U))))
% 20.87/21.08 (assume a30 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf64 U))))
% 20.87/21.08 (assume a31 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf63 U))))
% 20.87/21.08 (assume a32 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf62 U))))
% 20.87/21.08 (assume a33 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf61 U))))
% 20.87/21.08 (assume a34 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf60 U))))
% 20.87/21.08 (assume a35 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf59 U))))
% 20.87/21.08 (assume a36 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf58 U))))
% 20.87/21.08 (assume a37 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf57 U))))
% 20.87/21.08 (assume a38 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf56 U))))
% 20.87/21.08 (assume a39 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf55 U))))
% 20.87/21.08 (assume a40 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf54 U))))
% 20.87/21.08 (assume a41 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf53 U))))
% 20.87/21.08 (assume a42 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf52 U))))
% 20.87/21.08 (assume a43 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf51 U))))
% 20.87/21.08 (assume a44 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf50 U))))
% 20.87/21.08 (assume a45 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf49 U))))
% 20.87/21.08 (assume a46 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf44 U))))
% 20.87/21.08 (assume a47 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf48 U V))))
% 20.87/21.08 (assume a48 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf47 U V))))
% 20.87/21.08 (assume a49 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf46 U V))))
% 20.87/21.08 (assume a50 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf45 U V))))
% 20.87/21.08 (assume a51 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf43 U V))))
% 20.87/21.08 (assume a52 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf42 U V))))
% 20.87/21.08 (assume a53 (not (= tptp.skac3 tptp.skac2)))
% 20.87/21.08 (assume a54 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.geq U U))))
% 20.87/21.08 (assume a55 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U tptp.nil))))
% 20.87/21.08 (assume a56 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))
% 20.87/21.08 (assume a57 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.rearsegP U tptp.nil))))
% 20.87/21.08 (assume a58 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.rearsegP U U))))
% 20.87/21.08 (assume a59 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U tptp.nil))))
% 20.87/21.08 (assume a60 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U U))))
% 20.87/21.08 (assume a61 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.leq U U))))
% 20.87/21.08 (assume a62 (forall ((U $$unsorted)) (or (not (tptp.lt U U)) (not (tptp.ssItem U)))))
% 20.87/21.08 (assume a63 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.equalelemsP (tptp.cons U tptp.nil)))))
% 20.87/21.08 (assume a64 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))))
% 20.87/21.08 (assume a65 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U tptp.nil)))))
% 20.87/21.08 (assume a66 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U tptp.nil)))))
% 20.87/21.08 (assume a67 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.strictorderP (tptp.cons U tptp.nil)))))
% 20.87/21.08 (assume a68 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.totalorderP (tptp.cons U tptp.nil)))))
% 20.87/21.08 (assume a69 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.cyclefreeP (tptp.cons U tptp.nil)))))
% 20.87/21.08 (assume a70 (forall ((U $$unsorted)) (or (not (tptp.memberP tptp.nil U)) (not (tptp.ssItem U)))))
% 20.87/21.08 (assume a71 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (tptp.duplicatefreeP U) (tptp.ssItem V))))
% 20.87/21.08 (assume a72 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app U tptp.nil) U))))
% 20.87/21.08 (assume a73 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U))))
% 20.87/21.08 (assume a74 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssList (tptp.tl U)) (= tptp.nil U))))
% 20.87/21.08 (assume a75 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))))
% 20.87/21.08 (assume a76 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssList (tptp.tl U)) (= tptp.nil U))))
% 20.87/21.08 (assume a77 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))))
% 20.87/21.08 (assume a78 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.segmentP tptp.nil U))))
% 20.87/21.08 (assume a79 (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 20.87/21.08 (assume a80 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.rearsegP tptp.nil U))))
% 20.87/21.08 (assume a81 (forall ((U $$unsorted)) (or (not (tptp.rearsegP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 20.87/21.08 (assume a82 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.frontsegP tptp.nil U))))
% 20.87/21.08 (assume a83 (forall ((U $$unsorted)) (or (not (tptp.frontsegP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 20.87/21.08 (assume a84 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))))
% 20.87/21.08 (assume a85 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))))
% 20.87/21.08 (assume a86 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (tptp.leq (tptp.skaf50 U) (tptp.skaf49 U)))))
% 20.87/21.08 (assume a87 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (tptp.leq (tptp.skaf49 U) (tptp.skaf50 U)))))
% 20.87/21.08 (assume a88 (forall ((U $$unsorted)) (or (not (= (tptp.skaf79 U) (tptp.skaf78 U))) (not (tptp.ssList U)) (tptp.equalelemsP U))))
% 20.87/21.08 (assume a89 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf69 U) (tptp.skaf70 U))) (not (tptp.ssList U)) (tptp.strictorderedP U))))
% 20.87/21.08 (assume a90 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf64 U) (tptp.skaf65 U))) (not (tptp.ssList U)) (tptp.totalorderedP U))))
% 20.87/21.08 (assume a91 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf60 U) (tptp.skaf59 U))) (not (tptp.ssList U)) (tptp.strictorderP U))))
% 20.87/21.08 (assume a92 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf59 U) (tptp.skaf60 U))) (not (tptp.ssList U)) (tptp.strictorderP U))))
% 20.87/21.08 (assume a93 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf55 U) (tptp.skaf54 U))) (not (tptp.ssList U)) (tptp.totalorderP U))))
% 20.87/21.08 (assume a94 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf54 U) (tptp.skaf55 U))) (not (tptp.ssList U)) (tptp.totalorderP U))))
% 20.87/21.08 (assume a95 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.tl (tptp.cons U V)) V))))
% 20.87/21.08 (assume a96 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.hd (tptp.cons U V)) U))))
% 20.87/21.08 (assume a97 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))
% 20.87/21.08 (assume a98 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) V)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))
% 20.87/21.08 (assume a99 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= V U))))
% 20.87/21.08 (assume a100 (forall ((U $$unsorted)) (or (not (tptp.singletonP U)) (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf44 U) tptp.nil) U))))
% 20.87/21.08 (assume a101 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem V)) (tptp.neq V U) (= V U))))
% 20.87/21.08 (assume a102 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq U V))))
% 20.87/21.08 (assume a103 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= tptp.nil U))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (assume a108 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U))))
% 20.87/21.08 (assume a109 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.gt V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)))))
% 20.87/21.08 (assume a110 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.lt U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)))))
% 20.87/21.08 (assume a111 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.strictorderedP (tptp.cons V U)))))
% 20.87/21.08 (assume a112 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.totalorderedP (tptp.cons V U)))))
% 20.87/21.08 (assume a113 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.lt V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)))))
% 20.87/21.08 (assume a114 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssList V)) (not (tptp.ssList U)))))
% 20.87/21.08 (assume a115 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U tptp.nil) V)) (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.singletonP V))))
% 20.87/21.08 (assume a116 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)))))
% 20.87/21.08 (assume a117 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))))
% 20.87/21.08 (assume a118 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))))
% 20.87/21.08 (assume a119 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))))
% 20.87/21.08 (assume a120 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))))
% 20.87/21.08 (assume a121 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))))
% 20.87/21.08 (assume a122 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.hd (tptp.app V U)) (tptp.hd V)))))
% 20.87/21.08 (assume a123 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP V) (= tptp.nil V))))
% 20.87/21.08 (assume a124 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP V) (= tptp.nil V))))
% 20.87/21.08 (assume a125 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))))
% 20.87/21.08 (assume a126 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 20.87/21.08 (assume a127 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.rearsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 20.87/21.08 (assume a128 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 20.87/21.08 (assume a129 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))))
% 20.87/21.08 (assume a130 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app (tptp.skaf46 U V) V) U))))
% 20.87/21.08 (assume a131 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app V (tptp.skaf45 U V)) U))))
% 20.87/21.08 (assume a132 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.tl (tptp.app V U)) (tptp.app (tptp.tl V) U)))))
% 20.87/21.08 (assume a133 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.lt U (tptp.hd V)) (= tptp.nil V))))
% 20.87/21.08 (assume a134 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.leq U (tptp.hd V)) (= tptp.nil V))))
% 20.87/21.08 (assume a135 (forall ((U $$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))))
% 20.87/21.08 (assume a136 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP (tptp.app U W) V))))
% 20.87/21.08 (assume a137 (forall ((U $$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))))
% 20.87/21.08 (assume a138 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons W U) V))))
% 20.87/21.08 (assume a139 (forall ((U $$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))))
% 20.87/21.08 (assume a140 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.app W U) V))))
% 20.87/21.08 (assume a141 (forall ((U $$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))))
% 20.87/21.08 (assume a142 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (tptp.rearsegP W V))))
% 20.87/21.08 (assume a143 (forall ((U $$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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (assume a145 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.gt V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.gt U W))))
% 20.87/21.08 (assume a146 (forall ((U $$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))))
% 20.87/21.08 (assume a147 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.geq U W))))
% 20.87/21.08 (assume a148 (forall ((U $$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))))))
% 20.87/21.08 (assume a149 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) (tptp.app U W))) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (= V W))))
% 20.87/21.08 (assume a150 (forall ((U $$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))))
% 20.87/21.08 (assume a151 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.segmentP U W))))
% 20.87/21.08 (assume a152 (forall ((U $$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))))
% 20.87/21.08 (assume a153 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP U W))))
% 20.87/21.08 (assume a154 (forall ((U $$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))))
% 20.87/21.08 (assume a155 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq U W))))
% 20.87/21.08 (assume a156 (forall ((U $$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)))))
% 20.87/21.08 (assume a157 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP (tptp.app U V) W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (tptp.memberP V W) (tptp.memberP U W))))
% 20.87/21.08 (assume a158 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U (tptp.hd V))) (not (tptp.totalorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U V)) (= tptp.nil V))))
% 20.87/21.08 (assume a159 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U (tptp.hd V))) (not (tptp.strictorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U V)) (= tptp.nil V))))
% 20.87/21.08 (assume a160 (forall ((U $$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))))
% 20.87/21.08 (assume a161 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.duplicatefreeP U) (= (tptp.app (tptp.app (tptp.skaf75 U) (tptp.cons (tptp.skaf74 U) (tptp.skaf76 U))) (tptp.cons (tptp.skaf74 U) (tptp.skaf77 U))) U))))
% 20.87/21.08 (assume a162 (forall ((U $$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))))
% 20.87/21.08 (assume a163 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderedP U) (= (tptp.app (tptp.app (tptp.skaf66 U) (tptp.cons (tptp.skaf64 U) (tptp.skaf67 U))) (tptp.cons (tptp.skaf65 U) (tptp.skaf68 U))) U))))
% 20.87/21.08 (assume a164 (forall ((U $$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))))
% 20.87/21.08 (assume a165 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderP U) (= (tptp.app (tptp.app (tptp.skaf56 U) (tptp.cons (tptp.skaf54 U) (tptp.skaf57 U))) (tptp.cons (tptp.skaf55 U) (tptp.skaf58 U))) U))))
% 20.87/21.08 (assume a166 (forall ((U $$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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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)))))
% 20.87/21.08 (assume a178 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons V X)) Y)) (not (tptp.ssList X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (not (tptp.duplicatefreeP Y)) (not (tptp.ssList Y)))))
% 20.87/21.08 (assume a179 (forall ((U $$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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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))))
% 20.87/21.08 (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)))))
% 20.87/21.08 (assume a185 (tptp.ssList tptp.sk1))
% 20.87/21.08 (assume a186 (tptp.ssList tptp.sk2))
% 20.87/21.08 (assume a187 (tptp.ssList tptp.sk3))
% 20.87/21.08 (assume a188 (tptp.ssList tptp.sk4))
% 20.87/21.08 (assume a189 (= tptp.sk2 tptp.sk4))
% 20.87/21.08 (assume a190 (= tptp.sk1 tptp.sk3))
% 20.87/21.08 (assume a191 (tptp.ssList tptp.sk5))
% 20.87/21.08 (assume a192 (= (tptp.app tptp.sk3 tptp.sk5) tptp.sk4))
% 20.87/21.08 (assume a193 (tptp.equalelemsP tptp.sk3))
% 20.87/21.08 (assume a194 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.ssItem A)) (not (tptp.ssList B)) (not (= (tptp.app (tptp.cons A tptp.nil) B) tptp.sk5)) (not (tptp.ssList C)) (not (= (tptp.app C (tptp.cons A tptp.nil)) tptp.sk3)))))
% 20.87/21.08 (assume a195 (or (= tptp.nil tptp.sk4) (not (= tptp.nil tptp.sk3))))
% 20.87/21.08 (assume a196 (or (= tptp.nil tptp.sk2) (tptp.neq tptp.sk2 tptp.nil)))
% 20.87/21.08 (assume a197 (forall ((A $$unsorted)) (or (= tptp.nil tptp.sk2) (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A)))))
% 20.87/21.08 (assume a198 (or (not (= tptp.nil tptp.sk1)) (tptp.neq tptp.sk2 tptp.nil)))
% 20.87/21.08 (assume a199 (forall ((A $$unsorted)) (or (not (= tptp.nil tptp.sk1)) (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A)))))
% 20.87/21.08 (step t1 (cl (not (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)) :rule or_pos)
% 20.87/21.08 (step t2 (cl (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3) (not (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule reordering :premises (t1))
% 20.87/21.08 (step t3 (cl (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule and_neg)
% 20.87/21.08 (step t4 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t5)
% 20.87/21.08 (assume t5.a0 (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))
% 20.87/21.08 (assume t5.a1 (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))
% 20.87/21.08 (step t5.t1 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t5.t2)
% 20.87/21.08 (assume t5.t2.a0 (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))
% 20.87/21.08 (assume t5.t2.a1 (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))
% 20.87/21.08 (step t5.t2.t1 (cl (= (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)) true) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)))) :rule equiv_simplify)
% 20.87/21.08 (step t5.t2.t2 (cl (not (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)) true)) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule equiv1 :premises (t5.t2.t1))
% 20.87/21.08 (step t5.t2.t3 (cl (= (tptp.app tptp.nil tptp.sk3) tptp.sk3)) :rule symm :premises (t5.t2.a1))
% 20.87/21.08 (step t5.t2.t4 (cl (= tptp.sk5 tptp.sk5)) :rule refl)
% 20.87/21.08 (step t5.t2.t5 (cl (= (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) :rule cong :premises (t5.t2.t3 t5.t2.t4))
% 20.87/21.08 (step t5.t2.t6 (cl (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)) (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))) :rule cong :premises (t5.t2.t5))
% 20.87/21.08 (step t5.t2.t7 (cl (= (= (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) true) (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))) :rule equiv_simplify)
% 20.87/21.08 (step t5.t2.t8 (cl (= (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) true) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))) :rule equiv2 :premises (t5.t2.t7))
% 20.87/21.08 (step t5.t2.t9 (cl (= (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) true)) :rule resolution :premises (t5.t2.t8 t5.t2.a0))
% 20.87/21.08 (step t5.t2.t10 (cl (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)) true)) :rule trans :premises (t5.t2.t6 t5.t2.t9))
% 20.87/21.08 (step t5.t2.t11 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule resolution :premises (t5.t2.t2 t5.t2.t10))
% 20.87/21.08 (step t5.t2 (cl (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule subproof :discharge (t5.t2.a0 t5.t2.a1))
% 20.87/21.08 (step t5.t3 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) :rule and_pos)
% 20.87/21.08 (step t5.t4 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t5.t5 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)) (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule resolution :premises (t5.t2 t5.t3 t5.t4))
% 20.87/21.08 (step t5.t6 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule reordering :premises (t5.t5))
% 20.87/21.08 (step t5.t7 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule contraction :premises (t5.t6))
% 20.87/21.08 (step t5.t8 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule resolution :premises (t5.t1 t5.t7))
% 20.87/21.08 (step t5.t9 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)))) :rule implies_neg2)
% 20.87/21.08 (step t5.t10 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)))) :rule resolution :premises (t5.t8 t5.t9))
% 20.87/21.08 (step t5.t11 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)))) :rule contraction :premises (t5.t10))
% 20.87/21.08 (step t5.t12 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule implies :premises (t5.t11))
% 20.87/21.08 (step t5.t13 (cl (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule and_neg)
% 20.87/21.08 (step t5.t14 (cl (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule resolution :premises (t5.t13 t5.a0 t5.a1))
% 20.87/21.08 (step t5.t15 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule resolution :premises (t5.t12 t5.t14))
% 20.87/21.08 (step t5 (cl (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule subproof :discharge (t5.a0 t5.a1))
% 20.87/21.08 (step t6 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) :rule and_pos)
% 20.87/21.08 (step t7 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t8 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)) (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule resolution :premises (t5 t6 t7))
% 20.87/21.08 (step t9 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule reordering :premises (t8))
% 20.87/21.08 (step t10 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule contraction :premises (t9))
% 20.87/21.08 (step t11 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule resolution :premises (t4 t10))
% 20.87/21.08 (step t12 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)))) :rule implies_neg2)
% 20.87/21.08 (step t13 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)))) :rule resolution :premises (t11 t12))
% 20.87/21.08 (step t14 (cl (=> (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5)))) :rule contraction :premises (t13))
% 20.87/21.08 (step t15 (cl (not (and (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule implies :premises (t14))
% 20.87/21.08 (step t16 (cl (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule resolution :premises (t3 t15))
% 20.87/21.08 (step t17 (cl (not (= (tptp.ssList tptp.sk2) (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.ssList tptp.sk2)) (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) :rule equiv_pos2)
% 20.87/21.08 (step t18 (cl (and (= tptp.sk4 (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk1 tptp.sk3) (= tptp.sk2 tptp.sk4)) (not (= tptp.sk4 (tptp.app tptp.sk3 tptp.sk5))) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk2 tptp.sk4))) :rule and_neg)
% 20.87/21.08 (step t19 (cl (= tptp.sk4 (tptp.app tptp.sk3 tptp.sk5))) :rule symm :premises (a192))
% 20.87/21.08 (step t20 (cl (and (= tptp.sk4 (tptp.app tptp.sk3 tptp.sk5)) (= tptp.sk1 tptp.sk3) (= tptp.sk2 tptp.sk4))) :rule resolution :premises (t18 t19 a190 a189))
% 20.87/21.08 (step t21 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t20))
% 20.87/21.08 (step t22 (cl (= tptp.sk4 (tptp.app tptp.sk3 tptp.sk5))) :rule and :premises (t20))
% 20.87/21.08 (step t23 (cl (= tptp.sk2 (tptp.app tptp.sk3 tptp.sk5))) :rule trans :premises (t21 t22))
% 20.87/21.08 (step t24 (cl (= (tptp.ssList tptp.sk2) (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))) :rule cong :premises (t23))
% 20.87/21.08 (step t25 (cl (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) :rule resolution :premises (t17 t24 a186))
% 20.87/21.08 (step t26 (cl (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule or_pos)
% 20.87/21.08 (step t27 (cl (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule reordering :premises (t26))
% 20.87/21.08 (step t28 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t29)
% 20.87/21.08 (assume t29.a0 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))
% 20.87/21.08 (step t29.t1 (cl (or (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule forall_inst :args ((:= U tptp.sk3)))
% 20.87/21.08 (step t29.t2 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule or :premises (t29.t1))
% 20.87/21.08 (step t29.t3 (cl (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule resolution :premises (t29.t2 t29.a0))
% 20.87/21.08 (step t29 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule subproof :discharge (t29.a0))
% 20.87/21.08 (step t30 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule resolution :premises (t28 t29))
% 20.87/21.08 (step t31 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule implies_neg2)
% 20.87/21.08 (step t32 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule resolution :premises (t30 t31))
% 20.87/21.08 (step t33 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule contraction :premises (t32))
% 20.87/21.08 (step t34 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule implies :premises (t33))
% 20.87/21.08 (step t35 (cl (not (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) :rule equiv_pos2)
% 20.87/21.08 (anchor :step t36 :args ((U $$unsorted) (:= U U)))
% 20.87/21.08 (step t36.t1 (cl (= U U)) :rule refl)
% 20.87/21.08 (step t36.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 20.87/21.08 (step t36.t3 (cl (= (= (tptp.app tptp.nil U) U) (= U (tptp.app tptp.nil U)))) :rule all_simplify)
% 20.87/21.08 (step t36.t4 (cl (= (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) :rule cong :premises (t36.t2 t36.t3))
% 20.87/21.08 (step t36 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) :rule bind)
% 20.87/21.08 (step t37 (cl (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) :rule resolution :premises (t35 t36 a73))
% 20.87/21.08 (step t38 (cl (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule resolution :premises (t34 t37))
% 20.87/21.08 (step t39 (cl (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule resolution :premises (t27 a187 t38))
% 20.87/21.08 (step t40 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) :rule resolution :premises (t16 t25 t39))
% 20.87/21.08 (step t41 (cl (not (= (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))))) (not (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule equiv_pos2)
% 20.87/21.08 (step t42 (cl (= (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule refl)
% 20.87/21.08 (step t43 (cl (= (= (= (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) true) (= (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) :rule equiv_simplify)
% 20.87/21.08 (step t44 (cl (not (= (= (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) true)) (= (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) :rule equiv1 :premises (t43))
% 20.87/21.08 (step t45 (cl (= (= (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))))) :rule all_simplify)
% 20.87/21.08 (step t46 (cl (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) :rule refl)
% 20.87/21.08 (step t47 (cl (= (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) :rule all_simplify)
% 20.87/21.08 (step t48 (cl (= (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) :rule cong :premises (t46 t47))
% 20.87/21.08 (step t49 (cl (= (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) true)) :rule all_simplify)
% 20.87/21.08 (step t50 (cl (= (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) true)) :rule trans :premises (t48 t49))
% 20.87/21.08 (step t51 (cl (= (= (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) true)) :rule trans :premises (t45 t50))
% 20.87/21.08 (step t52 (cl (= (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) :rule resolution :premises (t44 t51))
% 20.87/21.08 (step t53 (cl (= (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule refl)
% 20.87/21.08 (step t54 (cl (= (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))))) :rule cong :premises (t42 t52 t53))
% 20.87/21.08 (step t55 (cl (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) :rule and_neg)
% 20.87/21.08 (step t56 (cl (=> (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t57)
% 20.87/21.08 (assume t57.a0 (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))
% 20.87/21.08 (assume t57.a1 (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))
% 20.87/21.08 (step t57.t1 (cl (=> (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t57.t2)
% 20.87/21.08 (assume t57.t2.a0 (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))
% 20.87/21.08 (assume t57.t2.a1 (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))
% 20.87/21.08 (step t57.t2.t1 (cl (= (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3) false) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule equiv_simplify)
% 20.87/21.08 (step t57.t2.t2 (cl (not (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3) false)) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule equiv1 :premises (t57.t2.t1))
% 20.87/21.08 (step t57.t2.t3 (cl (= (tptp.app tptp.nil tptp.sk3) tptp.sk3)) :rule symm :premises (t57.t2.a1))
% 20.87/21.08 (step t57.t2.t4 (cl (= tptp.sk5 tptp.sk5)) :rule refl)
% 20.87/21.08 (step t57.t2.t5 (cl (= (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) :rule cong :premises (t57.t2.t3 t57.t2.t4))
% 20.87/21.08 (step t57.t2.t6 (cl (= tptp.sk3 tptp.sk3)) :rule refl)
% 20.87/21.08 (step t57.t2.t7 (cl (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) :rule cong :premises (t57.t2.t5 t57.t2.t6))
% 20.87/21.08 (step t57.t2.t8 (cl (= (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) false) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) :rule equiv_simplify)
% 20.87/21.08 (step t57.t2.t9 (cl (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) false) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) :rule equiv2 :premises (t57.t2.t8))
% 20.87/21.08 (step t57.t2.t10 (cl (not (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) :rule not_not)
% 20.87/21.08 (step t57.t2.t11 (cl (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) false) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) :rule resolution :premises (t57.t2.t9 t57.t2.t10))
% 20.87/21.08 (step t57.t2.t12 (cl (= (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) false)) :rule resolution :premises (t57.t2.t11 t57.t2.a0))
% 20.87/21.08 (step t57.t2.t13 (cl (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3) false)) :rule trans :premises (t57.t2.t7 t57.t2.t12))
% 20.87/21.08 (step t57.t2.t14 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule resolution :premises (t57.t2.t2 t57.t2.t13))
% 20.87/21.08 (step t57.t2 (cl (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule subproof :discharge (t57.t2.a0 t57.t2.a1))
% 20.87/21.08 (step t57.t3 (cl (not (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t57.t4 (cl (not (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t57.t5 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)) (not (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule resolution :premises (t57.t2 t57.t3 t57.t4))
% 20.87/21.08 (step t57.t6 (cl (not (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule reordering :premises (t57.t5))
% 20.87/21.08 (step t57.t7 (cl (not (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule contraction :premises (t57.t6))
% 20.87/21.08 (step t57.t8 (cl (=> (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule resolution :premises (t57.t1 t57.t7))
% 20.87/21.08 (step t57.t9 (cl (=> (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (not (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule implies_neg2)
% 20.87/21.08 (step t57.t10 (cl (=> (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (=> (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule resolution :premises (t57.t8 t57.t9))
% 20.87/21.08 (step t57.t11 (cl (=> (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule contraction :premises (t57.t10))
% 20.87/21.08 (step t57.t12 (cl (not (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule implies :premises (t57.t11))
% 20.87/21.08 (step t57.t13 (cl (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule and_neg)
% 20.87/21.08 (step t57.t14 (cl (and (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule resolution :premises (t57.t13 t57.a1 t57.a0))
% 20.87/21.08 (step t57.t15 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule resolution :premises (t57.t12 t57.t14))
% 20.87/21.08 (step t57 (cl (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule subproof :discharge (t57.a0 t57.a1))
% 20.87/21.08 (step t58 (cl (not (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t59 (cl (not (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t60 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)) (not (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) (not (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))))) :rule resolution :premises (t57 t58 t59))
% 20.87/21.08 (step t61 (cl (not (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) (not (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule reordering :premises (t60))
% 20.87/21.08 (step t62 (cl (not (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule contraction :premises (t61))
% 20.87/21.08 (step t63 (cl (=> (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule resolution :premises (t56 t62))
% 20.87/21.08 (step t64 (cl (=> (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (not (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule implies_neg2)
% 20.87/21.08 (step t65 (cl (=> (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (=> (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule resolution :premises (t63 t64))
% 20.87/21.08 (step t66 (cl (=> (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule contraction :premises (t65))
% 20.87/21.08 (step t67 (cl (not (and (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule implies :premises (t66))
% 20.87/21.08 (step t68 (cl (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule resolution :premises (t55 t67))
% 20.87/21.08 (step t69 (cl (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (not (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule or_neg)
% 20.87/21.08 (step t70 (cl (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (not (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))))) :rule or_neg)
% 20.87/21.08 (step t71 (cl (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (not (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule or_neg)
% 20.87/21.08 (step t72 (cl (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule resolution :premises (t68 t69 t70 t71))
% 20.87/21.08 (step t73 (cl (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule contraction :premises (t72))
% 20.87/21.08 (step t74 (cl (or (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule resolution :premises (t41 t54 t73))
% 20.87/21.08 (step t75 (cl (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule or :premises (t74))
% 20.87/21.08 (step t76 (cl (not (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3))) :rule or_pos)
% 20.87/21.08 (step t77 (cl (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)) (not (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3))))) :rule reordering :premises (t76))
% 20.87/21.08 (step t78 (cl (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3)) :rule or_pos)
% 20.87/21.08 (step t79 (cl (= tptp.nil tptp.sk3) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3)))) :rule reordering :premises (t78))
% 20.87/21.08 (step t80 (cl (not (= (or (= tptp.nil tptp.sk4) (not (= tptp.nil tptp.sk3))) (or (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (= tptp.nil tptp.sk3))))) (not (or (= tptp.nil tptp.sk4) (not (= tptp.nil tptp.sk3)))) (or (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (= tptp.nil tptp.sk3)))) :rule equiv_pos2)
% 20.87/21.08 (step t81 (cl (= tptp.nil tptp.nil)) :rule refl)
% 20.87/21.08 (step t82 (cl (= tptp.sk4 (tptp.app tptp.sk3 tptp.sk5))) :rule and :premises (t20))
% 20.87/21.08 (step t83 (cl (= (= tptp.nil tptp.sk4) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) :rule cong :premises (t81 t82))
% 20.87/21.08 (step t84 (cl (= (not (= tptp.nil tptp.sk3)) (not (= tptp.nil tptp.sk3)))) :rule refl)
% 20.87/21.08 (step t85 (cl (= (or (= tptp.nil tptp.sk4) (not (= tptp.nil tptp.sk3))) (or (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (= tptp.nil tptp.sk3))))) :rule cong :premises (t83 t84))
% 20.87/21.08 (step t86 (cl (or (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (= tptp.nil tptp.sk3)))) :rule resolution :premises (t80 t85 a195))
% 20.87/21.08 (step t87 (cl (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (= tptp.nil tptp.sk3))) :rule or :premises (t86))
% 20.87/21.08 (step t88 (cl (not (= tptp.nil tptp.sk3)) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) :rule reordering :premises (t87))
% 20.87/21.08 (step t89 (cl (not (= (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))))) (not (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule equiv_pos2)
% 20.87/21.08 (step t90 (cl (= (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))))) :rule refl)
% 20.87/21.08 (step t91 (cl (= (= (= (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) true) (= (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) :rule equiv_simplify)
% 20.87/21.08 (step t92 (cl (not (= (= (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) true)) (= (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) :rule equiv1 :premises (t91))
% 20.87/21.08 (step t93 (cl (= (= (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))))) :rule all_simplify)
% 20.87/21.08 (step t94 (cl (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) :rule refl)
% 20.87/21.08 (step t95 (cl (= (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) :rule all_simplify)
% 20.87/21.08 (step t96 (cl (= (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) :rule cong :premises (t94 t95))
% 20.87/21.08 (step t97 (cl (= (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) true)) :rule all_simplify)
% 20.87/21.08 (step t98 (cl (= (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) true)) :rule trans :premises (t96 t97))
% 20.87/21.08 (step t99 (cl (= (= (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) true)) :rule trans :premises (t93 t98))
% 20.87/21.08 (step t100 (cl (= (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) :rule resolution :premises (t92 t99))
% 20.87/21.08 (step t101 (cl (= (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule refl)
% 20.87/21.08 (step t102 (cl (= (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))))) :rule cong :premises (t90 t100 t101))
% 20.87/21.08 (step t103 (cl (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) :rule and_neg)
% 20.87/21.08 (step t104 (cl (=> (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t105)
% 20.87/21.08 (assume t105.a0 (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))
% 20.87/21.08 (assume t105.a1 (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))
% 20.87/21.08 (step t105.t1 (cl (=> (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t105.t2)
% 20.87/21.08 (assume t105.t2.a0 (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))
% 20.87/21.08 (assume t105.t2.a1 (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))
% 20.87/21.08 (step t105.t2.t1 (cl (= (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil) false) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule equiv_simplify)
% 20.87/21.08 (step t105.t2.t2 (cl (not (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil) false)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule equiv1 :premises (t105.t2.t1))
% 20.87/21.08 (step t105.t2.t3 (cl (= (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) :rule refl)
% 20.87/21.08 (step t105.t2.t4 (cl (= (tptp.app tptp.sk3 tptp.sk5) tptp.nil)) :rule symm :premises (t105.t2.a1))
% 20.87/21.08 (step t105.t2.t5 (cl (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) :rule symm :premises (t105.t2.t4))
% 20.87/21.08 (step t105.t2.t6 (cl (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) :rule cong :premises (t105.t2.t3 t105.t2.t5))
% 20.87/21.08 (step t105.t2.t7 (cl (= (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) false) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) :rule equiv_simplify)
% 20.87/21.08 (step t105.t2.t8 (cl (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) false) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) :rule equiv2 :premises (t105.t2.t7))
% 20.87/21.08 (step t105.t2.t9 (cl (not (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) :rule not_not)
% 20.87/21.08 (step t105.t2.t10 (cl (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) false) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) :rule resolution :premises (t105.t2.t8 t105.t2.t9))
% 20.87/21.08 (step t105.t2.t11 (cl (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) false)) :rule resolution :premises (t105.t2.t10 t105.t2.a0))
% 20.87/21.08 (step t105.t2.t12 (cl (= (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil) false)) :rule trans :premises (t105.t2.t6 t105.t2.t11))
% 20.87/21.08 (step t105.t2.t13 (cl (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule resolution :premises (t105.t2.t2 t105.t2.t12))
% 20.87/21.08 (step t105.t2 (cl (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule subproof :discharge (t105.t2.a0 t105.t2.a1))
% 20.87/21.08 (step t105.t3 (cl (not (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) :rule and_pos)
% 20.87/21.08 (step t105.t4 (cl (not (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) :rule and_pos)
% 20.87/21.08 (step t105.t5 (cl (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)) (not (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) (not (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))))) :rule resolution :premises (t105.t2 t105.t3 t105.t4))
% 20.87/21.08 (step t105.t6 (cl (not (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) (not (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule reordering :premises (t105.t5))
% 20.87/21.08 (step t105.t7 (cl (not (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule contraction :premises (t105.t6))
% 20.87/21.08 (step t105.t8 (cl (=> (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule resolution :premises (t105.t1 t105.t7))
% 20.87/21.08 (step t105.t9 (cl (=> (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule implies_neg2)
% 20.87/21.08 (step t105.t10 (cl (=> (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (=> (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule resolution :premises (t105.t8 t105.t9))
% 20.87/21.08 (step t105.t11 (cl (=> (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule contraction :premises (t105.t10))
% 20.87/21.08 (step t105.t12 (cl (not (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule implies :premises (t105.t11))
% 20.87/21.08 (step t105.t13 (cl (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) :rule and_neg)
% 20.87/21.08 (step t105.t14 (cl (and (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) :rule resolution :premises (t105.t13 t105.a1 t105.a0))
% 20.87/21.08 (step t105.t15 (cl (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule resolution :premises (t105.t12 t105.t14))
% 20.87/21.08 (step t105 (cl (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule subproof :discharge (t105.a0 t105.a1))
% 20.87/21.08 (step t106 (cl (not (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) :rule and_pos)
% 20.87/21.08 (step t107 (cl (not (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) :rule and_pos)
% 20.87/21.08 (step t108 (cl (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)) (not (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) (not (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))))) :rule resolution :premises (t105 t106 t107))
% 20.87/21.08 (step t109 (cl (not (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) (not (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule reordering :premises (t108))
% 20.87/21.08 (step t110 (cl (not (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule contraction :premises (t109))
% 20.87/21.08 (step t111 (cl (=> (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule resolution :premises (t104 t110))
% 20.87/21.08 (step t112 (cl (=> (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule implies_neg2)
% 20.87/21.08 (step t113 (cl (=> (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (=> (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule resolution :premises (t111 t112))
% 20.87/21.08 (step t114 (cl (=> (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule contraction :premises (t113))
% 20.87/21.08 (step t115 (cl (not (and (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule implies :premises (t114))
% 20.87/21.08 (step t116 (cl (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule resolution :premises (t103 t115))
% 20.87/21.08 (step t117 (cl (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (not (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))))) :rule or_neg)
% 20.87/21.08 (step t118 (cl (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (not (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))))) :rule or_neg)
% 20.87/21.08 (step t119 (cl (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule or_neg)
% 20.87/21.08 (step t120 (cl (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule resolution :premises (t116 t117 t118 t119))
% 20.87/21.08 (step t121 (cl (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule contraction :premises (t120))
% 20.87/21.08 (step t122 (cl (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule resolution :premises (t89 t102 t121))
% 20.87/21.08 (step t123 (cl (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule or :premises (t122))
% 20.87/21.08 (step t124 (cl (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) :rule reordering :premises (t123))
% 20.87/21.08 (step t125 (cl (not (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))) :rule or_pos)
% 20.87/21.08 (step t126 (cl (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))))) :rule reordering :premises (t125))
% 20.87/21.08 (step t127 (cl (=> (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V))))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t128)
% 20.87/21.08 (assume t128.a0 (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))))
% 20.87/21.08 (step t128.t1 (cl (or (not (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V))))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))))) :rule forall_inst :args ((:= V (tptp.app tptp.sk3 tptp.sk5))))
% 20.87/21.08 (step t128.t2 (cl (not (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V))))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) :rule or :premises (t128.t1))
% 20.87/21.08 (step t128.t3 (cl (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) :rule resolution :premises (t128.t2 t128.a0))
% 20.87/21.08 (step t128 (cl (not (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V))))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) :rule subproof :discharge (t128.a0))
% 20.87/21.08 (step t129 (cl (=> (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) :rule resolution :premises (t127 t128))
% 20.87/21.08 (step t130 (cl (=> (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) (not (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))))) :rule implies_neg2)
% 20.87/21.08 (step t131 (cl (=> (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) (=> (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))))) :rule resolution :premises (t129 t130))
% 20.87/21.08 (step t132 (cl (=> (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5)))))) :rule contraction :premises (t131))
% 20.87/21.08 (step t133 (cl (not (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V))))) (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) :rule implies :premises (t132))
% 20.87/21.08 (step t134 (cl (not (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssList V)) (not (tptp.ssList U)))) (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))))) (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssList V)) (not (tptp.ssList U))))) (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V))))) :rule equiv_pos2)
% 20.87/21.08 (step t135 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssList V)) (not (tptp.ssList U)))) (forall ((V $$unsorted)) (or (not (= V V)) (not (tptp.neq V V)) (not (tptp.ssList V)) (not (tptp.ssList V)))))) :rule all_simplify)
% 20.87/21.08 (anchor :step t136 :args ((V $$unsorted) (:= V V)))
% 20.87/21.08 (step t136.t1 (cl (= V V)) :rule refl)
% 20.87/21.08 (step t136.t2 (cl (= (= V V) true)) :rule all_simplify)
% 20.87/21.08 (step t136.t3 (cl (= (not (= V V)) (not true))) :rule cong :premises (t136.t2))
% 20.87/21.08 (step t136.t4 (cl (= (not true) false)) :rule all_simplify)
% 20.87/21.08 (step t136.t5 (cl (= (not (= V V)) false)) :rule trans :premises (t136.t3 t136.t4))
% 20.87/21.08 (step t136.t6 (cl (= (not (tptp.neq V V)) (not (tptp.neq V V)))) :rule refl)
% 20.87/21.08 (step t136.t7 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 20.87/21.08 (step t136.t8 (cl (= (or (not (= V V)) (not (tptp.neq V V)) (not (tptp.ssList V)) (not (tptp.ssList V))) (or false (not (tptp.neq V V)) (not (tptp.ssList V)) (not (tptp.ssList V))))) :rule cong :premises (t136.t5 t136.t6 t136.t7 t136.t7))
% 20.87/21.08 (step t136.t9 (cl (= (or false (not (tptp.neq V V)) (not (tptp.ssList V)) (not (tptp.ssList V))) (or (not (tptp.neq V V)) (not (tptp.ssList V))))) :rule all_simplify)
% 20.87/21.08 (step t136.t10 (cl (= (or (not (= V V)) (not (tptp.neq V V)) (not (tptp.ssList V)) (not (tptp.ssList V))) (or (not (tptp.neq V V)) (not (tptp.ssList V))))) :rule trans :premises (t136.t8 t136.t9))
% 20.87/21.08 (step t136 (cl (= (forall ((V $$unsorted)) (or (not (= V V)) (not (tptp.neq V V)) (not (tptp.ssList V)) (not (tptp.ssList V)))) (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))))) :rule bind)
% 20.87/21.08 (step t137 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssList V)) (not (tptp.ssList U)))) (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V)))))) :rule trans :premises (t135 t136))
% 20.87/21.08 (step t138 (cl (forall ((V $$unsorted)) (or (not (tptp.neq V V)) (not (tptp.ssList V))))) :rule resolution :premises (t134 t137 a114))
% 20.87/21.08 (step t139 (cl (or (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList (tptp.app tptp.sk3 tptp.sk5))))) :rule resolution :premises (t133 t138))
% 20.87/21.08 (step t140 (cl (not (tptp.neq (tptp.app tptp.sk3 tptp.sk5) (tptp.app tptp.sk3 tptp.sk5)))) :rule resolution :premises (t126 t25 t139))
% 20.87/21.08 (step t141 (cl (not (= (or (not (= tptp.nil tptp.sk1)) (tptp.neq tptp.sk2 tptp.nil)) (or (not (= tptp.nil tptp.sk3)) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) (not (or (not (= tptp.nil tptp.sk1)) (tptp.neq tptp.sk2 tptp.nil))) (or (not (= tptp.nil tptp.sk3)) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule equiv_pos2)
% 20.87/21.08 (step t142 (cl (= tptp.nil tptp.nil)) :rule refl)
% 20.87/21.08 (step t143 (cl (= tptp.sk1 tptp.sk3)) :rule and :premises (t20))
% 20.87/21.08 (step t144 (cl (= (= tptp.nil tptp.sk1) (= tptp.nil tptp.sk3))) :rule cong :premises (t142 t143))
% 20.87/21.08 (step t145 (cl (= (not (= tptp.nil tptp.sk1)) (not (= tptp.nil tptp.sk3)))) :rule cong :premises (t144))
% 20.87/21.08 (step t146 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t20))
% 20.87/21.08 (step t147 (cl (= tptp.sk4 (tptp.app tptp.sk3 tptp.sk5))) :rule and :premises (t20))
% 20.87/21.08 (step t148 (cl (= tptp.sk2 (tptp.app tptp.sk3 tptp.sk5))) :rule trans :premises (t146 t147))
% 20.87/21.08 (step t149 (cl (= (tptp.neq tptp.sk2 tptp.nil) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule cong :premises (t148 t142))
% 20.87/21.08 (step t150 (cl (= (or (not (= tptp.nil tptp.sk1)) (tptp.neq tptp.sk2 tptp.nil)) (or (not (= tptp.nil tptp.sk3)) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)))) :rule cong :premises (t145 t149))
% 20.87/21.08 (step t151 (cl (or (not (= tptp.nil tptp.sk3)) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil))) :rule resolution :premises (t141 t150 a198))
% 20.87/21.08 (step t152 (cl (not (= tptp.nil tptp.sk3)) (tptp.neq (tptp.app tptp.sk3 tptp.sk5) tptp.nil)) :rule or :premises (t151))
% 20.87/21.08 (step t153 (cl (not (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3)) :rule or_pos)
% 20.87/21.08 (step t154 (cl (= tptp.nil tptp.sk3) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList tptp.sk5)) (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3)))) :rule reordering :premises (t153))
% 20.87/21.08 (step t155 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t156)
% 20.87/21.08 (assume t156.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))))
% 20.87/21.08 (step t156.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3)))) :rule forall_inst :args ((:= U tptp.sk3) (:= V tptp.sk5)))
% 20.87/21.08 (step t156.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) :rule or :premises (t156.t1))
% 20.87/21.08 (step t156.t3 (cl (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) :rule resolution :premises (t156.t2 t156.a0))
% 20.87/21.08 (step t156 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) :rule subproof :discharge (t156.a0))
% 20.87/21.08 (step t157 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) :rule resolution :premises (t155 t156))
% 20.87/21.08 (step t158 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) (not (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3)))) :rule implies_neg2)
% 20.87/21.08 (step t159 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3)))) :rule resolution :premises (t157 t158))
% 20.87/21.08 (step t160 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3)))) :rule contraction :premises (t159))
% 20.87/21.08 (step t161 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)))) (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) :rule implies :premises (t160))
% 20.87/21.08 (step t162 (cl (not (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))))) (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)))) :rule equiv_pos2)
% 20.87/21.08 (anchor :step t163 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 20.87/21.08 (step t163.t1 (cl (= U U)) :rule refl)
% 20.87/21.08 (step t163.t2 (cl (= V V)) :rule refl)
% 20.87/21.08 (step t163.t3 (cl (= (= (tptp.app U V) tptp.nil) (= tptp.nil (tptp.app U V)))) :rule all_simplify)
% 20.87/21.08 (step t163.t4 (cl (= (not (= (tptp.app U V) tptp.nil)) (not (= tptp.nil (tptp.app U V))))) :rule cong :premises (t163.t3))
% 20.87/21.08 (step t163.t5 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 20.87/21.08 (step t163.t6 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 20.87/21.08 (step t163.t7 (cl (= (= tptp.nil U) (= tptp.nil U))) :rule refl)
% 20.87/21.08 (step t163.t8 (cl (= (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)))) :rule cong :premises (t163.t4 t163.t5 t163.t6 t163.t7))
% 20.87/21.08 (step t163 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))))) :rule bind)
% 20.87/21.08 (step t164 (cl (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U)))) :rule resolution :premises (t162 t163 a117))
% 20.87/21.08 (step t165 (cl (or (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.sk3)) (= tptp.nil tptp.sk3))) :rule resolution :premises (t161 t164))
% 20.87/21.08 (step t166 (cl (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5))) (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) :rule resolution :premises (t124 t140 t152 t154 t165 a191 a187))
% 20.87/21.08 (step t167 (cl (not (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) :rule contraction :premises (t166))
% 20.87/21.08 (step t168 (cl (not (= tptp.nil tptp.sk3))) :rule resolution :premises (t88 t167))
% 20.87/21.08 (step t169 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t170)
% 20.87/21.08 (assume t170.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))))
% 20.87/21.08 (step t170.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V)))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3)))) :rule forall_inst :args ((:= U tptp.nil) (:= V tptp.sk3)))
% 20.87/21.08 (step t170.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V)))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) :rule or :premises (t170.t1))
% 20.87/21.08 (step t170.t3 (cl (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) :rule resolution :premises (t170.t2 t170.a0))
% 20.87/21.08 (step t170 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V)))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) :rule subproof :discharge (t170.a0))
% 20.87/21.08 (step t171 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) :rule resolution :premises (t169 t170))
% 20.87/21.08 (step t172 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3)))) :rule implies_neg2)
% 20.87/21.08 (step t173 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3)))) :rule resolution :premises (t171 t172))
% 20.87/21.08 (step t174 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3)))) :rule contraction :premises (t173))
% 20.87/21.08 (step t175 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V)))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) :rule implies :premises (t174))
% 20.87/21.08 (step t176 (cl (not (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= V U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))))) (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= V U)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V)))) :rule equiv_pos2)
% 20.87/21.08 (anchor :step t177 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 20.87/21.08 (step t177.t1 (cl (= U U)) :rule refl)
% 20.87/21.08 (step t177.t2 (cl (= V V)) :rule refl)
% 20.87/21.08 (step t177.t3 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 20.87/21.08 (step t177.t4 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 20.87/21.08 (step t177.t5 (cl (= (tptp.neq V U) (tptp.neq V U))) :rule refl)
% 20.87/21.08 (step t177.t6 (cl (= (= V U) (= U V))) :rule all_simplify)
% 20.87/21.08 (step t177.t7 (cl (= (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= V U)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V)))) :rule cong :premises (t177.t3 t177.t4 t177.t5 t177.t6))
% 20.87/21.08 (step t177 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= V U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))))) :rule bind)
% 20.87/21.08 (step t178 (cl (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V)))) :rule resolution :premises (t176 t177 a99))
% 20.87/21.08 (step t179 (cl (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (tptp.neq tptp.sk3 tptp.nil) (= tptp.nil tptp.sk3))) :rule resolution :premises (t175 t178))
% 20.87/21.08 (step t180 (cl (tptp.neq tptp.sk3 tptp.nil)) :rule resolution :premises (t79 t168 a7 a187 t179))
% 20.87/21.08 (step t181 (cl (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule and_neg)
% 20.87/21.08 (step t182 (cl (=> (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3)) (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t183)
% 20.87/21.08 (assume t183.a0 (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))
% 20.87/21.08 (assume t183.a1 (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))
% 20.87/21.08 (assume t183.a2 (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))
% 20.87/21.08 (step t183.t1 (cl (=> (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (tptp.segmentP tptp.sk3 tptp.sk3)) (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t183.t2)
% 20.87/21.08 (assume t183.t2.a0 (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))
% 20.87/21.08 (assume t183.t2.a1 (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))
% 20.87/21.08 (assume t183.t2.a2 (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))
% 20.87/21.08 (step t183.t2.t1 (cl (= (= (tptp.segmentP tptp.sk3 tptp.sk3) true) (tptp.segmentP tptp.sk3 tptp.sk3))) :rule equiv_simplify)
% 20.87/21.08 (step t183.t2.t2 (cl (not (= (tptp.segmentP tptp.sk3 tptp.sk3) true)) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule equiv1 :premises (t183.t2.t1))
% 20.87/21.08 (step t183.t2.t3 (cl (= (tptp.app tptp.sk3 tptp.nil) tptp.sk3)) :rule symm :premises (t183.t2.a2))
% 20.87/21.08 (step t183.t2.t4 (cl (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) :rule symm :premises (t183.t2.t3))
% 20.87/21.08 (step t183.t2.t5 (cl (= (tptp.app tptp.nil tptp.sk3) tptp.sk3)) :rule symm :premises (t183.t2.a1))
% 20.87/21.08 (step t183.t2.t6 (cl (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule symm :premises (t183.t2.t5))
% 20.87/21.08 (step t183.t2.t7 (cl (= tptp.nil tptp.nil)) :rule refl)
% 20.87/21.08 (step t183.t2.t8 (cl (= (tptp.app tptp.sk3 tptp.nil) (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule cong :premises (t183.t2.t6 t183.t2.t7))
% 20.87/21.08 (step t183.t2.t9 (cl (= tptp.sk3 (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule trans :premises (t183.t2.t4 t183.t2.t8))
% 20.87/21.08 (step t183.t2.t10 (cl (= tptp.sk3 tptp.sk3)) :rule refl)
% 20.87/21.08 (step t183.t2.t11 (cl (= (tptp.segmentP tptp.sk3 tptp.sk3) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule cong :premises (t183.t2.t9 t183.t2.t10))
% 20.87/21.08 (step t183.t2.t12 (cl (= (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) true) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule equiv_simplify)
% 20.87/21.08 (step t183.t2.t13 (cl (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) true) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule equiv2 :premises (t183.t2.t12))
% 20.87/21.08 (step t183.t2.t14 (cl (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) true)) :rule resolution :premises (t183.t2.t13 t183.t2.a0))
% 20.87/21.08 (step t183.t2.t15 (cl (= (tptp.segmentP tptp.sk3 tptp.sk3) true)) :rule trans :premises (t183.t2.t11 t183.t2.t14))
% 20.87/21.08 (step t183.t2.t16 (cl (tptp.segmentP tptp.sk3 tptp.sk3)) :rule resolution :premises (t183.t2.t2 t183.t2.t15))
% 20.87/21.08 (step t183.t2 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule subproof :discharge (t183.t2.a0 t183.t2.a1 t183.t2.a2))
% 20.87/21.08 (step t183.t3 (cl (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) :rule and_pos)
% 20.87/21.08 (step t183.t4 (cl (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t183.t5 (cl (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) :rule and_pos)
% 20.87/21.08 (step t183.t6 (cl (tptp.segmentP tptp.sk3 tptp.sk3) (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))))) :rule resolution :premises (t183.t2 t183.t3 t183.t4 t183.t5))
% 20.87/21.08 (step t183.t7 (cl (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule reordering :premises (t183.t6))
% 20.87/21.08 (step t183.t8 (cl (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule contraction :premises (t183.t7))
% 20.87/21.08 (step t183.t9 (cl (=> (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (tptp.segmentP tptp.sk3 tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule resolution :premises (t183.t1 t183.t8))
% 20.87/21.08 (step t183.t10 (cl (=> (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (tptp.segmentP tptp.sk3 tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3))) :rule implies_neg2)
% 20.87/21.08 (step t183.t11 (cl (=> (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (tptp.segmentP tptp.sk3 tptp.sk3)) (=> (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (tptp.segmentP tptp.sk3 tptp.sk3))) :rule resolution :premises (t183.t9 t183.t10))
% 20.87/21.08 (step t183.t12 (cl (=> (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (tptp.segmentP tptp.sk3 tptp.sk3))) :rule contraction :premises (t183.t11))
% 20.87/21.08 (step t183.t13 (cl (not (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule implies :premises (t183.t12))
% 20.87/21.08 (step t183.t14 (cl (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) :rule and_neg)
% 20.87/21.08 (step t183.t15 (cl (and (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) :rule resolution :premises (t183.t14 t183.a2 t183.a1 t183.a0))
% 20.87/21.08 (step t183.t16 (cl (tptp.segmentP tptp.sk3 tptp.sk3)) :rule resolution :premises (t183.t13 t183.t15))
% 20.87/21.08 (step t183 (cl (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule subproof :discharge (t183.a0 t183.a1 t183.a2))
% 20.87/21.08 (step t184 (cl (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) :rule and_pos)
% 20.87/21.08 (step t185 (cl (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t186 (cl (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) :rule and_pos)
% 20.87/21.08 (step t187 (cl (tptp.segmentP tptp.sk3 tptp.sk3) (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)))) :rule resolution :premises (t183 t184 t185 t186))
% 20.87/21.08 (step t188 (cl (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule reordering :premises (t187))
% 20.87/21.08 (step t189 (cl (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule contraction :premises (t188))
% 20.87/21.08 (step t190 (cl (=> (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule resolution :premises (t182 t189))
% 20.87/21.08 (step t191 (cl (=> (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3))) :rule implies_neg2)
% 20.87/21.08 (step t192 (cl (=> (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3)) (=> (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3))) :rule resolution :premises (t190 t191))
% 20.87/21.08 (step t193 (cl (=> (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3))) :rule contraction :premises (t192))
% 20.87/21.08 (step t194 (cl (not (and (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule implies :premises (t193))
% 20.87/21.08 (step t195 (cl (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) (tptp.segmentP tptp.sk3 tptp.sk3)) :rule resolution :premises (t181 t194))
% 20.87/21.08 (step t196 (cl (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.segmentP tptp.sk3 tptp.sk3) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule reordering :premises (t195))
% 20.87/21.08 (step t197 (cl (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) :rule or_pos)
% 20.87/21.08 (step t198 (cl (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))))) :rule reordering :premises (t197))
% 20.87/21.08 (step t199 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil))))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t200)
% 20.87/21.08 (assume t200.a0 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))
% 20.87/21.08 (step t200.t1 (cl (or (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil))))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))))) :rule forall_inst :args ((:= U tptp.sk3)))
% 20.87/21.08 (step t200.t2 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil))))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) :rule or :premises (t200.t1))
% 20.87/21.08 (step t200.t3 (cl (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) :rule resolution :premises (t200.t2 t200.a0))
% 20.87/21.08 (step t200 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil))))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) :rule subproof :discharge (t200.a0))
% 20.87/21.08 (step t201 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) :rule resolution :premises (t199 t200))
% 20.87/21.08 (step t202 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))))) :rule implies_neg2)
% 20.87/21.08 (step t203 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))))) :rule resolution :premises (t201 t202))
% 20.87/21.08 (step t204 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))))) :rule contraction :premises (t203))
% 20.87/21.08 (step t205 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil))))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) :rule implies :premises (t204))
% 20.87/21.08 (step t206 (cl (not (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app U tptp.nil) U)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil))))) :rule equiv_pos2)
% 20.87/21.08 (anchor :step t207 :args ((U $$unsorted) (:= U U)))
% 20.87/21.08 (step t207.t1 (cl (= U U)) :rule refl)
% 20.87/21.08 (step t207.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 20.87/21.08 (step t207.t3 (cl (= (= (tptp.app U tptp.nil) U) (= U (tptp.app U tptp.nil)))) :rule all_simplify)
% 20.87/21.08 (step t207.t4 (cl (= (or (not (tptp.ssList U)) (= (tptp.app U tptp.nil) U)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil))))) :rule cong :premises (t207.t2 t207.t3))
% 20.87/21.08 (step t207 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) :rule bind)
% 20.87/21.08 (step t208 (cl (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil))))) :rule resolution :premises (t206 t207 a72))
% 20.87/21.08 (step t209 (cl (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))) :rule resolution :premises (t205 t208))
% 20.87/21.08 (step t210 (cl (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) :rule resolution :premises (t198 a187 t209))
% 20.87/21.08 (step t211 (cl (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) :rule or_pos)
% 20.87/21.08 (step t212 (cl (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) :rule contraction :premises (t211))
% 20.87/21.08 (step t213 (cl (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3) (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)))) :rule reordering :premises (t212))
% 20.87/21.08 (step t214 (cl (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.ssList tptp.sk3)) (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule and_neg)
% 20.87/21.08 (step t215 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t216)
% 20.87/21.08 (assume t216.a0 (tptp.ssList tptp.sk3))
% 20.87/21.08 (assume t216.a1 (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))
% 20.87/21.08 (assume t216.a2 (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))
% 20.87/21.08 (step t216.t1 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t216.t2)
% 20.87/21.08 (assume t216.t2.a0 (tptp.ssList tptp.sk3))
% 20.87/21.08 (assume t216.t2.a1 (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)))
% 20.87/21.08 (assume t216.t2.a2 (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))
% 20.87/21.08 (step t216.t2.t1 (cl (= (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)) true) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)))) :rule equiv_simplify)
% 20.87/21.08 (step t216.t2.t2 (cl (not (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)) true)) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule equiv1 :premises (t216.t2.t1))
% 20.87/21.08 (step t216.t2.t3 (cl (= (tptp.app tptp.nil tptp.sk3) tptp.sk3)) :rule symm :premises (t216.t2.a2))
% 20.87/21.08 (step t216.t2.t4 (cl (= tptp.nil tptp.nil)) :rule refl)
% 20.87/21.08 (step t216.t2.t5 (cl (= (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) (tptp.app tptp.sk3 tptp.nil))) :rule cong :premises (t216.t2.t3 t216.t2.t4))
% 20.87/21.08 (step t216.t2.t6 (cl (= (tptp.app tptp.sk3 tptp.nil) tptp.sk3)) :rule symm :premises (t216.t2.a1))
% 20.87/21.08 (step t216.t2.t7 (cl (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) :rule symm :premises (t216.t2.t6))
% 20.87/21.08 (step t216.t2.t8 (cl (= (tptp.app tptp.sk3 tptp.nil) tptp.sk3)) :rule symm :premises (t216.t2.t7))
% 20.87/21.08 (step t216.t2.t9 (cl (= (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) :rule trans :premises (t216.t2.t5 t216.t2.t8))
% 20.87/21.08 (step t216.t2.t10 (cl (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)) (tptp.ssList tptp.sk3))) :rule cong :premises (t216.t2.t9))
% 20.87/21.08 (step t216.t2.t11 (cl (= (= (tptp.ssList tptp.sk3) true) (tptp.ssList tptp.sk3))) :rule equiv_simplify)
% 20.87/21.08 (step t216.t2.t12 (cl (= (tptp.ssList tptp.sk3) true) (not (tptp.ssList tptp.sk3))) :rule equiv2 :premises (t216.t2.t11))
% 20.87/21.08 (step t216.t2.t13 (cl (= (tptp.ssList tptp.sk3) true)) :rule resolution :premises (t216.t2.t12 t216.t2.a0))
% 20.87/21.08 (step t216.t2.t14 (cl (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)) true)) :rule trans :premises (t216.t2.t10 t216.t2.t13))
% 20.87/21.08 (step t216.t2.t15 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule resolution :premises (t216.t2.t2 t216.t2.t14))
% 20.87/21.08 (step t216.t2 (cl (not (tptp.ssList tptp.sk3)) (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule subproof :discharge (t216.t2.a0 t216.t2.a1 t216.t2.a2))
% 20.87/21.08 (step t216.t3 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList tptp.sk3)) :rule and_pos)
% 20.87/21.08 (step t216.t4 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) :rule and_pos)
% 20.87/21.08 (step t216.t5 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t216.t6 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule resolution :premises (t216.t2 t216.t3 t216.t4 t216.t5))
% 20.87/21.08 (step t216.t7 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule reordering :premises (t216.t6))
% 20.87/21.08 (step t216.t8 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule contraction :premises (t216.t7))
% 20.87/21.08 (step t216.t9 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule resolution :premises (t216.t1 t216.t8))
% 20.87/21.08 (step t216.t10 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)))) :rule implies_neg2)
% 20.87/21.08 (step t216.t11 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)))) :rule resolution :premises (t216.t9 t216.t10))
% 20.87/21.08 (step t216.t12 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)))) :rule contraction :premises (t216.t11))
% 20.87/21.08 (step t216.t13 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule implies :premises (t216.t12))
% 20.87/21.08 (step t216.t14 (cl (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (not (tptp.ssList tptp.sk3)) (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule and_neg)
% 20.87/21.08 (step t216.t15 (cl (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) :rule resolution :premises (t216.t14 t216.a0 t216.a1 t216.a2))
% 20.87/21.08 (step t216.t16 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule resolution :premises (t216.t13 t216.t15))
% 20.87/21.08 (step t216 (cl (not (tptp.ssList tptp.sk3)) (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule subproof :discharge (t216.a0 t216.a1 t216.a2))
% 20.87/21.08 (step t217 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList tptp.sk3)) :rule and_pos)
% 20.87/21.08 (step t218 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) :rule and_pos)
% 20.87/21.08 (step t219 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) :rule and_pos)
% 20.87/21.08 (step t220 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))))) :rule resolution :premises (t216 t217 t218 t219))
% 20.87/21.08 (step t221 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule reordering :premises (t220))
% 20.87/21.08 (step t222 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule contraction :premises (t221))
% 20.87/21.08 (step t223 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule resolution :premises (t215 t222))
% 20.87/21.08 (step t224 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)))) :rule implies_neg2)
% 20.87/21.08 (step t225 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)))) :rule resolution :premises (t223 t224))
% 20.87/21.08 (step t226 (cl (=> (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil)))) :rule contraction :premises (t225))
% 20.87/21.08 (step t227 (cl (not (and (tptp.ssList tptp.sk3) (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil)) (= tptp.sk3 (tptp.app tptp.nil tptp.sk3)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule implies :premises (t226))
% 20.87/21.08 (step t228 (cl (not (tptp.ssList tptp.sk3)) (not (= tptp.sk3 (tptp.app tptp.sk3 tptp.nil))) (not (= tptp.sk3 (tptp.app tptp.nil tptp.sk3))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule resolution :premises (t214 t227))
% 20.87/21.08 (step t229 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) :rule resolution :premises (t228 a187 t210 t39))
% 20.87/21.08 (step t230 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t231)
% 20.87/21.08 (assume t231.a0 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))
% 20.87/21.08 (step t231.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)))) :rule forall_inst :args ((:= U tptp.nil) (:= V tptp.sk3) (:= W tptp.nil)))
% 20.87/21.08 (step t231.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule or :premises (t231.t1))
% 20.87/21.08 (step t231.t3 (cl (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule resolution :premises (t231.t2 t231.a0))
% 20.87/21.08 (step t231 (cl (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule subproof :discharge (t231.a0))
% 20.87/21.08 (step t232 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule resolution :premises (t230 t231))
% 20.87/21.08 (step t233 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (not (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)))) :rule implies_neg2)
% 20.87/21.08 (step t234 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)))) :rule resolution :premises (t232 t233))
% 20.87/21.08 (step t235 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)))) :rule contraction :premises (t234))
% 20.87/21.08 (step t236 (cl (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule implies :premises (t235))
% 20.87/21.08 (step t237 (cl (not (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) (not (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)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule equiv_pos2)
% 20.87/21.08 (anchor :step t238 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V) (W $$unsorted) (:= W W) (X $$unsorted) (:= X X)))
% 20.87/21.08 (step t238.t1 (cl (= U U)) :rule refl)
% 20.87/21.08 (step t238.t2 (cl (= V V)) :rule refl)
% 20.87/21.08 (step t238.t3 (cl (= W W)) :rule refl)
% 20.87/21.08 (step t238.t4 (cl (= X X)) :rule refl)
% 20.87/21.08 (step t238.t5 (cl (= (= (tptp.app (tptp.app U V) W) X) (= X (tptp.app (tptp.app U V) W)))) :rule all_simplify)
% 20.87/21.08 (step t238.t6 (cl (= (not (= (tptp.app (tptp.app U V) W) X)) (not (= X (tptp.app (tptp.app U V) W))))) :rule cong :premises (t238.t5))
% 20.87/21.08 (step t238.t7 (cl (= (not (tptp.ssList W)) (not (tptp.ssList W)))) :rule refl)
% 20.87/21.08 (step t238.t8 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 20.87/21.08 (step t238.t9 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 20.87/21.08 (step t238.t10 (cl (= (not (tptp.ssList X)) (not (tptp.ssList X)))) :rule refl)
% 20.87/21.08 (step t238.t11 (cl (= (tptp.segmentP X V) (tptp.segmentP X V))) :rule refl)
% 20.87/21.08 (step t238.t12 (cl (= (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V)) (or (not (= X (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V)))) :rule cong :premises (t238.t6 t238.t7 t238.t8 t238.t9 t238.t10 t238.t11))
% 20.87/21.08 (step t238 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= X (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))))) :rule bind)
% 20.87/21.08 (step t239 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= X (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) :rule all_simplify)
% 20.87/21.08 (anchor :step t240 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V) (W $$unsorted) (:= W W)))
% 20.87/21.08 (step t240.t1 (cl (= U U)) :rule refl)
% 20.87/21.08 (step t240.t2 (cl (= V V)) :rule refl)
% 20.87/21.08 (step t240.t3 (cl (= W W)) :rule refl)
% 20.87/21.08 (step t240.t4 (cl (= (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W)) true)) :rule all_simplify)
% 20.87/21.08 (step t240.t5 (cl (= (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not true))) :rule cong :premises (t240.t4))
% 20.87/21.08 (step t240.t6 (cl (= (not true) false)) :rule all_simplify)
% 20.87/21.08 (step t240.t7 (cl (= (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) false)) :rule trans :premises (t240.t5 t240.t6))
% 20.87/21.08 (step t240.t8 (cl (= (not (tptp.ssList W)) (not (tptp.ssList W)))) :rule refl)
% 20.87/21.08 (step t240.t9 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 20.87/21.08 (step t240.t10 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 20.87/21.08 (step t240.t11 (cl (= (not (tptp.ssList (tptp.app (tptp.app U V) W))) (not (tptp.ssList (tptp.app (tptp.app U V) W))))) :rule refl)
% 20.87/21.08 (step t240.t12 (cl (= (tptp.segmentP (tptp.app (tptp.app U V) W) V) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) :rule refl)
% 20.87/21.08 (step t240.t13 (cl (= (or (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)) (or false (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule cong :premises (t240.t7 t240.t8 t240.t9 t240.t10 t240.t11 t240.t12))
% 20.87/21.08 (step t240.t14 (cl (= (or false (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule all_simplify)
% 20.87/21.08 (step t240.t15 (cl (= (or (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule trans :premises (t240.t13 t240.t14))
% 20.87/21.08 (step t240 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) :rule bind)
% 20.87/21.08 (step t241 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= X (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) :rule trans :premises (t239 t240))
% 20.87/21.08 (step t242 (cl (= (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))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) :rule trans :premises (t238 t241))
% 20.87/21.08 (step t243 (cl (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule resolution :premises (t237 t242 a172))
% 20.87/21.08 (step t244 (cl (or (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3))) :rule resolution :premises (t236 t243))
% 20.87/21.08 (step t245 (cl (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.nil) tptp.sk3)) :rule resolution :premises (t213 a7 a187 t229 t244))
% 20.87/21.08 (step t246 (cl (tptp.segmentP tptp.sk3 tptp.sk3)) :rule resolution :premises (t196 t210 t39 t245))
% 20.87/21.08 (step t247 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t248)
% 20.87/21.08 (assume t248.a0 (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))))
% 20.87/21.08 (step t248.t1 (cl (or (not (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3))))) :rule forall_inst :args ((:= A tptp.sk3)))
% 20.87/21.08 (step t248.t2 (cl (not (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) :rule or :premises (t248.t1))
% 20.87/21.08 (step t248.t3 (cl (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) :rule resolution :premises (t248.t2 t248.a0))
% 20.87/21.08 (step t248 (cl (not (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) :rule subproof :discharge (t248.a0))
% 20.87/21.08 (step t249 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) :rule resolution :premises (t247 t248))
% 20.87/21.08 (step t250 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) (not (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3))))) :rule implies_neg2)
% 20.87/21.08 (step t251 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) (=> (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3))))) :rule resolution :premises (t249 t250))
% 20.87/21.08 (step t252 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3))))) :rule contraction :premises (t251))
% 20.87/21.08 (step t253 (cl (not (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))) (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) :rule implies :premises (t252))
% 20.87/21.08 (step t254 (cl (not (= (forall ((A $$unsorted)) (or (= tptp.nil tptp.sk2) (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A)))) (or (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))))) (not (forall ((A $$unsorted)) (or (= tptp.nil tptp.sk2) (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A))))) (or (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))))) :rule equiv_pos2)
% 20.87/21.08 (step t255 (cl (= (forall ((A $$unsorted)) (or (= tptp.nil tptp.sk2) (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A)))) (or (= tptp.nil tptp.sk2) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A))))))) :rule all_simplify)
% 20.87/21.08 (step t256 (cl (= tptp.nil tptp.nil)) :rule refl)
% 20.87/21.08 (step t257 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t20))
% 20.87/21.08 (step t258 (cl (= tptp.sk4 (tptp.app tptp.sk3 tptp.sk5))) :rule and :premises (t20))
% 20.87/21.08 (step t259 (cl (= tptp.sk2 (tptp.app tptp.sk3 tptp.sk5))) :rule trans :premises (t257 t258))
% 20.87/21.08 (step t260 (cl (= (= tptp.nil tptp.sk2) (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)))) :rule cong :premises (t256 t259))
% 20.87/21.08 (anchor :step t261 :args ((A $$unsorted) (:= A A)))
% 20.87/21.08 (step t261.t1 (cl (= A A)) :rule refl)
% 20.87/21.08 (step t261.t2 (cl (= (not (tptp.ssList A)) (not (tptp.ssList A)))) :rule refl)
% 20.87/21.08 (step t261.t3 (cl (= (not (tptp.neq A tptp.nil)) (not (tptp.neq A tptp.nil)))) :rule refl)
% 20.87/21.08 (step t261.t4 (cl (= A A)) :rule refl)
% 20.87/21.08 (step t261.t5 (cl (= (tptp.segmentP tptp.sk2 A) (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A))) :rule cong :premises (t259 t261.t4))
% 20.87/21.08 (step t261.t6 (cl (= (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)))) :rule cong :premises (t261.t5))
% 20.87/21.08 (step t261.t7 (cl (= tptp.sk1 tptp.sk3)) :rule and :premises (t20))
% 20.87/21.08 (step t261.t8 (cl (= (tptp.segmentP tptp.sk1 A) (tptp.segmentP tptp.sk3 A))) :rule cong :premises (t261.t7 t261.t4))
% 20.87/21.08 (step t261.t9 (cl (= (not (tptp.segmentP tptp.sk1 A)) (not (tptp.segmentP tptp.sk3 A)))) :rule cong :premises (t261.t8))
% 20.87/21.08 (step t261.t10 (cl (= (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A))) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))) :rule cong :premises (t261.t2 t261.t3 t261.t6 t261.t9))
% 20.87/21.08 (step t261 (cl (= (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A)))) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))))) :rule bind)
% 20.87/21.08 (step t262 (cl (= (or (= tptp.nil tptp.sk2) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A))))) (or (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))))) :rule cong :premises (t260 t261))
% 20.87/21.08 (step t263 (cl (= (forall ((A $$unsorted)) (or (= tptp.nil tptp.sk2) (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A)))) (or (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))))) :rule trans :premises (t255 t262))
% 20.87/21.08 (step t264 (cl (or (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A)))))) :rule resolution :premises (t254 t263 a197))
% 20.87/21.08 (step t265 (cl (= tptp.nil (tptp.app tptp.sk3 tptp.sk5)) (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))) :rule or :premises (t264))
% 20.87/21.08 (step t266 (cl (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) A)) (not (tptp.segmentP tptp.sk3 A))))) :rule resolution :premises (t265 t167))
% 20.87/21.08 (step t267 (cl (or (not (tptp.ssList tptp.sk3)) (not (tptp.neq tptp.sk3 tptp.nil)) (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3)) (not (tptp.segmentP tptp.sk3 tptp.sk3)))) :rule resolution :premises (t253 t266))
% 20.87/21.08 (step t268 (cl (not (tptp.segmentP (tptp.app tptp.sk3 tptp.sk5) tptp.sk3))) :rule resolution :premises (t77 a187 t180 t246 t267))
% 20.87/21.08 (step t269 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule resolution :premises (t75 t39 t268))
% 20.87/21.08 (step t270 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule implies_neg1)
% 20.87/21.08 (anchor :step t271)
% 20.87/21.08 (assume t271.a0 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))
% 20.87/21.08 (step t271.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule forall_inst :args ((:= U tptp.nil) (:= V tptp.sk3) (:= W tptp.sk5)))
% 20.87/21.08 (step t271.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule or :premises (t271.t1))
% 20.87/21.08 (step t271.t3 (cl (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule resolution :premises (t271.t2 t271.a0))
% 20.87/21.08 (step t271 (cl (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule subproof :discharge (t271.a0))
% 20.87/21.08 (step t272 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule resolution :premises (t270 t271))
% 20.87/21.08 (step t273 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (not (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule implies_neg2)
% 20.87/21.08 (step t274 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule resolution :premises (t272 t273))
% 20.87/21.08 (step t275 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3)))) :rule contraction :premises (t274))
% 20.87/21.08 (step t276 (cl (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule implies :premises (t275))
% 20.87/21.08 (step t277 (cl (or (not (tptp.ssList tptp.sk5)) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk3)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk3) tptp.sk5) tptp.sk3))) :rule resolution :premises (t276 t243))
% 20.87/21.08 (step t278 (cl) :rule resolution :premises (t2 t40 t269 t277 a191 a187 a7))
% 20.87/21.08
% 20.87/21.08 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.zFPkPDXVLc/cvc5---1.0.5_18497.smt2
% 20.87/21.08 % cvc5---1.0.5 exiting
% 20.87/21.09 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------