TSTP Solution File: SWC045-1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC045-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n023.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 18:00:03 EDT 2024
% Result : Unsatisfiable 76.72s 76.94s
% Output : Proof 76.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SWC045-1 : TPTP v8.2.0. Released v2.4.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 26 15:08:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.54 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.46/10.68 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.47/15.70 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.53/20.73 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.51/25.76 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.60/30.80 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 35.64/35.83 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 40.64/40.87 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 45.63/45.91 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 50.72/50.94 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 55.71/55.97 --- Run --relevant-triggers --full-saturate-quant at 5...
% 60.79/61.01 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 65.82/66.09 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 75.90/76.12 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 76.72/76.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.KFFxBuJ92E/cvc5---1.0.5_23609.smt2
% 76.72/76.94 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.KFFxBuJ92E/cvc5---1.0.5_23609.smt2
% 76.72/76.97 (assume a0 (tptp.equalelemsP tptp.nil))
% 76.72/76.97 (assume a1 (tptp.duplicatefreeP tptp.nil))
% 76.72/76.97 (assume a2 (tptp.strictorderedP tptp.nil))
% 76.72/76.97 (assume a3 (tptp.totalorderedP tptp.nil))
% 76.72/76.97 (assume a4 (tptp.strictorderP tptp.nil))
% 76.72/76.97 (assume a5 (tptp.totalorderP tptp.nil))
% 76.72/76.97 (assume a6 (tptp.cyclefreeP tptp.nil))
% 76.72/76.97 (assume a7 (tptp.ssList tptp.nil))
% 76.72/76.97 (assume a8 (tptp.ssItem tptp.skac3))
% 76.72/76.97 (assume a9 (tptp.ssItem tptp.skac2))
% 76.72/76.97 (assume a10 (not (tptp.singletonP tptp.nil)))
% 76.72/76.97 (assume a11 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))))
% 76.72/76.97 (assume a12 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))))
% 76.72/76.97 (assume a13 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf81 U))))
% 76.72/76.97 (assume a14 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf80 U))))
% 76.72/76.97 (assume a15 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf79 U))))
% 76.72/76.97 (assume a16 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf78 U))))
% 76.72/76.97 (assume a17 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf77 U))))
% 76.72/76.97 (assume a18 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf76 U))))
% 76.72/76.97 (assume a19 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf75 U))))
% 76.72/76.97 (assume a20 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf74 U))))
% 76.72/76.97 (assume a21 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf73 U))))
% 76.72/76.97 (assume a22 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf72 U))))
% 76.72/76.97 (assume a23 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf71 U))))
% 76.72/76.97 (assume a24 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf70 U))))
% 76.72/76.97 (assume a25 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf69 U))))
% 76.72/76.97 (assume a26 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf68 U))))
% 76.72/76.97 (assume a27 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf67 U))))
% 76.72/76.97 (assume a28 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf66 U))))
% 76.72/76.97 (assume a29 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf65 U))))
% 76.72/76.97 (assume a30 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf64 U))))
% 76.72/76.97 (assume a31 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf63 U))))
% 76.72/76.97 (assume a32 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf62 U))))
% 76.72/76.97 (assume a33 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf61 U))))
% 76.72/76.97 (assume a34 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf60 U))))
% 76.72/76.97 (assume a35 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf59 U))))
% 76.72/76.97 (assume a36 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf58 U))))
% 76.72/76.97 (assume a37 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf57 U))))
% 76.72/76.97 (assume a38 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf56 U))))
% 76.72/76.97 (assume a39 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf55 U))))
% 76.72/76.97 (assume a40 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf54 U))))
% 76.72/76.97 (assume a41 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf53 U))))
% 76.72/76.97 (assume a42 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf52 U))))
% 76.72/76.97 (assume a43 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf51 U))))
% 76.72/76.97 (assume a44 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf50 U))))
% 76.72/76.97 (assume a45 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf49 U))))
% 76.72/76.97 (assume a46 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf44 U))))
% 76.72/76.97 (assume a47 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf48 U V))))
% 76.72/76.97 (assume a48 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf47 U V))))
% 76.72/76.97 (assume a49 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf46 U V))))
% 76.72/76.97 (assume a50 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf45 U V))))
% 76.72/76.97 (assume a51 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf43 U V))))
% 76.72/76.97 (assume a52 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf42 U V))))
% 76.72/76.97 (assume a53 (not (= tptp.skac3 tptp.skac2)))
% 76.72/76.97 (assume a54 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.geq U U))))
% 76.72/76.97 (assume a55 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U tptp.nil))))
% 76.72/76.97 (assume a56 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))
% 76.72/76.97 (assume a57 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.rearsegP U tptp.nil))))
% 76.72/76.97 (assume a58 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.rearsegP U U))))
% 76.72/76.97 (assume a59 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U tptp.nil))))
% 76.72/76.97 (assume a60 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U U))))
% 76.72/76.97 (assume a61 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.leq U U))))
% 76.72/76.97 (assume a62 (forall ((U $$unsorted)) (or (not (tptp.lt U U)) (not (tptp.ssItem U)))))
% 76.72/76.97 (assume a63 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.equalelemsP (tptp.cons U tptp.nil)))))
% 76.72/76.97 (assume a64 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))))
% 76.72/76.97 (assume a65 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U tptp.nil)))))
% 76.72/76.97 (assume a66 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U tptp.nil)))))
% 76.72/76.97 (assume a67 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.strictorderP (tptp.cons U tptp.nil)))))
% 76.72/76.97 (assume a68 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.totalorderP (tptp.cons U tptp.nil)))))
% 76.72/76.97 (assume a69 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.cyclefreeP (tptp.cons U tptp.nil)))))
% 76.72/76.97 (assume a70 (forall ((U $$unsorted)) (or (not (tptp.memberP tptp.nil U)) (not (tptp.ssItem U)))))
% 76.72/76.97 (assume a71 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (tptp.duplicatefreeP U) (tptp.ssItem V))))
% 76.72/76.97 (assume a72 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app U tptp.nil) U))))
% 76.72/76.97 (assume a73 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U))))
% 76.72/76.97 (assume a74 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssList (tptp.tl U)) (= tptp.nil U))))
% 76.72/76.97 (assume a75 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))))
% 76.72/76.97 (assume a76 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssList (tptp.tl U)) (= tptp.nil U))))
% 76.72/76.97 (assume a77 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))))
% 76.72/76.97 (assume a78 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.segmentP tptp.nil U))))
% 76.72/76.97 (assume a79 (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 76.72/76.97 (assume a80 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.rearsegP tptp.nil U))))
% 76.72/76.97 (assume a81 (forall ((U $$unsorted)) (or (not (tptp.rearsegP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 76.72/76.97 (assume a82 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.frontsegP tptp.nil U))))
% 76.72/76.97 (assume a83 (forall ((U $$unsorted)) (or (not (tptp.frontsegP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 76.72/76.97 (assume a84 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))))
% 76.72/76.97 (assume a85 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))))
% 76.72/76.97 (assume a86 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (tptp.leq (tptp.skaf50 U) (tptp.skaf49 U)))))
% 76.72/76.97 (assume a87 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (tptp.leq (tptp.skaf49 U) (tptp.skaf50 U)))))
% 76.72/76.97 (assume a88 (forall ((U $$unsorted)) (or (not (= (tptp.skaf79 U) (tptp.skaf78 U))) (not (tptp.ssList U)) (tptp.equalelemsP U))))
% 76.72/76.97 (assume a89 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf69 U) (tptp.skaf70 U))) (not (tptp.ssList U)) (tptp.strictorderedP U))))
% 76.72/76.97 (assume a90 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf64 U) (tptp.skaf65 U))) (not (tptp.ssList U)) (tptp.totalorderedP U))))
% 76.72/76.97 (assume a91 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf60 U) (tptp.skaf59 U))) (not (tptp.ssList U)) (tptp.strictorderP U))))
% 76.72/76.97 (assume a92 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf59 U) (tptp.skaf60 U))) (not (tptp.ssList U)) (tptp.strictorderP U))))
% 76.72/76.97 (assume a93 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf55 U) (tptp.skaf54 U))) (not (tptp.ssList U)) (tptp.totalorderP U))))
% 76.72/76.97 (assume a94 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf54 U) (tptp.skaf55 U))) (not (tptp.ssList U)) (tptp.totalorderP U))))
% 76.72/76.97 (assume a95 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.tl (tptp.cons U V)) V))))
% 76.72/76.97 (assume a96 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.hd (tptp.cons U V)) U))))
% 76.72/76.97 (assume a97 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))
% 76.72/76.97 (assume a98 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) V)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))
% 76.72/76.97 (assume a99 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= V U))))
% 76.72/76.97 (assume a100 (forall ((U $$unsorted)) (or (not (tptp.singletonP U)) (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf44 U) tptp.nil) U))))
% 76.72/76.97 (assume a101 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem V)) (tptp.neq V U) (= V U))))
% 76.72/76.97 (assume a102 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq U V))))
% 76.72/76.97 (assume a103 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= tptp.nil U))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (assume a108 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U))))
% 76.72/76.97 (assume a109 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.gt V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)))))
% 76.72/76.97 (assume a110 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.lt U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)))))
% 76.72/76.97 (assume a111 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.strictorderedP (tptp.cons V U)))))
% 76.72/76.97 (assume a112 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.totalorderedP (tptp.cons V U)))))
% 76.72/76.97 (assume a113 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.lt V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)))))
% 76.72/76.97 (assume a114 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssList V)) (not (tptp.ssList U)))))
% 76.72/76.97 (assume a115 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U tptp.nil) V)) (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.singletonP V))))
% 76.72/76.97 (assume a116 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)))))
% 76.72/76.97 (assume a117 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))))
% 76.72/76.97 (assume a118 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))))
% 76.72/76.97 (assume a119 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))))
% 76.72/76.97 (assume a120 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))))
% 76.72/76.97 (assume a121 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))))
% 76.72/76.97 (assume a122 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.hd (tptp.app V U)) (tptp.hd V)))))
% 76.72/76.97 (assume a123 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP V) (= tptp.nil V))))
% 76.72/76.97 (assume a124 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP V) (= tptp.nil V))))
% 76.72/76.97 (assume a125 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))))
% 76.72/76.97 (assume a126 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 76.72/76.97 (assume a127 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.rearsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 76.72/76.97 (assume a128 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 76.72/76.97 (assume a129 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))))
% 76.72/76.97 (assume a130 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app (tptp.skaf46 U V) V) U))))
% 76.72/76.97 (assume a131 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app V (tptp.skaf45 U V)) U))))
% 76.72/76.97 (assume a132 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.tl (tptp.app V U)) (tptp.app (tptp.tl V) U)))))
% 76.72/76.97 (assume a133 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.lt U (tptp.hd V)) (= tptp.nil V))))
% 76.72/76.97 (assume a134 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.leq U (tptp.hd V)) (= tptp.nil V))))
% 76.72/76.97 (assume a135 (forall ((U $$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))))
% 76.72/76.97 (assume a136 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP (tptp.app U W) V))))
% 76.72/76.97 (assume a137 (forall ((U $$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))))
% 76.72/76.97 (assume a138 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons W U) V))))
% 76.72/76.97 (assume a139 (forall ((U $$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))))
% 76.72/76.97 (assume a140 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.app W U) V))))
% 76.72/76.97 (assume a141 (forall ((U $$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))))
% 76.72/76.97 (assume a142 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (tptp.rearsegP W V))))
% 76.72/76.97 (assume a143 (forall ((U $$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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (assume a145 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.gt V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.gt U W))))
% 76.72/76.97 (assume a146 (forall ((U $$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))))
% 76.72/76.97 (assume a147 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.geq U W))))
% 76.72/76.97 (assume a148 (forall ((U $$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))))))
% 76.72/76.97 (assume a149 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) (tptp.app U W))) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (= V W))))
% 76.72/76.97 (assume a150 (forall ((U $$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))))
% 76.72/76.97 (assume a151 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.segmentP U W))))
% 76.72/76.97 (assume a152 (forall ((U $$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))))
% 76.72/76.97 (assume a153 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP U W))))
% 76.72/76.97 (assume a154 (forall ((U $$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))))
% 76.72/76.97 (assume a155 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq U W))))
% 76.72/76.97 (assume a156 (forall ((U $$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)))))
% 76.72/76.97 (assume a157 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP (tptp.app U V) W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (tptp.memberP V W) (tptp.memberP U W))))
% 76.72/76.97 (assume a158 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U (tptp.hd V))) (not (tptp.totalorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U V)) (= tptp.nil V))))
% 76.72/76.97 (assume a159 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U (tptp.hd V))) (not (tptp.strictorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U V)) (= tptp.nil V))))
% 76.72/76.97 (assume a160 (forall ((U $$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))))
% 76.72/76.97 (assume a161 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.duplicatefreeP U) (= (tptp.app (tptp.app (tptp.skaf75 U) (tptp.cons (tptp.skaf74 U) (tptp.skaf76 U))) (tptp.cons (tptp.skaf74 U) (tptp.skaf77 U))) U))))
% 76.72/76.97 (assume a162 (forall ((U $$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))))
% 76.72/76.97 (assume a163 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderedP U) (= (tptp.app (tptp.app (tptp.skaf66 U) (tptp.cons (tptp.skaf64 U) (tptp.skaf67 U))) (tptp.cons (tptp.skaf65 U) (tptp.skaf68 U))) U))))
% 76.72/76.97 (assume a164 (forall ((U $$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))))
% 76.72/76.97 (assume a165 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderP U) (= (tptp.app (tptp.app (tptp.skaf56 U) (tptp.cons (tptp.skaf54 U) (tptp.skaf57 U))) (tptp.cons (tptp.skaf55 U) (tptp.skaf58 U))) U))))
% 76.72/76.97 (assume a166 (forall ((U $$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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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)))))
% 76.72/76.97 (assume a178 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons V X)) Y)) (not (tptp.ssList X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (not (tptp.duplicatefreeP Y)) (not (tptp.ssList Y)))))
% 76.72/76.97 (assume a179 (forall ((U $$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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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))))
% 76.72/76.97 (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)))))
% 76.72/76.97 (assume a185 (tptp.ssList tptp.sk1))
% 76.72/76.97 (assume a186 (tptp.ssList tptp.sk2))
% 76.72/76.97 (assume a187 (tptp.ssList tptp.sk3))
% 76.72/76.97 (assume a188 (tptp.ssList tptp.sk4))
% 76.72/76.97 (assume a189 (= tptp.nil tptp.sk2))
% 76.72/76.97 (assume a190 (= tptp.sk2 tptp.sk4))
% 76.72/76.97 (assume a191 (= tptp.sk1 tptp.sk3))
% 76.72/76.97 (assume a192 (not (= tptp.nil tptp.sk1)))
% 76.72/76.97 (assume a193 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ssItem A)) (tptp.memberP tptp.sk3 A) (not (tptp.ssList B)) (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.nil) B) (tptp.cons A tptp.nil)))))))
% 76.72/76.97 (assume a194 (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A)))))
% 76.72/76.97 (assume a195 (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.nil) (tptp.sk5 A)) (tptp.cons A tptp.nil))) (not (tptp.memberP tptp.sk3 A)))))
% 76.72/76.97 (step t1 (cl (not (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule or_pos)
% 76.72/76.97 (step t2 (cl (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule reordering :premises (t1))
% 76.72/76.97 (step t3 (cl (not (or (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) :rule or_pos)
% 76.72/76.97 (step t4 (cl (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (or (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule reordering :premises (t3))
% 76.72/76.97 (step t5 (cl (not (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) :rule or_pos)
% 76.72/76.97 (step t6 (cl (not (tptp.ssList tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) (not (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule reordering :premises (t5))
% 76.72/76.97 (step t7 (cl (not (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4)) :rule or_pos)
% 76.72/76.97 (step t8 (cl (= tptp.sk3 tptp.sk4) (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (not (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4)))) :rule reordering :premises (t7))
% 76.72/76.97 (step t9 (cl (not (= (not (= tptp.nil tptp.sk1)) (not (= tptp.sk3 tptp.sk4)))) (not (not (= tptp.nil tptp.sk1))) (not (= tptp.sk3 tptp.sk4))) :rule equiv_pos2)
% 76.72/76.97 (step t10 (cl (and (= tptp.sk1 tptp.sk3) (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2)) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.nil tptp.sk2))) :rule and_neg)
% 76.72/76.97 (step t11 (cl (and (= tptp.sk1 tptp.sk3) (= tptp.sk2 tptp.sk4) (= tptp.nil tptp.sk2))) :rule resolution :premises (t10 a191 a190 a189))
% 76.72/76.97 (step t12 (cl (= tptp.nil tptp.sk2)) :rule and :premises (t11))
% 76.72/76.97 (step t13 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t11))
% 76.72/76.97 (step t14 (cl (= tptp.nil tptp.sk4)) :rule trans :premises (t12 t13))
% 76.72/76.97 (step t15 (cl (= tptp.sk1 tptp.sk3)) :rule and :premises (t11))
% 76.72/76.97 (step t16 (cl (= (= tptp.nil tptp.sk1) (= tptp.sk4 tptp.sk3))) :rule cong :premises (t14 t15))
% 76.72/76.97 (step t17 (cl (= (not (= tptp.nil tptp.sk1)) (not (= tptp.sk4 tptp.sk3)))) :rule cong :premises (t16))
% 76.72/76.97 (step t18 (cl (= (= tptp.sk4 tptp.sk3) (= tptp.sk3 tptp.sk4))) :rule all_simplify)
% 76.72/76.97 (step t19 (cl (= (not (= tptp.sk4 tptp.sk3)) (not (= tptp.sk3 tptp.sk4)))) :rule cong :premises (t18))
% 76.72/76.97 (step t20 (cl (= (not (= tptp.nil tptp.sk1)) (not (= tptp.sk3 tptp.sk4)))) :rule trans :premises (t17 t19))
% 76.72/76.97 (step t21 (cl (not (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t9 t20 a192))
% 76.72/76.97 (step t22 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4)))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t23)
% 76.72/76.97 (assume t23.a0 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))))
% 76.72/76.97 (step t23.t1 (cl (or (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4)))) :rule forall_inst :args ((:= U tptp.sk3)))
% 76.72/76.97 (step t23.t2 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) :rule or :premises (t23.t1))
% 76.72/76.97 (step t23.t3 (cl (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t23.t2 t23.a0))
% 76.72/76.97 (step t23 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) :rule subproof :discharge (t23.a0))
% 76.72/76.97 (step t24 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t22 t23))
% 76.72/76.97 (step t25 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) (not (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4)))) :rule implies_neg2)
% 76.72/76.97 (step t26 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4)))) :rule resolution :premises (t24 t25))
% 76.72/76.97 (step t27 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4)))) :rule contraction :premises (t26))
% 76.72/76.97 (step t28 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) :rule implies :premises (t27))
% 76.72/76.97 (step t29 (cl (not (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))))) (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4)))) :rule equiv_pos2)
% 76.72/76.97 (anchor :step t30 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t30.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t30.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t30.t3 (cl (= (tptp.ssItem (tptp.hd U)) (tptp.ssItem (tptp.hd U)))) :rule refl)
% 76.72/76.97 (step t30.t4 (cl (= tptp.nil tptp.sk2)) :rule and :premises (t11))
% 76.72/76.97 (step t30.t5 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t11))
% 76.72/76.97 (step t30.t6 (cl (= tptp.nil tptp.sk4)) :rule trans :premises (t30.t4 t30.t5))
% 76.72/76.97 (step t30.t7 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t30.t8 (cl (= (= tptp.nil U) (= tptp.sk4 U))) :rule cong :premises (t30.t6 t30.t7))
% 76.72/76.97 (step t30.t9 (cl (= (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.sk4 U)))) :rule cong :premises (t30.t2 t30.t3 t30.t8))
% 76.72/76.97 (step t30 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.sk4 U))))) :rule bind)
% 76.72/76.97 (anchor :step t31 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t31.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t31.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t31.t3 (cl (= (tptp.ssItem (tptp.hd U)) (tptp.ssItem (tptp.hd U)))) :rule refl)
% 76.72/76.97 (step t31.t4 (cl (= (= tptp.sk4 U) (= U tptp.sk4))) :rule all_simplify)
% 76.72/76.97 (step t31.t5 (cl (= (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.sk4 U)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4)))) :rule cong :premises (t31.t2 t31.t3 t31.t4))
% 76.72/76.97 (step t31 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.sk4 U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))))) :rule bind)
% 76.72/76.97 (step t32 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4))))) :rule trans :premises (t30 t31))
% 76.72/76.97 (step t33 (cl (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= U tptp.sk4)))) :rule resolution :premises (t29 t32 a75))
% 76.72/76.97 (step t34 (cl (or (not (tptp.ssList tptp.sk3)) (tptp.ssItem (tptp.hd tptp.sk3)) (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t28 t33))
% 76.72/76.97 (step t35 (cl (tptp.ssItem (tptp.hd tptp.sk3))) :rule resolution :premises (t8 t21 a187 t34))
% 76.72/76.97 (step t36 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t37)
% 76.72/76.97 (assume t37.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))))
% 76.72/76.97 (step t37.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule forall_inst :args ((:= U (tptp.hd tptp.sk3)) (:= V tptp.sk4)))
% 76.72/76.97 (step t37.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule or :premises (t37.t1))
% 76.72/76.97 (step t37.t3 (cl (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule resolution :premises (t37.t2 t37.a0))
% 76.72/76.97 (step t37 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule subproof :discharge (t37.a0))
% 76.72/76.97 (step t38 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule resolution :premises (t36 t37))
% 76.72/76.97 (step t39 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule implies_neg2)
% 76.72/76.97 (step t40 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule resolution :premises (t38 t39))
% 76.72/76.97 (step t41 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule contraction :premises (t40))
% 76.72/76.97 (step t42 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule implies :premises (t41))
% 76.72/76.97 (step t43 (cl (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)) (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule resolution :premises (t42 a85))
% 76.72/76.97 (step t44 (cl (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) :rule resolution :premises (t6 a188 t35 t43))
% 76.72/76.97 (step t45 (cl (not (or (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))) :rule or_pos)
% 76.72/76.97 (step t46 (cl (not (tptp.ssList tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (or (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))))) :rule reordering :premises (t45))
% 76.72/76.97 (step t47 (cl (not (= (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))))) (not (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))))) :rule equiv_pos2)
% 76.72/76.97 (step t48 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))) :rule refl)
% 76.72/76.97 (step t49 (cl (= (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule all_simplify)
% 76.72/76.97 (step t50 (cl (= (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule cong :premises (t49))
% 76.72/76.97 (step t51 (cl (= (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssItem (tptp.hd tptp.sk3))))) :rule refl)
% 76.72/76.97 (step t52 (cl (= (not (tptp.ssList tptp.sk4)) (not (tptp.ssList tptp.sk4)))) :rule refl)
% 76.72/76.97 (step t53 (cl (= (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))) (or (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))))) :rule cong :premises (t50 t51 t52))
% 76.72/76.97 (step t54 (cl (= (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))))) :rule cong :premises (t48 t53))
% 76.72/76.97 (step t55 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V))))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t56)
% 76.72/76.97 (assume t56.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))
% 76.72/76.97 (step t56.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V))))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))))) :rule forall_inst :args ((:= U (tptp.hd tptp.sk3)) (:= V tptp.sk4)))
% 76.72/76.97 (step t56.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V))))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) :rule or :premises (t56.t1))
% 76.72/76.97 (step t56.t3 (cl (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) :rule resolution :premises (t56.t2 t56.a0))
% 76.72/76.97 (step t56 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V))))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) :rule subproof :discharge (t56.a0))
% 76.72/76.97 (step t57 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) :rule resolution :premises (t55 t56))
% 76.72/76.97 (step t58 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) (not (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))))) :rule implies_neg2)
% 76.72/76.97 (step t59 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))))) :rule resolution :premises (t57 t58))
% 76.72/76.97 (step t60 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))))) :rule contraction :premises (t59))
% 76.72/76.97 (step t61 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (or (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4))))) :rule resolution :premises (t47 t54 t60))
% 76.72/76.97 (step t62 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V))))) (or (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) :rule implies :premises (t61))
% 76.72/76.97 (step t63 (cl (not (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))) (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V))))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V))))) :rule equiv_pos2)
% 76.72/76.97 (anchor :step t64 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 76.72/76.97 (step t64.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t64.t2 (cl (= V V)) :rule refl)
% 76.72/76.97 (step t64.t3 (cl (= (= (tptp.cons U V) tptp.nil) (= tptp.nil (tptp.cons U V)))) :rule all_simplify)
% 76.72/76.97 (step t64.t4 (cl (= (not (= (tptp.cons U V) tptp.nil)) (not (= tptp.nil (tptp.cons U V))))) :rule cong :premises (t64.t3))
% 76.72/76.97 (step t64.t5 (cl (= (not (tptp.ssItem U)) (not (tptp.ssItem U)))) :rule refl)
% 76.72/76.97 (step t64.t6 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 76.72/76.97 (step t64.t7 (cl (= (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V))) (or (not (= tptp.nil (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V))))) :rule cong :premises (t64.t4 t64.t5 t64.t6))
% 76.72/76.97 (step t64 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V)))))) :rule bind)
% 76.72/76.97 (anchor :step t65 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 76.72/76.97 (step t65.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t65.t2 (cl (= V V)) :rule refl)
% 76.72/76.97 (step t65.t3 (cl (= tptp.nil tptp.sk2)) :rule and :premises (t11))
% 76.72/76.97 (step t65.t4 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t11))
% 76.72/76.97 (step t65.t5 (cl (= tptp.nil tptp.sk4)) :rule trans :premises (t65.t3 t65.t4))
% 76.72/76.97 (step t65.t6 (cl (= (tptp.cons U V) (tptp.cons U V))) :rule refl)
% 76.72/76.97 (step t65.t7 (cl (= (= tptp.nil (tptp.cons U V)) (= tptp.sk4 (tptp.cons U V)))) :rule cong :premises (t65.t5 t65.t6))
% 76.72/76.97 (step t65.t8 (cl (= (not (= tptp.nil (tptp.cons U V))) (not (= tptp.sk4 (tptp.cons U V))))) :rule cong :premises (t65.t7))
% 76.72/76.97 (step t65.t9 (cl (= (not (tptp.ssItem U)) (not (tptp.ssItem U)))) :rule refl)
% 76.72/76.97 (step t65.t10 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 76.72/76.97 (step t65.t11 (cl (= (or (not (= tptp.nil (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V))) (or (not (= tptp.sk4 (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V))))) :rule cong :premises (t65.t8 t65.t9 t65.t10))
% 76.72/76.97 (step t65 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.sk4 (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V)))))) :rule bind)
% 76.72/76.97 (anchor :step t66 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 76.72/76.97 (step t66.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t66.t2 (cl (= V V)) :rule refl)
% 76.72/76.97 (step t66.t3 (cl (= (= tptp.sk4 (tptp.cons U V)) (= (tptp.cons U V) tptp.sk4))) :rule all_simplify)
% 76.72/76.97 (step t66.t4 (cl (= (not (= tptp.sk4 (tptp.cons U V))) (not (= (tptp.cons U V) tptp.sk4)))) :rule cong :premises (t66.t3))
% 76.72/76.97 (step t66.t5 (cl (= (not (tptp.ssItem U)) (not (tptp.ssItem U)))) :rule refl)
% 76.72/76.97 (step t66.t6 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 76.72/76.97 (step t66.t7 (cl (= (or (not (= tptp.sk4 (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V))) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V))))) :rule cong :premises (t66.t4 t66.t5 t66.t6))
% 76.72/76.97 (step t66 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.sk4 (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))) :rule bind)
% 76.72/76.97 (step t67 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))) :rule trans :premises (t65 t66))
% 76.72/76.97 (step t68 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))) :rule trans :premises (t64 t67))
% 76.72/76.97 (step t69 (cl (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.sk4)) (not (tptp.ssItem U)) (not (tptp.ssList V))))) :rule resolution :premises (t63 t68 a97))
% 76.72/76.97 (step t70 (cl (or (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.ssList tptp.sk4)))) :rule resolution :premises (t62 t69))
% 76.72/76.97 (step t71 (cl (not (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule resolution :premises (t46 a188 t35 t70))
% 76.72/76.97 (step t72 (cl (not (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) :rule or_pos)
% 76.72/76.97 (step t73 (cl (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))) (not (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))))) :rule reordering :premises (t72))
% 76.72/76.97 (step t74 (cl (not (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))) :rule or_pos)
% 76.72/76.97 (step t75 (cl (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (not (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule reordering :premises (t74))
% 76.72/76.97 (step t76 (cl (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (not (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)))) (not (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (not (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (not (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule and_neg)
% 76.72/76.97 (step t77 (cl (=> (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t78)
% 76.72/76.97 (assume t78.a0 (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))))
% 76.72/76.97 (assume t78.a1 (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))
% 76.72/76.97 (assume t78.a2 (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))
% 76.72/76.97 (assume t78.a3 (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))
% 76.72/76.97 (step t78.t1 (cl (=> (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t78.t2)
% 76.72/76.97 (assume t78.t2.a0 (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))
% 76.72/76.97 (assume t78.t2.a1 (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))
% 76.72/76.97 (assume t78.t2.a2 (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))))
% 76.72/76.97 (assume t78.t2.a3 (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))
% 76.72/76.97 (step t78.t2.t1 (cl (= (= (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)) true) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))) :rule equiv_simplify)
% 76.72/76.97 (step t78.t2.t2 (cl (not (= (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)) true)) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule equiv1 :premises (t78.t2.t1))
% 76.72/76.97 (step t78.t2.t3 (cl (= (tptp.hd tptp.sk3) (tptp.hd tptp.sk3))) :rule refl)
% 76.72/76.97 (step t78.t2.t4 (cl (= (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)) (tptp.memberP (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)) (tptp.hd tptp.sk3)))) :rule cong :premises (t78.t2.a2 t78.t2.t3))
% 76.72/76.97 (step t78.t2.t5 (cl (= (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)) tptp.sk3)) :rule symm :premises (t78.t2.a2))
% 76.72/76.97 (step t78.t2.t6 (cl (= (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) tptp.sk3)) :rule symm :premises (t78.t2.a1))
% 76.72/76.97 (step t78.t2.t7 (cl (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) :rule symm :premises (t78.t2.t6))
% 76.72/76.97 (step t78.t2.t8 (cl (= (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)) (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) :rule trans :premises (t78.t2.t5 t78.t2.t7))
% 76.72/76.97 (step t78.t2.t9 (cl (= (tptp.hd tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) :rule cong :premises (t78.t2.t7))
% 76.72/76.97 (step t78.t2.t10 (cl (= (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (tptp.skaf83 tptp.sk3))) :rule symm :premises (t78.t2.a3))
% 76.72/76.97 (step t78.t2.t11 (cl (= (tptp.hd tptp.sk3) (tptp.skaf83 tptp.sk3))) :rule trans :premises (t78.t2.t9 t78.t2.t10))
% 76.72/76.97 (step t78.t2.t12 (cl (= (tptp.memberP (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)) (tptp.hd tptp.sk3)) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule cong :premises (t78.t2.t8 t78.t2.t11))
% 76.72/76.97 (step t78.t2.t13 (cl (= (= (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) true) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule equiv_simplify)
% 76.72/76.97 (step t78.t2.t14 (cl (= (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) true) (not (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule equiv2 :premises (t78.t2.t13))
% 76.72/76.97 (step t78.t2.t15 (cl (= (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) true)) :rule resolution :premises (t78.t2.t14 t78.t2.a0))
% 76.72/76.97 (step t78.t2.t16 (cl (= (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)) true)) :rule trans :premises (t78.t2.t4 t78.t2.t12 t78.t2.t15))
% 76.72/76.97 (step t78.t2.t17 (cl (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule resolution :premises (t78.t2.t2 t78.t2.t16))
% 76.72/76.97 (step t78.t2 (cl (not (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (not (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (not (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)))) (not (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule subproof :discharge (t78.t2.a0 t78.t2.a1 t78.t2.a2 t78.t2.a3))
% 76.72/76.97 (step t78.t3 (cl (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) :rule and_pos)
% 76.72/76.97 (step t78.t4 (cl (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) :rule and_pos)
% 76.72/76.97 (step t78.t5 (cl (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)))) :rule and_pos)
% 76.72/76.97 (step t78.t6 (cl (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) :rule and_pos)
% 76.72/76.97 (step t78.t7 (cl (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)) (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))))) :rule resolution :premises (t78.t2 t78.t3 t78.t4 t78.t5 t78.t6))
% 76.72/76.97 (step t78.t8 (cl (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule reordering :premises (t78.t7))
% 76.72/76.97 (step t78.t9 (cl (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule contraction :premises (t78.t8))
% 76.72/76.97 (step t78.t10 (cl (=> (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule resolution :premises (t78.t1 t78.t9))
% 76.72/76.97 (step t78.t11 (cl (=> (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))) :rule implies_neg2)
% 76.72/76.97 (step t78.t12 (cl (=> (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (=> (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))) :rule resolution :premises (t78.t10 t78.t11))
% 76.72/76.97 (step t78.t13 (cl (=> (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))) :rule contraction :premises (t78.t12))
% 76.72/76.97 (step t78.t14 (cl (not (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule implies :premises (t78.t13))
% 76.72/76.97 (step t78.t15 (cl (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (not (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (not (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (not (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)))) (not (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) :rule and_neg)
% 76.72/76.97 (step t78.t16 (cl (and (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) :rule resolution :premises (t78.t15 t78.a3 t78.a1 t78.a0 t78.a2))
% 76.72/76.97 (step t78.t17 (cl (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule resolution :premises (t78.t14 t78.t16))
% 76.72/76.97 (step t78 (cl (not (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)))) (not (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (not (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (not (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule subproof :discharge (t78.a0 t78.a1 t78.a2 t78.a3))
% 76.72/76.97 (step t79 (cl (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)))) :rule and_pos)
% 76.72/76.97 (step t80 (cl (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) :rule and_pos)
% 76.72/76.97 (step t81 (cl (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) :rule and_pos)
% 76.72/76.97 (step t82 (cl (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) :rule and_pos)
% 76.72/76.97 (step t83 (cl (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)) (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))))) :rule resolution :premises (t78 t79 t80 t81 t82))
% 76.72/76.97 (step t84 (cl (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule reordering :premises (t83))
% 76.72/76.97 (step t85 (cl (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule contraction :premises (t84))
% 76.72/76.97 (step t86 (cl (=> (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule resolution :premises (t77 t85))
% 76.72/76.97 (step t87 (cl (=> (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))) :rule implies_neg2)
% 76.72/76.97 (step t88 (cl (=> (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (=> (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))) :rule resolution :premises (t86 t87))
% 76.72/76.97 (step t89 (cl (=> (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))) :rule contraction :premises (t88))
% 76.72/76.97 (step t90 (cl (not (and (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule implies :premises (t89))
% 76.72/76.97 (step t91 (cl (not (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)))) (not (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (not (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (not (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule resolution :premises (t76 t90))
% 76.72/76.97 (step t92 (cl (not (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)))) (not (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)) (not (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) (not (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule reordering :premises (t91))
% 76.72/76.97 (step t93 (cl (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4)) :rule or_pos)
% 76.72/76.97 (step t94 (cl (= tptp.sk3 tptp.sk4) (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule reordering :premises (t93))
% 76.72/76.97 (step t95 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4)))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t96)
% 76.72/76.97 (assume t96.a0 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))))
% 76.72/76.97 (step t96.t1 (cl (or (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule forall_inst :args ((:= U tptp.sk3)))
% 76.72/76.97 (step t96.t2 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule or :premises (t96.t1))
% 76.72/76.97 (step t96.t3 (cl (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t96.t2 t96.a0))
% 76.72/76.97 (step t96 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule subproof :discharge (t96.a0))
% 76.72/76.97 (step t97 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t95 t96))
% 76.72/76.97 (step t98 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule implies_neg2)
% 76.72/76.97 (step t99 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule resolution :premises (t97 t98))
% 76.72/76.97 (step t100 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule contraction :premises (t99))
% 76.72/76.97 (step t101 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule implies :premises (t100))
% 76.72/76.97 (step t102 (cl (not (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))))) (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= tptp.nil U)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4)))) :rule equiv_pos2)
% 76.72/76.97 (anchor :step t103 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t103.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t103.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t103.t3 (cl (= (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))) :rule all_simplify)
% 76.72/76.97 (step t103.t4 (cl (= (= tptp.nil U) (= tptp.nil U))) :rule refl)
% 76.72/76.97 (step t103.t5 (cl (= (or (not (tptp.ssList U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= tptp.nil U)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= tptp.nil U)))) :rule cong :premises (t103.t2 t103.t3 t103.t4))
% 76.72/76.97 (step t103 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= tptp.nil U))))) :rule bind)
% 76.72/76.97 (anchor :step t104 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t104.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t104.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t104.t3 (cl (= (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))) :rule refl)
% 76.72/76.97 (step t104.t4 (cl (= tptp.nil tptp.sk2)) :rule and :premises (t11))
% 76.72/76.97 (step t104.t5 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t11))
% 76.72/76.97 (step t104.t6 (cl (= tptp.nil tptp.sk4)) :rule trans :premises (t104.t4 t104.t5))
% 76.72/76.97 (step t104.t7 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t104.t8 (cl (= (= tptp.nil U) (= tptp.sk4 U))) :rule cong :premises (t104.t6 t104.t7))
% 76.72/76.97 (step t104.t9 (cl (= (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= tptp.nil U)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= tptp.sk4 U)))) :rule cong :premises (t104.t2 t104.t3 t104.t8))
% 76.72/76.97 (step t104 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= tptp.sk4 U))))) :rule bind)
% 76.72/76.97 (anchor :step t105 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t105.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t105.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t105.t3 (cl (= (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))) :rule refl)
% 76.72/76.97 (step t105.t4 (cl (= (= tptp.sk4 U) (= U tptp.sk4))) :rule all_simplify)
% 76.72/76.97 (step t105.t5 (cl (= (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= tptp.sk4 U)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4)))) :rule cong :premises (t105.t2 t105.t3 t105.t4))
% 76.72/76.97 (step t105 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= tptp.sk4 U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))))) :rule bind)
% 76.72/76.97 (step t106 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))))) :rule trans :premises (t104 t105))
% 76.72/76.97 (step t107 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4))))) :rule trans :premises (t103 t106))
% 76.72/76.97 (step t108 (cl (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.hd U) (tptp.tl U))) (= U tptp.sk4)))) :rule resolution :premises (t102 t107 a103))
% 76.72/76.97 (step t109 (cl (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t101 t108))
% 76.72/76.97 (step t110 (cl (= tptp.sk3 (tptp.cons (tptp.hd tptp.sk3) (tptp.tl tptp.sk3)))) :rule resolution :premises (t94 t21 a187 t109))
% 76.72/76.97 (step t111 (cl (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4)) :rule or_pos)
% 76.72/76.97 (step t112 (cl (= tptp.sk3 tptp.sk4) (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule reordering :premises (t111))
% 76.72/76.97 (step t113 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4)))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t114)
% 76.72/76.97 (assume t114.a0 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))))
% 76.72/76.97 (step t114.t1 (cl (or (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule forall_inst :args ((:= U tptp.sk3)))
% 76.72/76.97 (step t114.t2 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule or :premises (t114.t1))
% 76.72/76.97 (step t114.t3 (cl (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t114.t2 t114.a0))
% 76.72/76.97 (step t114 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule subproof :discharge (t114.a0))
% 76.72/76.97 (step t115 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t113 t114))
% 76.72/76.97 (step t116 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) (not (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule implies_neg2)
% 76.72/76.97 (step t117 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule resolution :premises (t115 t116))
% 76.72/76.97 (step t118 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4)))) :rule contraction :premises (t117))
% 76.72/76.97 (step t119 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4)))) (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule implies :premises (t118))
% 76.72/76.97 (step t120 (cl (not (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))))) (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4)))) :rule equiv_pos2)
% 76.72/76.97 (anchor :step t121 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t121.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t121.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t121.t3 (cl (= (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))))) :rule all_simplify)
% 76.72/76.97 (step t121.t4 (cl (= (= tptp.nil U) (= tptp.nil U))) :rule refl)
% 76.72/76.97 (step t121.t5 (cl (= (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)))) :rule cong :premises (t121.t2 t121.t3 t121.t4))
% 76.72/76.97 (step t121 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))))) :rule bind)
% 76.72/76.97 (anchor :step t122 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t122.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t122.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t122.t3 (cl (= (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))))) :rule refl)
% 76.72/76.97 (step t122.t4 (cl (= tptp.nil tptp.sk2)) :rule and :premises (t11))
% 76.72/76.97 (step t122.t5 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t11))
% 76.72/76.97 (step t122.t6 (cl (= tptp.nil tptp.sk4)) :rule trans :premises (t122.t4 t122.t5))
% 76.72/76.97 (step t122.t7 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t122.t8 (cl (= (= tptp.nil U) (= tptp.sk4 U))) :rule cong :premises (t122.t6 t122.t7))
% 76.72/76.97 (step t122.t9 (cl (= (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.sk4 U)))) :rule cong :premises (t122.t2 t122.t3 t122.t8))
% 76.72/76.97 (step t122 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.sk4 U))))) :rule bind)
% 76.72/76.97 (anchor :step t123 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t123.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t123.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t123.t3 (cl (= (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))))) :rule refl)
% 76.72/76.97 (step t123.t4 (cl (= (= tptp.sk4 U) (= U tptp.sk4))) :rule all_simplify)
% 76.72/76.97 (step t123.t5 (cl (= (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.sk4 U)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4)))) :rule cong :premises (t123.t2 t123.t3 t123.t4))
% 76.72/76.97 (step t123 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.sk4 U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))))) :rule bind)
% 76.72/76.97 (step t124 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))))) :rule trans :premises (t122 t123))
% 76.72/76.97 (step t125 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4))))) :rule trans :premises (t121 t124))
% 76.72/76.97 (step t126 (cl (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U))) (= U tptp.sk4)))) :rule resolution :premises (t120 t125 a108))
% 76.72/76.97 (step t127 (cl (or (not (tptp.ssList tptp.sk3)) (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))) (= tptp.sk3 tptp.sk4))) :rule resolution :premises (t119 t126))
% 76.72/76.97 (step t128 (cl (= tptp.sk3 (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) :rule resolution :premises (t112 t21 a187 t127))
% 76.72/76.97 (step t129 (cl (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) :rule or_pos)
% 76.72/76.97 (step t130 (cl (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))) (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))))) :rule reordering :premises (t129))
% 76.72/76.97 (step t131 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk3))) (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t132)
% 76.72/76.97 (assume t132.a0 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))))
% 76.72/76.97 (step t132.t1 (cl (or (not (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) (tptp.ssItem (tptp.skaf83 tptp.sk3)))) :rule forall_inst :args ((:= U tptp.sk3)))
% 76.72/76.97 (step t132.t2 (cl (not (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) (tptp.ssItem (tptp.skaf83 tptp.sk3))) :rule or :premises (t132.t1))
% 76.72/76.97 (step t132.t3 (cl (tptp.ssItem (tptp.skaf83 tptp.sk3))) :rule resolution :premises (t132.t2 t132.a0))
% 76.72/76.97 (step t132 (cl (not (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) (tptp.ssItem (tptp.skaf83 tptp.sk3))) :rule subproof :discharge (t132.a0))
% 76.72/76.97 (step t133 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.ssItem (tptp.skaf83 tptp.sk3))) :rule resolution :premises (t131 t132))
% 76.72/76.97 (step t134 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3)))) :rule implies_neg2)
% 76.72/76.97 (step t135 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk3))) (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk3)))) :rule resolution :premises (t133 t134))
% 76.72/76.97 (step t136 (cl (=> (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))) (tptp.ssItem (tptp.skaf83 tptp.sk3)))) :rule contraction :premises (t135))
% 76.72/76.97 (step t137 (cl (not (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U)))) (tptp.ssItem (tptp.skaf83 tptp.sk3))) :rule implies :premises (t136))
% 76.72/76.97 (step t138 (cl (tptp.ssItem (tptp.skaf83 tptp.sk3))) :rule resolution :premises (t137 a11))
% 76.72/76.97 (step t139 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk3))) (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t140)
% 76.72/76.97 (assume t140.a0 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))))
% 76.72/76.97 (step t140.t1 (cl (or (not (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) (tptp.ssList (tptp.skaf82 tptp.sk3)))) :rule forall_inst :args ((:= U tptp.sk3)))
% 76.72/76.97 (step t140.t2 (cl (not (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) (tptp.ssList (tptp.skaf82 tptp.sk3))) :rule or :premises (t140.t1))
% 76.72/76.97 (step t140.t3 (cl (tptp.ssList (tptp.skaf82 tptp.sk3))) :rule resolution :premises (t140.t2 t140.a0))
% 76.72/76.97 (step t140 (cl (not (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) (tptp.ssList (tptp.skaf82 tptp.sk3))) :rule subproof :discharge (t140.a0))
% 76.72/76.97 (step t141 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk3))) (tptp.ssList (tptp.skaf82 tptp.sk3))) :rule resolution :premises (t139 t140))
% 76.72/76.97 (step t142 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3)))) :rule implies_neg2)
% 76.72/76.97 (step t143 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk3))) (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk3)))) :rule resolution :premises (t141 t142))
% 76.72/76.97 (step t144 (cl (=> (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))) (tptp.ssList (tptp.skaf82 tptp.sk3)))) :rule contraction :premises (t143))
% 76.72/76.97 (step t145 (cl (not (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U)))) (tptp.ssList (tptp.skaf82 tptp.sk3))) :rule implies :premises (t144))
% 76.72/76.97 (step t146 (cl (tptp.ssList (tptp.skaf82 tptp.sk3))) :rule resolution :premises (t145 a12))
% 76.72/76.97 (step t147 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V)))))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t148)
% 76.72/76.97 (assume t148.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V))))))
% 76.72/76.97 (step t148.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))))) :rule forall_inst :args ((:= U (tptp.skaf83 tptp.sk3)) (:= V (tptp.skaf82 tptp.sk3))))
% 76.72/76.97 (step t148.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) :rule or :premises (t148.t1))
% 76.72/76.97 (step t148.t3 (cl (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) :rule resolution :premises (t148.t2 t148.a0))
% 76.72/76.97 (step t148 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) :rule subproof :discharge (t148.a0))
% 76.72/76.97 (step t149 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) :rule resolution :premises (t147 t148))
% 76.72/76.97 (step t150 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (not (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))))) :rule implies_neg2)
% 76.72/76.97 (step t151 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))))) :rule resolution :premises (t149 t150))
% 76.72/76.97 (step t152 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))))) :rule contraction :premises (t151))
% 76.72/76.97 (step t153 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V)))))) (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) :rule implies :premises (t152))
% 76.72/76.97 (step t154 (cl (not (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.hd (tptp.cons U V)) U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V))))))) (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.hd (tptp.cons U V)) U)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V)))))) :rule equiv_pos2)
% 76.72/76.97 (anchor :step t155 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 76.72/76.97 (step t155.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t155.t2 (cl (= V V)) :rule refl)
% 76.72/76.97 (step t155.t3 (cl (= (not (tptp.ssItem U)) (not (tptp.ssItem U)))) :rule refl)
% 76.72/76.97 (step t155.t4 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 76.72/76.97 (step t155.t5 (cl (= (= (tptp.hd (tptp.cons U V)) U) (= U (tptp.hd (tptp.cons U V))))) :rule all_simplify)
% 76.72/76.97 (step t155.t6 (cl (= (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.hd (tptp.cons U V)) U)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V)))))) :rule cong :premises (t155.t3 t155.t4 t155.t5))
% 76.72/76.97 (step t155 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.hd (tptp.cons U V)) U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V))))))) :rule bind)
% 76.72/76.97 (step t156 (cl (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= U (tptp.hd (tptp.cons U V)))))) :rule resolution :premises (t154 t155 a96))
% 76.72/76.97 (step t157 (cl (or (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)))))) :rule resolution :premises (t153 t156))
% 76.72/76.97 (step t158 (cl (= (tptp.skaf83 tptp.sk3) (tptp.hd (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3))))) :rule resolution :premises (t130 t138 t146 t157))
% 76.72/76.97 (step t159 (cl (not (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) :rule or_pos)
% 76.72/76.97 (step t160 (cl (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)) (not (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))))) :rule reordering :premises (t159))
% 76.72/76.97 (step t161 (cl (=> (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t162)
% 76.72/76.97 (assume t162.a0 (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))))
% 76.72/76.97 (step t162.t1 (cl (or (not (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))))) :rule forall_inst :args ((:= V (tptp.skaf83 tptp.sk3)) (:= W (tptp.skaf82 tptp.sk3))))
% 76.72/76.97 (step t162.t2 (cl (not (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule or :premises (t162.t1))
% 76.72/76.97 (step t162.t3 (cl (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule resolution :premises (t162.t2 t162.a0))
% 76.72/76.97 (step t162 (cl (not (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule subproof :discharge (t162.a0))
% 76.72/76.97 (step t163 (cl (=> (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule resolution :premises (t161 t162))
% 76.72/76.97 (step t164 (cl (=> (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (not (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))))) :rule implies_neg2)
% 76.72/76.97 (step t165 (cl (=> (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) (=> (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))))) :rule resolution :premises (t163 t164))
% 76.72/76.97 (step t166 (cl (=> (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))))) :rule contraction :premises (t165))
% 76.72/76.97 (step t167 (cl (not (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule implies :premises (t166))
% 76.72/76.97 (step t168 (cl (not (= (forall ((U $$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))) (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))))) (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= U V)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.memberP (tptp.cons V W) U)))) (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) :rule equiv_pos2)
% 76.72/76.97 (step t169 (cl (= (forall ((U $$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))) (forall ((V $$unsorted) (W $$unsorted)) (or (not (= V V)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))))) :rule all_simplify)
% 76.72/76.97 (anchor :step t170 :args ((V $$unsorted) (:= V V) (W $$unsorted) (:= W W)))
% 76.72/76.97 (step t170.t1 (cl (= V V)) :rule refl)
% 76.72/76.97 (step t170.t2 (cl (= W W)) :rule refl)
% 76.72/76.97 (step t170.t3 (cl (= (= V V) true)) :rule all_simplify)
% 76.72/76.97 (step t170.t4 (cl (= (not (= V V)) (not true))) :rule cong :premises (t170.t3))
% 76.72/76.97 (step t170.t5 (cl (= (not true) false)) :rule all_simplify)
% 76.72/76.97 (step t170.t6 (cl (= (not (= V V)) false)) :rule trans :premises (t170.t4 t170.t5))
% 76.72/76.97 (step t170.t7 (cl (= (not (tptp.ssList W)) (not (tptp.ssList W)))) :rule refl)
% 76.72/76.97 (step t170.t8 (cl (= (not (tptp.ssItem V)) (not (tptp.ssItem V)))) :rule refl)
% 76.72/76.97 (step t170.t9 (cl (= (tptp.memberP (tptp.cons V W) V) (tptp.memberP (tptp.cons V W) V))) :rule refl)
% 76.72/76.97 (step t170.t10 (cl (= (or (not (= V V)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)) (or false (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) :rule cong :premises (t170.t6 t170.t7 t170.t8 t170.t8 t170.t9))
% 76.72/76.97 (step t170.t11 (cl (= (or false (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) :rule all_simplify)
% 76.72/76.97 (step t170.t12 (cl (= (or (not (= V V)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) :rule trans :premises (t170.t10 t170.t11))
% 76.72/76.97 (step t170 (cl (= (forall ((V $$unsorted) (W $$unsorted)) (or (not (= V V)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))) (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))))) :rule bind)
% 76.72/76.97 (step t171 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= U V)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.memberP (tptp.cons V W) U))) (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V))))) :rule trans :premises (t169 t170))
% 76.72/76.97 (step t172 (cl (forall ((V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons V W) V)))) :rule resolution :premises (t168 t171 a137))
% 76.72/76.97 (step t173 (cl (or (not (tptp.ssList (tptp.skaf82 tptp.sk3))) (not (tptp.ssItem (tptp.skaf83 tptp.sk3))) (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3)))) :rule resolution :premises (t167 t172))
% 76.72/76.97 (step t174 (cl (tptp.memberP (tptp.cons (tptp.skaf83 tptp.sk3) (tptp.skaf82 tptp.sk3)) (tptp.skaf83 tptp.sk3))) :rule resolution :premises (t160 t138 t146 t173))
% 76.72/76.97 (step t175 (cl (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) :rule resolution :premises (t92 t110 t128 t158 t174))
% 76.72/76.97 (step t176 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A))))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t177)
% 76.72/76.97 (assume t177.a0 (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A)))))
% 76.72/76.97 (step t177.t1 (cl (or (not (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule forall_inst :args ((:= A (tptp.hd tptp.sk3))))
% 76.72/76.97 (step t177.t2 (cl (not (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule or :premises (t177.t1))
% 76.72/76.97 (step t177.t3 (cl (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule resolution :premises (t177.t2 t177.a0))
% 76.72/76.97 (step t177 (cl (not (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule subproof :discharge (t177.a0))
% 76.72/76.97 (step t178 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule resolution :premises (t176 t177))
% 76.72/76.97 (step t179 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (not (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule implies_neg2)
% 76.72/76.97 (step t180 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule resolution :premises (t178 t179))
% 76.72/76.97 (step t181 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule contraction :premises (t180))
% 76.72/76.97 (step t182 (cl (not (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.ssList (tptp.sk5 A)) (not (tptp.memberP tptp.sk3 A))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule implies :premises (t181))
% 76.72/76.97 (step t183 (cl (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule resolution :premises (t182 a194))
% 76.72/76.97 (step t184 (cl (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) :rule resolution :premises (t75 t35 t175 t183))
% 76.72/76.97 (step t185 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t186)
% 76.72/76.97 (assume t186.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))))
% 76.72/76.97 (step t186.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))))) :rule forall_inst :args ((:= U (tptp.sk5 (tptp.hd tptp.sk3))) (:= V (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))
% 76.72/76.97 (step t186.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) :rule or :premises (t186.t1))
% 76.72/76.97 (step t186.t3 (cl (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) :rule resolution :premises (t186.t2 t186.a0))
% 76.72/76.97 (step t186 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) :rule subproof :discharge (t186.a0))
% 76.72/76.97 (step t187 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) :rule resolution :premises (t185 t186))
% 76.72/76.97 (step t188 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) (not (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))))) :rule implies_neg2)
% 76.72/76.97 (step t189 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))))) :rule resolution :premises (t187 t188))
% 76.72/76.97 (step t190 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))))) :rule contraction :premises (t189))
% 76.72/76.97 (step t191 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) :rule implies :premises (t190))
% 76.72/76.97 (step t192 (cl (or (not (tptp.ssList (tptp.sk5 (tptp.hd tptp.sk3)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))))) :rule resolution :premises (t191 a84))
% 76.72/76.97 (step t193 (cl (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) :rule resolution :premises (t73 t44 t184 t192))
% 76.72/76.97 (step t194 (cl (not (= (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) (not (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule equiv_pos2)
% 76.72/76.97 (step t195 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))))) :rule refl)
% 76.72/76.97 (step t196 (cl (= (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule all_simplify)
% 76.72/76.97 (step t197 (cl (= (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule cong :premises (t196))
% 76.72/76.97 (step t198 (cl (= (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule refl)
% 76.72/76.97 (step t199 (cl (= (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))))) :rule refl)
% 76.72/76.97 (step t200 (cl (= (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)) (or (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule cong :premises (t197 t198 t199 t49))
% 76.72/76.97 (step t201 (cl (= (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule cong :premises (t195 t200))
% 76.72/76.97 (step t202 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4)))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t203)
% 76.72/76.97 (assume t203.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))))
% 76.72/76.97 (step t203.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4)))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)))) :rule forall_inst :args ((:= U (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3)))) (:= V (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))
% 76.72/76.97 (step t203.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4)))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) :rule or :premises (t203.t1))
% 76.72/76.97 (step t203.t3 (cl (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) :rule resolution :premises (t203.t2 t203.a0))
% 76.72/76.97 (step t203 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4)))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) :rule subproof :discharge (t203.a0))
% 76.72/76.97 (step t204 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) :rule resolution :premises (t202 t203))
% 76.72/76.97 (step t205 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) (not (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)))) :rule implies_neg2)
% 76.72/76.97 (step t206 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)))) :rule resolution :premises (t204 t205))
% 76.72/76.97 (step t207 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) tptp.sk4)))) :rule contraction :premises (t206))
% 76.72/76.97 (step t208 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))) (or (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule resolution :premises (t194 t201 t207))
% 76.72/76.97 (step t209 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4)))) (or (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule implies :premises (t208))
% 76.72/76.97 (step t210 (cl (not (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))))) (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4)))) :rule equiv_pos2)
% 76.72/76.97 (anchor :step t211 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 76.72/76.97 (step t211.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t211.t2 (cl (= V V)) :rule refl)
% 76.72/76.97 (step t211.t3 (cl (= (= (tptp.app U V) tptp.nil) (= tptp.nil (tptp.app U V)))) :rule all_simplify)
% 76.72/76.97 (step t211.t4 (cl (= (not (= (tptp.app U V) tptp.nil)) (not (= tptp.nil (tptp.app U V))))) :rule cong :premises (t211.t3))
% 76.72/76.97 (step t211.t5 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 76.72/76.97 (step t211.t6 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t211.t7 (cl (= (= tptp.nil V) (= tptp.nil V))) :rule refl)
% 76.72/76.97 (step t211.t8 (cl (= (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V)))) :rule cong :premises (t211.t4 t211.t5 t211.t6 t211.t7))
% 76.72/76.97 (step t211 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))))) :rule bind)
% 76.72/76.97 (anchor :step t212 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 76.72/76.97 (step t212.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t212.t2 (cl (= V V)) :rule refl)
% 76.72/76.97 (step t212.t3 (cl (= tptp.nil tptp.sk2)) :rule and :premises (t11))
% 76.72/76.97 (step t212.t4 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t11))
% 76.72/76.97 (step t212.t5 (cl (= tptp.nil tptp.sk4)) :rule trans :premises (t212.t3 t212.t4))
% 76.72/76.97 (step t212.t6 (cl (= (tptp.app U V) (tptp.app U V))) :rule refl)
% 76.72/76.97 (step t212.t7 (cl (= (= tptp.nil (tptp.app U V)) (= tptp.sk4 (tptp.app U V)))) :rule cong :premises (t212.t5 t212.t6))
% 76.72/76.97 (step t212.t8 (cl (= (not (= tptp.nil (tptp.app U V))) (not (= tptp.sk4 (tptp.app U V))))) :rule cong :premises (t212.t7))
% 76.72/76.97 (step t212.t9 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 76.72/76.97 (step t212.t10 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t212.t11 (cl (= V V)) :rule refl)
% 76.72/76.97 (step t212.t12 (cl (= (= tptp.nil V) (= tptp.sk4 V))) :rule cong :premises (t212.t5 t212.t11))
% 76.72/76.97 (step t212.t13 (cl (= (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V)) (or (not (= tptp.sk4 (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.sk4 V)))) :rule cong :premises (t212.t8 t212.t9 t212.t10 t212.t12))
% 76.72/76.97 (step t212 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.sk4 (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.sk4 V))))) :rule bind)
% 76.72/76.97 (anchor :step t213 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V)))
% 76.72/76.97 (step t213.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t213.t2 (cl (= V V)) :rule refl)
% 76.72/76.97 (step t213.t3 (cl (= (= tptp.sk4 (tptp.app U V)) (= (tptp.app U V) tptp.sk4))) :rule all_simplify)
% 76.72/76.97 (step t213.t4 (cl (= (not (= tptp.sk4 (tptp.app U V))) (not (= (tptp.app U V) tptp.sk4)))) :rule cong :premises (t213.t3))
% 76.72/76.97 (step t213.t5 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 76.72/76.97 (step t213.t6 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t213.t7 (cl (= (= tptp.sk4 V) (= V tptp.sk4))) :rule all_simplify)
% 76.72/76.97 (step t213.t8 (cl (= (or (not (= tptp.sk4 (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.sk4 V)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4)))) :rule cong :premises (t213.t4 t213.t5 t213.t6 t213.t7))
% 76.72/76.97 (step t213 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.sk4 (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.sk4 V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))))) :rule bind)
% 76.72/76.97 (step t214 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))))) :rule trans :premises (t212 t213))
% 76.72/76.97 (step t215 (cl (= (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4))))) :rule trans :premises (t211 t214))
% 76.72/76.97 (step t216 (cl (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.sk4)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= V tptp.sk4)))) :rule resolution :premises (t210 t215 a118))
% 76.72/76.97 (step t217 (cl (or (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (= tptp.sk4 (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule resolution :premises (t209 t216))
% 76.72/76.97 (step t218 (cl (not (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule resolution :premises (t4 t44 t71 t193 t217))
% 76.72/76.97 (step t219 (cl (not (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule or_pos)
% 76.72/76.97 (step t220 (cl (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (not (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule reordering :premises (t219))
% 76.72/76.97 (step t221 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t222)
% 76.72/76.97 (assume t222.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))))
% 76.72/76.97 (step t222.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule forall_inst :args ((:= U (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) (:= V (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))))
% 76.72/76.97 (step t222.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule or :premises (t222.t1))
% 76.72/76.97 (step t222.t3 (cl (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule resolution :premises (t222.t2 t222.a0))
% 76.72/76.97 (step t222 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule subproof :discharge (t222.a0))
% 76.72/76.97 (step t223 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule resolution :premises (t221 t222))
% 76.72/76.97 (step t224 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) (not (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule implies_neg2)
% 76.72/76.97 (step t225 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule resolution :premises (t223 t224))
% 76.72/76.97 (step t226 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule contraction :premises (t225))
% 76.72/76.97 (step t227 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U))))) (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule implies :premises (t226))
% 76.72/76.97 (step t228 (cl (or (not (tptp.ssList (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.ssList (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))))) (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule resolution :premises (t227 a84))
% 76.72/76.97 (step t229 (cl (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule resolution :premises (t220 t44 t193 t228))
% 76.72/76.97 (step t230 (cl (not (= (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))))) (not (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)))) (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule equiv_pos2)
% 76.72/76.97 (step t231 (cl (= (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))))) :rule refl)
% 76.72/76.97 (step t232 (cl (= (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule refl)
% 76.72/76.97 (step t233 (cl (= (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule refl)
% 76.72/76.97 (step t234 (cl (= (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule cong :premises (t232 t233 t196))
% 76.72/76.97 (step t235 (cl (= (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))))) :rule cong :premises (t231 t234))
% 76.72/76.97 (step t236 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4)))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t237)
% 76.72/76.97 (assume t237.a0 (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))))
% 76.72/76.97 (step t237.t1 (cl (or (not (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4)))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)))) :rule forall_inst :args ((:= U (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))
% 76.72/76.97 (step t237.t2 (cl (not (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4)))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) :rule or :premises (t237.t1))
% 76.72/76.97 (step t237.t3 (cl (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) :rule resolution :premises (t237.t2 t237.a0))
% 76.72/76.97 (step t237 (cl (not (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4)))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) :rule subproof :discharge (t237.a0))
% 76.72/76.97 (step t238 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) :rule resolution :premises (t236 t237))
% 76.72/76.97 (step t239 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) (not (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)))) :rule implies_neg2)
% 76.72/76.97 (step t240 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4))) (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)))) :rule resolution :premises (t238 t239))
% 76.72/76.97 (step t241 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)) tptp.sk4)))) :rule contraction :premises (t240))
% 76.72/76.97 (step t242 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))))) :rule resolution :premises (t230 t235 t241))
% 76.72/76.97 (step t243 (cl (not (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4)))) (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule implies :premises (t242))
% 76.72/76.97 (step t244 (cl (not (= (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))))) (not (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U)))) (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4)))) :rule equiv_pos2)
% 76.72/76.97 (anchor :step t245 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t245.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t245.t2 (cl (= tptp.nil tptp.sk2)) :rule and :premises (t11))
% 76.72/76.97 (step t245.t3 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t11))
% 76.72/76.97 (step t245.t4 (cl (= tptp.nil tptp.sk4)) :rule trans :premises (t245.t2 t245.t3))
% 76.72/76.97 (step t245.t5 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t245.t6 (cl (= (tptp.segmentP tptp.nil U) (tptp.segmentP tptp.sk4 U))) :rule cong :premises (t245.t4 t245.t5))
% 76.72/76.97 (step t245.t7 (cl (= (not (tptp.segmentP tptp.nil U)) (not (tptp.segmentP tptp.sk4 U)))) :rule cong :premises (t245.t6))
% 76.72/76.97 (step t245.t8 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t245.t9 (cl (= (= tptp.nil U) (= tptp.sk4 U))) :rule cong :premises (t245.t4 t245.t5))
% 76.72/76.97 (step t245.t10 (cl (= (or (not (tptp.segmentP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= tptp.sk4 U)))) :rule cong :premises (t245.t7 t245.t8 t245.t9))
% 76.72/76.97 (step t245 (cl (= (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= tptp.sk4 U))))) :rule bind)
% 76.72/76.97 (anchor :step t246 :args ((U $$unsorted) (:= U U)))
% 76.72/76.97 (step t246.t1 (cl (= U U)) :rule refl)
% 76.72/76.97 (step t246.t2 (cl (= (not (tptp.segmentP tptp.sk4 U)) (not (tptp.segmentP tptp.sk4 U)))) :rule refl)
% 76.72/76.97 (step t246.t3 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 76.72/76.97 (step t246.t4 (cl (= (= tptp.sk4 U) (= U tptp.sk4))) :rule all_simplify)
% 76.72/76.97 (step t246.t5 (cl (= (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= tptp.sk4 U)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4)))) :rule cong :premises (t246.t2 t246.t3 t246.t4))
% 76.72/76.97 (step t246 (cl (= (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= tptp.sk4 U))) (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))))) :rule bind)
% 76.72/76.97 (step t247 (cl (= (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))) (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4))))) :rule trans :premises (t245 t246))
% 76.72/76.97 (step t248 (cl (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.sk4 U)) (not (tptp.ssList U)) (= U tptp.sk4)))) :rule resolution :premises (t244 t247 a79))
% 76.72/76.97 (step t249 (cl (or (not (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (not (tptp.ssList (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) (= tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))))) :rule resolution :premises (t243 t248))
% 76.72/76.97 (step t250 (cl (not (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))) :rule or_pos)
% 76.72/76.97 (step t251 (cl (not (tptp.ssItem (tptp.hd tptp.sk3))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule reordering :premises (t250))
% 76.72/76.97 (step t252 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A))))) :rule implies_neg1)
% 76.72/76.97 (anchor :step t253)
% 76.72/76.97 (assume t253.a0 (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A)))))
% 76.72/76.97 (step t253.t1 (cl (or (not (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule forall_inst :args ((:= A (tptp.hd tptp.sk3))))
% 76.72/76.97 (step t253.t2 (cl (not (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule or :premises (t253.t1))
% 76.72/76.97 (step t253.t3 (cl (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule resolution :premises (t253.t2 t253.a0))
% 76.72/76.97 (step t253 (cl (not (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule subproof :discharge (t253.a0))
% 76.72/76.97 (step t254 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule resolution :premises (t252 t253))
% 76.72/76.97 (step t255 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (not (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule implies_neg2)
% 76.72/76.97 (step t256 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule resolution :premises (t254 t255))
% 76.72/76.97 (step t257 (cl (=> (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A)))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3)))))) :rule contraction :premises (t256))
% 76.72/76.97 (step t258 (cl (not (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A))))) (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule implies :premises (t257))
% 76.72/76.97 (step t259 (cl (not (= (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.nil) (tptp.sk5 A)) (tptp.cons A tptp.nil))) (not (tptp.memberP tptp.sk3 A)))) (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A)))))) (not (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.nil) (tptp.sk5 A)) (tptp.cons A tptp.nil))) (not (tptp.memberP tptp.sk3 A))))) (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A))))) :rule equiv_pos2)
% 76.72/76.97 (anchor :step t260 :args ((A $$unsorted) (:= A A)))
% 76.72/76.97 (step t260.t1 (cl (= A A)) :rule refl)
% 76.72/76.97 (step t260.t2 (cl (= (not (tptp.ssItem A)) (not (tptp.ssItem A)))) :rule refl)
% 76.72/76.97 (step t260.t3 (cl (= tptp.sk4 tptp.sk4)) :rule refl)
% 76.72/76.97 (step t260.t4 (cl (= A A)) :rule refl)
% 76.72/76.97 (step t260.t5 (cl (= tptp.nil tptp.sk2)) :rule and :premises (t11))
% 76.72/76.97 (step t260.t6 (cl (= tptp.sk2 tptp.sk4)) :rule and :premises (t11))
% 76.72/76.97 (step t260.t7 (cl (= tptp.nil tptp.sk4)) :rule trans :premises (t260.t5 t260.t6))
% 76.72/76.97 (step t260.t8 (cl (= (tptp.cons A tptp.nil) (tptp.cons A tptp.sk4))) :rule cong :premises (t260.t4 t260.t7))
% 76.72/76.97 (step t260.t9 (cl (= (tptp.sk5 A) (tptp.sk5 A))) :rule refl)
% 76.72/76.97 (step t260.t10 (cl (= (tptp.app (tptp.cons A tptp.nil) (tptp.sk5 A)) (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)))) :rule cong :premises (t260.t8 t260.t9))
% 76.72/76.97 (step t260.t11 (cl (= (tptp.app (tptp.app (tptp.cons A tptp.nil) (tptp.sk5 A)) (tptp.cons A tptp.nil)) (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4)))) :rule cong :premises (t260.t10 t260.t8))
% 76.72/76.97 (step t260.t12 (cl (= (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.nil) (tptp.sk5 A)) (tptp.cons A tptp.nil))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))))) :rule cong :premises (t260.t3 t260.t11))
% 76.72/76.97 (step t260.t13 (cl (= (not (tptp.memberP tptp.sk3 A)) (not (tptp.memberP tptp.sk3 A)))) :rule refl)
% 76.72/76.97 (step t260.t14 (cl (= (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.nil) (tptp.sk5 A)) (tptp.cons A tptp.nil))) (not (tptp.memberP tptp.sk3 A))) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A))))) :rule cong :premises (t260.t2 t260.t12 t260.t13))
% 76.72/76.97 (step t260 (cl (= (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.nil) (tptp.sk5 A)) (tptp.cons A tptp.nil))) (not (tptp.memberP tptp.sk3 A)))) (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A)))))) :rule bind)
% 76.72/76.97 (step t261 (cl (forall ((A $$unsorted)) (or (not (tptp.ssItem A)) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons A tptp.sk4) (tptp.sk5 A)) (tptp.cons A tptp.sk4))) (not (tptp.memberP tptp.sk3 A))))) :rule resolution :premises (t259 t260 a195))
% 76.72/76.97 (step t262 (cl (or (not (tptp.ssItem (tptp.hd tptp.sk3))) (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4))) (not (tptp.memberP tptp.sk3 (tptp.hd tptp.sk3))))) :rule resolution :premises (t258 t261))
% 76.72/76.97 (step t263 (cl (tptp.segmentP tptp.sk4 (tptp.app (tptp.app (tptp.cons (tptp.hd tptp.sk3) tptp.sk4) (tptp.sk5 (tptp.hd tptp.sk3))) (tptp.cons (tptp.hd tptp.sk3) tptp.sk4)))) :rule resolution :premises (t251 t35 t175 t262))
% 76.72/76.97 (step t264 (cl) :rule resolution :premises (t2 t218 t229 t249 t263))
% 76.72/76.97
% 76.72/76.98 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.KFFxBuJ92E/cvc5---1.0.5_23609.smt2
% 76.72/76.98 % cvc5---1.0.5 exiting
% 76.72/76.98 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------