TSTP Solution File: SWC355-1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC355-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 18:01:41 EDT 2024
% Result : Unsatisfiable 0.37s 0.88s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWC355-1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 26 15:03:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.37/0.53 %----Proving TF0_NAR, FOF, or CNF
% 0.37/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.37/0.88 % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.jbNoZnJxgB/cvc5---1.0.5_4304.smt2
% 0.37/0.88 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.jbNoZnJxgB/cvc5---1.0.5_4304.smt2
% 0.37/0.90 (assume a0 (tptp.equalelemsP tptp.nil))
% 0.37/0.90 (assume a1 (tptp.duplicatefreeP tptp.nil))
% 0.37/0.90 (assume a2 (tptp.strictorderedP tptp.nil))
% 0.37/0.90 (assume a3 (tptp.totalorderedP tptp.nil))
% 0.37/0.90 (assume a4 (tptp.strictorderP tptp.nil))
% 0.37/0.90 (assume a5 (tptp.totalorderP tptp.nil))
% 0.37/0.90 (assume a6 (tptp.cyclefreeP tptp.nil))
% 0.37/0.90 (assume a7 (tptp.ssList tptp.nil))
% 0.37/0.90 (assume a8 (tptp.ssItem tptp.skac3))
% 0.37/0.90 (assume a9 (tptp.ssItem tptp.skac2))
% 0.37/0.90 (assume a10 (not (tptp.singletonP tptp.nil)))
% 0.37/0.90 (assume a11 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf83 U))))
% 0.37/0.90 (assume a12 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf82 U))))
% 0.37/0.90 (assume a13 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf81 U))))
% 0.37/0.90 (assume a14 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf80 U))))
% 0.37/0.90 (assume a15 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf79 U))))
% 0.37/0.90 (assume a16 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf78 U))))
% 0.37/0.90 (assume a17 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf77 U))))
% 0.37/0.90 (assume a18 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf76 U))))
% 0.37/0.90 (assume a19 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf75 U))))
% 0.37/0.90 (assume a20 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf74 U))))
% 0.37/0.90 (assume a21 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf73 U))))
% 0.37/0.90 (assume a22 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf72 U))))
% 0.37/0.90 (assume a23 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf71 U))))
% 0.37/0.90 (assume a24 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf70 U))))
% 0.37/0.90 (assume a25 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf69 U))))
% 0.37/0.90 (assume a26 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf68 U))))
% 0.37/0.90 (assume a27 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf67 U))))
% 0.37/0.90 (assume a28 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf66 U))))
% 0.37/0.90 (assume a29 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf65 U))))
% 0.37/0.90 (assume a30 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf64 U))))
% 0.37/0.90 (assume a31 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf63 U))))
% 0.37/0.90 (assume a32 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf62 U))))
% 0.37/0.90 (assume a33 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf61 U))))
% 0.37/0.90 (assume a34 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf60 U))))
% 0.37/0.90 (assume a35 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf59 U))))
% 0.37/0.90 (assume a36 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf58 U))))
% 0.37/0.90 (assume a37 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf57 U))))
% 0.37/0.90 (assume a38 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf56 U))))
% 0.37/0.90 (assume a39 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf55 U))))
% 0.37/0.90 (assume a40 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf54 U))))
% 0.37/0.90 (assume a41 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf53 U))))
% 0.37/0.90 (assume a42 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf52 U))))
% 0.37/0.90 (assume a43 (forall ((U $$unsorted)) (tptp.ssList (tptp.skaf51 U))))
% 0.37/0.90 (assume a44 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf50 U))))
% 0.37/0.90 (assume a45 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf49 U))))
% 0.37/0.90 (assume a46 (forall ((U $$unsorted)) (tptp.ssItem (tptp.skaf44 U))))
% 0.37/0.90 (assume a47 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf48 U V))))
% 0.37/0.90 (assume a48 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf47 U V))))
% 0.37/0.90 (assume a49 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf46 U V))))
% 0.37/0.90 (assume a50 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf45 U V))))
% 0.37/0.90 (assume a51 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf43 U V))))
% 0.37/0.90 (assume a52 (forall ((U $$unsorted) (V $$unsorted)) (tptp.ssList (tptp.skaf42 U V))))
% 0.37/0.90 (assume a53 (not (= tptp.skac3 tptp.skac2)))
% 0.37/0.90 (assume a54 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.geq U U))))
% 0.37/0.90 (assume a55 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U tptp.nil))))
% 0.37/0.90 (assume a56 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))
% 0.37/0.90 (assume a57 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.rearsegP U tptp.nil))))
% 0.37/0.90 (assume a58 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.rearsegP U U))))
% 0.37/0.90 (assume a59 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U tptp.nil))))
% 0.37/0.90 (assume a60 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U U))))
% 0.37/0.90 (assume a61 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.leq U U))))
% 0.37/0.90 (assume a62 (forall ((U $$unsorted)) (or (not (tptp.lt U U)) (not (tptp.ssItem U)))))
% 0.37/0.90 (assume a63 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.equalelemsP (tptp.cons U tptp.nil)))))
% 0.37/0.90 (assume a64 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))))
% 0.37/0.90 (assume a65 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U tptp.nil)))))
% 0.37/0.90 (assume a66 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U tptp.nil)))))
% 0.37/0.90 (assume a67 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.strictorderP (tptp.cons U tptp.nil)))))
% 0.37/0.90 (assume a68 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.totalorderP (tptp.cons U tptp.nil)))))
% 0.37/0.90 (assume a69 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.cyclefreeP (tptp.cons U tptp.nil)))))
% 0.37/0.90 (assume a70 (forall ((U $$unsorted)) (or (not (tptp.memberP tptp.nil U)) (not (tptp.ssItem U)))))
% 0.37/0.90 (assume a71 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (tptp.duplicatefreeP U) (tptp.ssItem V))))
% 0.37/0.90 (assume a72 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app U tptp.nil) U))))
% 0.37/0.90 (assume a73 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U))))
% 0.37/0.90 (assume a74 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssList (tptp.tl U)) (= tptp.nil U))))
% 0.37/0.90 (assume a75 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))))
% 0.37/0.90 (assume a76 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssList (tptp.tl U)) (= tptp.nil U))))
% 0.37/0.90 (assume a77 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.ssItem (tptp.hd U)) (= tptp.nil U))))
% 0.37/0.90 (assume a78 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.segmentP tptp.nil U))))
% 0.37/0.90 (assume a79 (forall ((U $$unsorted)) (or (not (tptp.segmentP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 0.37/0.90 (assume a80 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.rearsegP tptp.nil U))))
% 0.37/0.90 (assume a81 (forall ((U $$unsorted)) (or (not (tptp.rearsegP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 0.37/0.90 (assume a82 (forall ((U $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (tptp.frontsegP tptp.nil U))))
% 0.37/0.90 (assume a83 (forall ((U $$unsorted)) (or (not (tptp.frontsegP tptp.nil U)) (not (tptp.ssList U)) (= tptp.nil U))))
% 0.37/0.90 (assume a84 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.ssList (tptp.app V U)))))
% 0.37/0.90 (assume a85 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))))
% 0.37/0.90 (assume a86 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (tptp.leq (tptp.skaf50 U) (tptp.skaf49 U)))))
% 0.37/0.90 (assume a87 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (tptp.leq (tptp.skaf49 U) (tptp.skaf50 U)))))
% 0.37/0.90 (assume a88 (forall ((U $$unsorted)) (or (not (= (tptp.skaf79 U) (tptp.skaf78 U))) (not (tptp.ssList U)) (tptp.equalelemsP U))))
% 0.37/0.90 (assume a89 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf69 U) (tptp.skaf70 U))) (not (tptp.ssList U)) (tptp.strictorderedP U))))
% 0.37/0.90 (assume a90 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf64 U) (tptp.skaf65 U))) (not (tptp.ssList U)) (tptp.totalorderedP U))))
% 0.37/0.90 (assume a91 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf60 U) (tptp.skaf59 U))) (not (tptp.ssList U)) (tptp.strictorderP U))))
% 0.37/0.90 (assume a92 (forall ((U $$unsorted)) (or (not (tptp.lt (tptp.skaf59 U) (tptp.skaf60 U))) (not (tptp.ssList U)) (tptp.strictorderP U))))
% 0.37/0.90 (assume a93 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf55 U) (tptp.skaf54 U))) (not (tptp.ssList U)) (tptp.totalorderP U))))
% 0.37/0.90 (assume a94 (forall ((U $$unsorted)) (or (not (tptp.leq (tptp.skaf54 U) (tptp.skaf55 U))) (not (tptp.ssList U)) (tptp.totalorderP U))))
% 0.37/0.90 (assume a95 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.tl (tptp.cons U V)) V))))
% 0.37/0.90 (assume a96 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.hd (tptp.cons U V)) U))))
% 0.37/0.90 (assume a97 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))
% 0.37/0.90 (assume a98 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) V)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))
% 0.37/0.90 (assume a99 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= V U))))
% 0.37/0.90 (assume a100 (forall ((U $$unsorted)) (or (not (tptp.singletonP U)) (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf44 U) tptp.nil) U))))
% 0.37/0.90 (assume a101 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem V)) (tptp.neq V U) (= V U))))
% 0.37/0.90 (assume a102 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq U V))))
% 0.37/0.90 (assume a103 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U) (= tptp.nil U))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (assume a108 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cons (tptp.skaf83 U) (tptp.skaf82 U)) U) (= tptp.nil U))))
% 0.37/0.90 (assume a109 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.gt V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)))))
% 0.37/0.90 (assume a110 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.lt U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)))))
% 0.37/0.90 (assume a111 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.strictorderedP (tptp.cons V U)))))
% 0.37/0.90 (assume a112 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.totalorderedP (tptp.cons V U)))))
% 0.37/0.90 (assume a113 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.lt V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)))))
% 0.37/0.90 (assume a114 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssList V)) (not (tptp.ssList U)))))
% 0.37/0.90 (assume a115 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U tptp.nil) V)) (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.singletonP V))))
% 0.37/0.90 (assume a116 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (not (tptp.neq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)))))
% 0.37/0.90 (assume a117 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))))
% 0.37/0.90 (assume a118 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))))
% 0.37/0.90 (assume a119 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))))
% 0.37/0.90 (assume a120 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))))
% 0.37/0.90 (assume a121 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))))
% 0.37/0.90 (assume a122 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.hd (tptp.app V U)) (tptp.hd V)))))
% 0.37/0.90 (assume a123 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP V) (= tptp.nil V))))
% 0.37/0.90 (assume a124 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP V) (= tptp.nil V))))
% 0.37/0.90 (assume a125 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))))
% 0.37/0.90 (assume a126 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 0.37/0.90 (assume a127 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.rearsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 0.37/0.90 (assume a128 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))))
% 0.37/0.90 (assume a129 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))))
% 0.37/0.90 (assume a130 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app (tptp.skaf46 U V) V) U))))
% 0.37/0.90 (assume a131 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app V (tptp.skaf45 U V)) U))))
% 0.37/0.90 (assume a132 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.tl (tptp.app V U)) (tptp.app (tptp.tl V) U)))))
% 0.37/0.90 (assume a133 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.lt U (tptp.hd V)) (= tptp.nil V))))
% 0.37/0.90 (assume a134 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.leq U (tptp.hd V)) (= tptp.nil V))))
% 0.37/0.90 (assume a135 (forall ((U $$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))))
% 0.37/0.90 (assume a136 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP (tptp.app U W) V))))
% 0.37/0.90 (assume a137 (forall ((U $$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))))
% 0.37/0.90 (assume a138 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons W U) V))))
% 0.37/0.90 (assume a139 (forall ((U $$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))))
% 0.37/0.90 (assume a140 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.app W U) V))))
% 0.37/0.90 (assume a141 (forall ((U $$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))))
% 0.37/0.90 (assume a142 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (tptp.rearsegP W V))))
% 0.37/0.90 (assume a143 (forall ((U $$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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (assume a145 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.gt V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.gt U W))))
% 0.37/0.90 (assume a146 (forall ((U $$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))))
% 0.37/0.90 (assume a147 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.geq U W))))
% 0.37/0.90 (assume a148 (forall ((U $$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))))))
% 0.37/0.90 (assume a149 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) (tptp.app U W))) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (= V W))))
% 0.37/0.90 (assume a150 (forall ((U $$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))))
% 0.37/0.90 (assume a151 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.segmentP U W))))
% 0.37/0.90 (assume a152 (forall ((U $$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))))
% 0.37/0.90 (assume a153 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP U W))))
% 0.37/0.90 (assume a154 (forall ((U $$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))))
% 0.37/0.90 (assume a155 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq U W))))
% 0.37/0.90 (assume a156 (forall ((U $$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)))))
% 0.37/0.90 (assume a157 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP (tptp.app U V) W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (tptp.memberP V W) (tptp.memberP U W))))
% 0.37/0.90 (assume a158 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U (tptp.hd V))) (not (tptp.totalorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U V)) (= tptp.nil V))))
% 0.37/0.90 (assume a159 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U (tptp.hd V))) (not (tptp.strictorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U V)) (= tptp.nil V))))
% 0.37/0.90 (assume a160 (forall ((U $$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))))
% 0.37/0.90 (assume a161 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.duplicatefreeP U) (= (tptp.app (tptp.app (tptp.skaf75 U) (tptp.cons (tptp.skaf74 U) (tptp.skaf76 U))) (tptp.cons (tptp.skaf74 U) (tptp.skaf77 U))) U))))
% 0.37/0.90 (assume a162 (forall ((U $$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))))
% 0.37/0.90 (assume a163 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderedP U) (= (tptp.app (tptp.app (tptp.skaf66 U) (tptp.cons (tptp.skaf64 U) (tptp.skaf67 U))) (tptp.cons (tptp.skaf65 U) (tptp.skaf68 U))) U))))
% 0.37/0.90 (assume a164 (forall ((U $$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))))
% 0.37/0.90 (assume a165 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderP U) (= (tptp.app (tptp.app (tptp.skaf56 U) (tptp.cons (tptp.skaf54 U) (tptp.skaf57 U))) (tptp.cons (tptp.skaf55 U) (tptp.skaf58 U))) U))))
% 0.37/0.90 (assume a166 (forall ((U $$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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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)))))
% 0.37/0.90 (assume a178 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons V X)) Y)) (not (tptp.ssList X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (not (tptp.duplicatefreeP Y)) (not (tptp.ssList Y)))))
% 0.37/0.90 (assume a179 (forall ((U $$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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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))))
% 0.37/0.90 (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)))))
% 0.37/0.90 (assume a185 (tptp.ssList tptp.sk1))
% 0.37/0.90 (assume a186 (tptp.ssList tptp.sk2))
% 0.37/0.90 (assume a187 (tptp.ssList tptp.sk3))
% 0.37/0.90 (assume a188 (tptp.ssList tptp.sk4))
% 0.37/0.90 (assume a189 (= tptp.sk2 tptp.sk4))
% 0.37/0.90 (assume a190 (= tptp.sk1 tptp.sk3))
% 0.37/0.90 (assume a191 (or (tptp.neq tptp.sk2 tptp.nil) (tptp.neq tptp.sk2 tptp.nil)))
% 0.37/0.90 (assume a192 (or (tptp.neq tptp.sk2 tptp.nil) (not (tptp.neq tptp.sk4 tptp.nil))))
% 0.37/0.90 (assume a193 (or (tptp.ssItem tptp.sk5) (tptp.neq tptp.sk2 tptp.nil)))
% 0.37/0.90 (assume a194 (or (= (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)) tptp.sk4) (tptp.neq tptp.sk2 tptp.nil)))
% 0.37/0.90 (assume a195 (or (not (tptp.segmentP tptp.sk2 tptp.sk1)) (tptp.neq tptp.sk2 tptp.nil)))
% 0.37/0.90 (assume a196 (or (tptp.ssItem tptp.sk5) (not (tptp.neq tptp.sk4 tptp.nil))))
% 0.37/0.90 (assume a197 (or (= (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)) tptp.sk4) (not (tptp.neq tptp.sk4 tptp.nil))))
% 0.37/0.90 (assume a198 (or (not (tptp.segmentP tptp.sk2 tptp.sk1)) (not (tptp.neq tptp.sk4 tptp.nil))))
% 0.37/0.90 (step t1 (cl (not (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)) :rule or_pos)
% 0.37/0.90 (step t2 (cl (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1) (not (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule reordering :premises (t1))
% 0.37/0.90 (step t3 (cl (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.ssList tptp.sk2)) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule and_neg)
% 0.37/0.90 (step t4 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule implies_neg1)
% 0.37/0.90 (anchor :step t5)
% 0.37/0.90 (assume t5.a0 (tptp.ssList tptp.sk2))
% 0.37/0.90 (assume t5.a1 (= tptp.sk2 tptp.sk4))
% 0.37/0.90 (assume t5.a2 (= tptp.sk1 tptp.sk3))
% 0.37/0.90 (assume t5.a3 (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))))
% 0.37/0.90 (assume t5.a4 (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))
% 0.37/0.90 (step t5.t1 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule implies_neg1)
% 0.37/0.90 (anchor :step t5.t2)
% 0.37/0.90 (assume t5.t2.a0 (tptp.ssList tptp.sk2))
% 0.37/0.90 (assume t5.t2.a1 (= tptp.sk2 tptp.sk4))
% 0.37/0.90 (assume t5.t2.a2 (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))))
% 0.37/0.90 (assume t5.t2.a3 (= tptp.sk1 tptp.sk3))
% 0.37/0.90 (assume t5.t2.a4 (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))
% 0.37/0.90 (step t5.t2.t1 (cl (= (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))) true) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))))) :rule equiv_simplify)
% 0.37/0.90 (step t5.t2.t2 (cl (not (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))) true)) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule equiv1 :premises (t5.t2.t1))
% 0.37/0.90 (step t5.t2.t3 (cl (= (tptp.app tptp.nil tptp.sk1) tptp.sk1)) :rule symm :premises (t5.t2.a4))
% 0.37/0.90 (step t5.t2.t4 (cl (= tptp.sk3 tptp.sk1)) :rule symm :premises (t5.t2.a3))
% 0.37/0.90 (step t5.t2.t5 (cl (= tptp.sk1 tptp.sk3)) :rule symm :premises (t5.t2.t4))
% 0.37/0.90 (step t5.t2.t6 (cl (= (tptp.app tptp.nil tptp.sk1) tptp.sk3)) :rule trans :premises (t5.t2.t3 t5.t2.t5))
% 0.37/0.90 (step t5.t2.t7 (cl (= (tptp.cons tptp.sk5 tptp.nil) (tptp.cons tptp.sk5 tptp.nil))) :rule refl)
% 0.37/0.90 (step t5.t2.t8 (cl (= (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) :rule cong :premises (t5.t2.t6 t5.t2.t7))
% 0.37/0.90 (step t5.t2.t9 (cl (= (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)) tptp.sk4)) :rule symm :premises (t5.t2.a2))
% 0.37/0.90 (step t5.t2.t10 (cl (= tptp.sk4 tptp.sk2)) :rule symm :premises (t5.t2.a1))
% 0.37/0.90 (step t5.t2.t11 (cl (= (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk2)) :rule trans :premises (t5.t2.t8 t5.t2.t9 t5.t2.t10))
% 0.37/0.90 (step t5.t2.t12 (cl (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))) (tptp.ssList tptp.sk2))) :rule cong :premises (t5.t2.t11))
% 0.37/0.90 (step t5.t2.t13 (cl (= (= (tptp.ssList tptp.sk2) true) (tptp.ssList tptp.sk2))) :rule equiv_simplify)
% 0.37/0.90 (step t5.t2.t14 (cl (= (tptp.ssList tptp.sk2) true) (not (tptp.ssList tptp.sk2))) :rule equiv2 :premises (t5.t2.t13))
% 0.37/0.90 (step t5.t2.t15 (cl (= (tptp.ssList tptp.sk2) true)) :rule resolution :premises (t5.t2.t14 t5.t2.a0))
% 0.37/0.90 (step t5.t2.t16 (cl (= (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))) true)) :rule trans :premises (t5.t2.t12 t5.t2.t15))
% 0.37/0.90 (step t5.t2.t17 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t5.t2.t2 t5.t2.t16))
% 0.37/0.90 (step t5.t2 (cl (not (tptp.ssList tptp.sk2)) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule subproof :discharge (t5.t2.a0 t5.t2.a1 t5.t2.a2 t5.t2.a3 t5.t2.a4))
% 0.37/0.90 (step t5.t3 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (tptp.ssList tptp.sk2)) :rule and_pos)
% 0.37/0.90 (step t5.t4 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 0.37/0.90 (step t5.t5 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) :rule and_pos)
% 0.37/0.90 (step t5.t6 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk1 tptp.sk3)) :rule and_pos)
% 0.37/0.90 (step t5.t7 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) :rule and_pos)
% 0.37/0.90 (step t5.t8 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule resolution :premises (t5.t2 t5.t3 t5.t4 t5.t5 t5.t6 t5.t7))
% 0.37/0.90 (step t5.t9 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule reordering :premises (t5.t8))
% 0.37/0.90 (step t5.t10 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule contraction :premises (t5.t9))
% 0.37/0.90 (step t5.t11 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t5.t1 t5.t10))
% 0.37/0.90 (step t5.t12 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))))) :rule implies_neg2)
% 0.37/0.90 (step t5.t13 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))))) :rule resolution :premises (t5.t11 t5.t12))
% 0.37/0.90 (step t5.t14 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))))) :rule contraction :premises (t5.t13))
% 0.37/0.90 (step t5.t15 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule implies :premises (t5.t14))
% 0.37/0.90 (step t5.t16 (cl (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.ssList tptp.sk2)) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule and_neg)
% 0.37/0.90 (step t5.t17 (cl (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule resolution :premises (t5.t16 t5.a0 t5.a1 t5.a3 t5.a2 t5.a4))
% 0.37/0.90 (step t5.t18 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t5.t15 t5.t17))
% 0.37/0.90 (step t5 (cl (not (tptp.ssList tptp.sk2)) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule subproof :discharge (t5.a0 t5.a1 t5.a2 t5.a3 t5.a4))
% 0.37/0.90 (step t6 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (tptp.ssList tptp.sk2)) :rule and_pos)
% 0.37/0.90 (step t7 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 0.37/0.90 (step t8 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk1 tptp.sk3)) :rule and_pos)
% 0.37/0.90 (step t9 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) :rule and_pos)
% 0.37/0.90 (step t10 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) :rule and_pos)
% 0.37/0.90 (step t11 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule resolution :premises (t5 t6 t7 t8 t9 t10))
% 0.37/0.90 (step t12 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule reordering :premises (t11))
% 0.37/0.90 (step t13 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule contraction :premises (t12))
% 0.37/0.90 (step t14 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t4 t13))
% 0.37/0.90 (step t15 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))))) :rule implies_neg2)
% 0.37/0.90 (step t16 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))))) :rule resolution :premises (t14 t15))
% 0.37/0.90 (step t17 (cl (=> (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil))))) :rule contraction :premises (t16))
% 0.37/0.90 (step t18 (cl (not (and (tptp.ssList tptp.sk2) (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule implies :premises (t17))
% 0.37/0.90 (step t19 (cl (not (tptp.ssList tptp.sk2)) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t3 t18))
% 0.37/0.90 (step t20 (cl (not (= (or (= (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)) tptp.sk4) (not (tptp.neq tptp.sk4 tptp.nil))) (or (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.neq tptp.sk4 tptp.nil))))) (not (or (= (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)) tptp.sk4) (not (tptp.neq tptp.sk4 tptp.nil)))) (or (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.neq tptp.sk4 tptp.nil)))) :rule equiv_pos2)
% 0.37/0.90 (step t21 (cl (= (= (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)) tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))))) :rule all_simplify)
% 0.37/0.90 (step t22 (cl (= (not (tptp.neq tptp.sk4 tptp.nil)) (not (tptp.neq tptp.sk4 tptp.nil)))) :rule refl)
% 0.37/0.90 (step t23 (cl (= (or (= (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)) tptp.sk4) (not (tptp.neq tptp.sk4 tptp.nil))) (or (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.neq tptp.sk4 tptp.nil))))) :rule cong :premises (t21 t22))
% 0.37/0.90 (step t24 (cl (or (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.neq tptp.sk4 tptp.nil)))) :rule resolution :premises (t20 t23 a197))
% 0.37/0.90 (step t25 (cl (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.neq tptp.sk4 tptp.nil))) :rule or :premises (t24))
% 0.37/0.90 (step t26 (cl (not (tptp.neq tptp.sk4 tptp.nil)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) :rule reordering :premises (t25))
% 0.37/0.90 (step t27 (cl (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil)) (not (= tptp.sk2 tptp.sk4)) (not (tptp.neq tptp.sk2 tptp.nil))) :rule and_neg)
% 0.37/0.90 (step t28 (cl (=> (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil)) (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil))) :rule implies_neg1)
% 0.37/0.90 (anchor :step t29)
% 0.37/0.90 (assume t29.a0 (= tptp.sk2 tptp.sk4))
% 0.37/0.90 (assume t29.a1 (tptp.neq tptp.sk2 tptp.nil))
% 0.37/0.90 (step t29.t1 (cl (=> (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4)) (tptp.neq tptp.sk4 tptp.nil)) (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4))) :rule implies_neg1)
% 0.37/0.90 (anchor :step t29.t2)
% 0.37/0.90 (assume t29.t2.a0 (tptp.neq tptp.sk2 tptp.nil))
% 0.37/0.90 (assume t29.t2.a1 (= tptp.sk2 tptp.sk4))
% 0.37/0.90 (step t29.t2.t1 (cl (= (= (tptp.neq tptp.sk4 tptp.nil) true) (tptp.neq tptp.sk4 tptp.nil))) :rule equiv_simplify)
% 0.37/0.90 (step t29.t2.t2 (cl (not (= (tptp.neq tptp.sk4 tptp.nil) true)) (tptp.neq tptp.sk4 tptp.nil)) :rule equiv1 :premises (t29.t2.t1))
% 0.37/0.90 (step t29.t2.t3 (cl (= tptp.sk4 tptp.sk2)) :rule symm :premises (t29.t2.a1))
% 0.37/0.90 (step t29.t2.t4 (cl (= tptp.nil tptp.nil)) :rule refl)
% 0.37/0.90 (step t29.t2.t5 (cl (= (tptp.neq tptp.sk4 tptp.nil) (tptp.neq tptp.sk2 tptp.nil))) :rule cong :premises (t29.t2.t3 t29.t2.t4))
% 0.37/0.90 (step t29.t2.t6 (cl (= (= (tptp.neq tptp.sk2 tptp.nil) true) (tptp.neq tptp.sk2 tptp.nil))) :rule equiv_simplify)
% 0.37/0.90 (step t29.t2.t7 (cl (= (tptp.neq tptp.sk2 tptp.nil) true) (not (tptp.neq tptp.sk2 tptp.nil))) :rule equiv2 :premises (t29.t2.t6))
% 0.37/0.90 (step t29.t2.t8 (cl (= (tptp.neq tptp.sk2 tptp.nil) true)) :rule resolution :premises (t29.t2.t7 t29.t2.a0))
% 0.37/0.90 (step t29.t2.t9 (cl (= (tptp.neq tptp.sk4 tptp.nil) true)) :rule trans :premises (t29.t2.t5 t29.t2.t8))
% 0.37/0.90 (step t29.t2.t10 (cl (tptp.neq tptp.sk4 tptp.nil)) :rule resolution :premises (t29.t2.t2 t29.t2.t9))
% 0.37/0.90 (step t29.t2 (cl (not (tptp.neq tptp.sk2 tptp.nil)) (not (= tptp.sk2 tptp.sk4)) (tptp.neq tptp.sk4 tptp.nil)) :rule subproof :discharge (t29.t2.a0 t29.t2.a1))
% 0.37/0.90 (step t29.t3 (cl (not (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4))) (tptp.neq tptp.sk2 tptp.nil)) :rule and_pos)
% 0.37/0.90 (step t29.t4 (cl (not (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 0.37/0.90 (step t29.t5 (cl (tptp.neq tptp.sk4 tptp.nil) (not (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4))) (not (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4)))) :rule resolution :premises (t29.t2 t29.t3 t29.t4))
% 0.37/0.90 (step t29.t6 (cl (not (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4))) (not (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4))) (tptp.neq tptp.sk4 tptp.nil)) :rule reordering :premises (t29.t5))
% 0.37/0.90 (step t29.t7 (cl (not (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4))) (tptp.neq tptp.sk4 tptp.nil)) :rule contraction :premises (t29.t6))
% 0.37/0.90 (step t29.t8 (cl (=> (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4)) (tptp.neq tptp.sk4 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil)) :rule resolution :premises (t29.t1 t29.t7))
% 0.37/0.90 (step t29.t9 (cl (=> (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4)) (tptp.neq tptp.sk4 tptp.nil)) (not (tptp.neq tptp.sk4 tptp.nil))) :rule implies_neg2)
% 0.37/0.90 (step t29.t10 (cl (=> (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4)) (tptp.neq tptp.sk4 tptp.nil)) (=> (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4)) (tptp.neq tptp.sk4 tptp.nil))) :rule resolution :premises (t29.t8 t29.t9))
% 0.37/0.90 (step t29.t11 (cl (=> (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4)) (tptp.neq tptp.sk4 tptp.nil))) :rule contraction :premises (t29.t10))
% 0.37/0.90 (step t29.t12 (cl (not (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4))) (tptp.neq tptp.sk4 tptp.nil)) :rule implies :premises (t29.t11))
% 0.37/0.90 (step t29.t13 (cl (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4)) (not (tptp.neq tptp.sk2 tptp.nil)) (not (= tptp.sk2 tptp.sk4))) :rule and_neg)
% 0.37/0.90 (step t29.t14 (cl (and (tptp.neq tptp.sk2 tptp.nil) (= tptp.sk2 tptp.sk4))) :rule resolution :premises (t29.t13 t29.a1 t29.a0))
% 0.37/0.90 (step t29.t15 (cl (tptp.neq tptp.sk4 tptp.nil)) :rule resolution :premises (t29.t12 t29.t14))
% 0.37/0.90 (step t29 (cl (not (= tptp.sk2 tptp.sk4)) (not (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil)) :rule subproof :discharge (t29.a0 t29.a1))
% 0.37/0.90 (step t30 (cl (not (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 0.37/0.90 (step t31 (cl (not (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil))) (tptp.neq tptp.sk2 tptp.nil)) :rule and_pos)
% 0.37/0.90 (step t32 (cl (tptp.neq tptp.sk4 tptp.nil) (not (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil))) (not (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil)))) :rule resolution :premises (t29 t30 t31))
% 0.37/0.90 (step t33 (cl (not (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil))) (not (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil))) (tptp.neq tptp.sk4 tptp.nil)) :rule reordering :premises (t32))
% 0.37/0.90 (step t34 (cl (not (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil))) (tptp.neq tptp.sk4 tptp.nil)) :rule contraction :premises (t33))
% 0.37/0.90 (step t35 (cl (=> (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil)) :rule resolution :premises (t28 t34))
% 0.37/0.90 (step t36 (cl (=> (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil)) (not (tptp.neq tptp.sk4 tptp.nil))) :rule implies_neg2)
% 0.37/0.90 (step t37 (cl (=> (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil)) (=> (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil))) :rule resolution :premises (t35 t36))
% 0.37/0.90 (step t38 (cl (=> (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil))) :rule contraction :premises (t37))
% 0.37/0.90 (step t39 (cl (not (and (= tptp.sk2 tptp.sk4) (tptp.neq tptp.sk2 tptp.nil))) (tptp.neq tptp.sk4 tptp.nil)) :rule implies :premises (t38))
% 0.37/0.90 (step t40 (cl (not (= tptp.sk2 tptp.sk4)) (not (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk4 tptp.nil)) :rule resolution :premises (t27 t39))
% 0.37/0.90 (step t41 (cl (tptp.neq tptp.sk4 tptp.nil) (not (= tptp.sk2 tptp.sk4)) (not (tptp.neq tptp.sk2 tptp.nil))) :rule reordering :premises (t40))
% 0.37/0.90 (step t42 (cl (not (= (or (tptp.neq tptp.sk2 tptp.nil) (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk2 tptp.nil))) (not (or (tptp.neq tptp.sk2 tptp.nil) (tptp.neq tptp.sk2 tptp.nil))) (tptp.neq tptp.sk2 tptp.nil)) :rule equiv_pos2)
% 0.37/0.90 (step t43 (cl (= (or (tptp.neq tptp.sk2 tptp.nil) (tptp.neq tptp.sk2 tptp.nil)) (tptp.neq tptp.sk2 tptp.nil))) :rule all_simplify)
% 0.37/0.90 (step t44 (cl (tptp.neq tptp.sk2 tptp.nil)) :rule resolution :premises (t42 t43 a191))
% 0.37/0.90 (step t45 (cl (tptp.neq tptp.sk4 tptp.nil)) :rule resolution :premises (t41 a189 t44))
% 0.37/0.90 (step t46 (cl (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t26 t45))
% 0.37/0.90 (step t47 (cl (not (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) :rule or_pos)
% 0.37/0.90 (step t48 (cl (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)) (not (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule reordering :premises (t47))
% 0.37/0.90 (step t49 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) :rule implies_neg1)
% 0.37/0.90 (anchor :step t50)
% 0.37/0.90 (assume t50.a0 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))
% 0.37/0.90 (step t50.t1 (cl (or (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule forall_inst :args ((:= U tptp.sk1)))
% 0.37/0.90 (step t50.t2 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule or :premises (t50.t1))
% 0.37/0.90 (step t50.t3 (cl (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule resolution :premises (t50.t2 t50.a0))
% 0.37/0.90 (step t50 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule subproof :discharge (t50.a0))
% 0.37/0.90 (step t51 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule resolution :premises (t49 t50))
% 0.37/0.90 (step t52 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule implies_neg2)
% 0.37/0.90 (step t53 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule resolution :premises (t51 t52))
% 0.37/0.90 (step t54 (cl (=> (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule contraction :premises (t53))
% 0.37/0.90 (step t55 (cl (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule implies :premises (t54))
% 0.37/0.90 (step t56 (cl (not (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (not (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) :rule equiv_pos2)
% 0.37/0.90 (anchor :step t57 :args ((U $$unsorted) (:= U U)))
% 0.37/0.90 (step t57.t1 (cl (= U U)) :rule refl)
% 0.37/0.90 (step t57.t2 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 0.37/0.90 (step t57.t3 (cl (= (= (tptp.app tptp.nil U) U) (= U (tptp.app tptp.nil U)))) :rule all_simplify)
% 0.37/0.90 (step t57.t4 (cl (= (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) :rule cong :premises (t57.t2 t57.t3))
% 0.37/0.90 (step t57 (cl (= (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) :rule bind)
% 0.37/0.90 (step t58 (cl (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U))))) :rule resolution :premises (t56 t57 a73))
% 0.37/0.90 (step t59 (cl (or (not (tptp.ssList tptp.sk1)) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule resolution :premises (t55 t58))
% 0.37/0.90 (step t60 (cl (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) :rule resolution :premises (t48 a185 t59))
% 0.37/0.90 (step t61 (cl (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t19 a186 a189 a190 t46 t60))
% 0.37/0.90 (step t62 (cl (not (= (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (tptp.segmentP tptp.sk2 tptp.sk1) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))))) (not (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (tptp.segmentP tptp.sk2 tptp.sk1) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule equiv_pos2)
% 0.37/0.90 (step t63 (cl (= (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk2 tptp.sk4)))) :rule refl)
% 0.37/0.90 (step t64 (cl (= (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk1 tptp.sk3)))) :rule refl)
% 0.37/0.90 (step t65 (cl (= (= (= (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (tptp.segmentP tptp.sk2 tptp.sk1)) true) (= (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (tptp.segmentP tptp.sk2 tptp.sk1)))) :rule equiv_simplify)
% 0.37/0.90 (step t66 (cl (not (= (= (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (tptp.segmentP tptp.sk2 tptp.sk1)) true)) (= (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (tptp.segmentP tptp.sk2 tptp.sk1))) :rule equiv1 :premises (t65))
% 0.37/0.90 (step t67 (cl (= (= (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (tptp.segmentP tptp.sk2 tptp.sk1)) (= (tptp.segmentP tptp.sk2 tptp.sk1) (not (not (tptp.segmentP tptp.sk2 tptp.sk1)))))) :rule all_simplify)
% 0.37/0.90 (step t68 (cl (= (tptp.segmentP tptp.sk2 tptp.sk1) (tptp.segmentP tptp.sk2 tptp.sk1))) :rule refl)
% 0.37/0.90 (step t69 (cl (= (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (tptp.segmentP tptp.sk2 tptp.sk1))) :rule all_simplify)
% 0.37/0.90 (step t70 (cl (= (= (tptp.segmentP tptp.sk2 tptp.sk1) (not (not (tptp.segmentP tptp.sk2 tptp.sk1)))) (= (tptp.segmentP tptp.sk2 tptp.sk1) (tptp.segmentP tptp.sk2 tptp.sk1)))) :rule cong :premises (t68 t69))
% 0.37/0.90 (step t71 (cl (= (= (tptp.segmentP tptp.sk2 tptp.sk1) (tptp.segmentP tptp.sk2 tptp.sk1)) true)) :rule all_simplify)
% 0.37/0.90 (step t72 (cl (= (= (tptp.segmentP tptp.sk2 tptp.sk1) (not (not (tptp.segmentP tptp.sk2 tptp.sk1)))) true)) :rule trans :premises (t70 t71))
% 0.37/0.90 (step t73 (cl (= (= (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (tptp.segmentP tptp.sk2 tptp.sk1)) true)) :rule trans :premises (t67 t72))
% 0.37/0.90 (step t74 (cl (= (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (tptp.segmentP tptp.sk2 tptp.sk1))) :rule resolution :premises (t66 t73))
% 0.37/0.90 (step t75 (cl (= (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))))) :rule refl)
% 0.37/0.90 (step t76 (cl (= (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule refl)
% 0.37/0.90 (step t77 (cl (= (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule refl)
% 0.37/0.90 (step t78 (cl (= (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (tptp.segmentP tptp.sk2 tptp.sk1) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))))) :rule cong :premises (t63 t64 t74 t75 t76 t77))
% 0.37/0.90 (step t79 (cl (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule and_neg)
% 0.37/0.90 (step t80 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule implies_neg1)
% 0.37/0.90 (anchor :step t81)
% 0.37/0.90 (assume t81.a0 (= tptp.sk2 tptp.sk4))
% 0.37/0.90 (assume t81.a1 (= tptp.sk1 tptp.sk3))
% 0.37/0.90 (assume t81.a2 (not (tptp.segmentP tptp.sk2 tptp.sk1)))
% 0.37/0.90 (assume t81.a3 (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))))
% 0.37/0.90 (assume t81.a4 (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))
% 0.37/0.90 (step t81.t1 (cl (=> (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule implies_neg1)
% 0.37/0.90 (anchor :step t81.t2)
% 0.37/0.90 (assume t81.t2.a0 (not (tptp.segmentP tptp.sk2 tptp.sk1)))
% 0.37/0.90 (assume t81.t2.a1 (= tptp.sk2 tptp.sk4))
% 0.37/0.90 (assume t81.t2.a2 (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))))
% 0.37/0.90 (assume t81.t2.a3 (= tptp.sk1 tptp.sk3))
% 0.37/0.90 (assume t81.t2.a4 (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))
% 0.37/0.90 (step t81.t2.t1 (cl (= (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1) false) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule equiv_simplify)
% 0.37/0.90 (step t81.t2.t2 (cl (not (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1) false)) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule equiv1 :premises (t81.t2.t1))
% 0.37/0.90 (step t81.t2.t3 (cl (= (tptp.app tptp.nil tptp.sk1) tptp.sk1)) :rule symm :premises (t81.t2.a4))
% 0.37/0.90 (step t81.t2.t4 (cl (= tptp.sk3 tptp.sk1)) :rule symm :premises (t81.t2.a3))
% 0.37/0.90 (step t81.t2.t5 (cl (= tptp.sk1 tptp.sk3)) :rule symm :premises (t81.t2.t4))
% 0.37/0.90 (step t81.t2.t6 (cl (= (tptp.app tptp.nil tptp.sk1) tptp.sk3)) :rule trans :premises (t81.t2.t3 t81.t2.t5))
% 0.37/0.90 (step t81.t2.t7 (cl (= (tptp.cons tptp.sk5 tptp.nil) (tptp.cons tptp.sk5 tptp.nil))) :rule refl)
% 0.37/0.90 (step t81.t2.t8 (cl (= (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) :rule cong :premises (t81.t2.t6 t81.t2.t7))
% 0.37/0.90 (step t81.t2.t9 (cl (= (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)) tptp.sk4)) :rule symm :premises (t81.t2.a2))
% 0.37/0.90 (step t81.t2.t10 (cl (= tptp.sk4 tptp.sk2)) :rule symm :premises (t81.t2.a1))
% 0.37/0.90 (step t81.t2.t11 (cl (= (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk2)) :rule trans :premises (t81.t2.t8 t81.t2.t9 t81.t2.t10))
% 0.37/0.90 (step t81.t2.t12 (cl (= tptp.sk1 tptp.sk1)) :rule refl)
% 0.37/0.90 (step t81.t2.t13 (cl (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1) (tptp.segmentP tptp.sk2 tptp.sk1))) :rule cong :premises (t81.t2.t11 t81.t2.t12))
% 0.37/0.90 (step t81.t2.t14 (cl (= (= (tptp.segmentP tptp.sk2 tptp.sk1) false) (not (tptp.segmentP tptp.sk2 tptp.sk1)))) :rule equiv_simplify)
% 0.37/0.90 (step t81.t2.t15 (cl (= (tptp.segmentP tptp.sk2 tptp.sk1) false) (not (not (tptp.segmentP tptp.sk2 tptp.sk1)))) :rule equiv2 :premises (t81.t2.t14))
% 0.37/0.90 (step t81.t2.t16 (cl (not (not (not (tptp.segmentP tptp.sk2 tptp.sk1)))) (tptp.segmentP tptp.sk2 tptp.sk1)) :rule not_not)
% 0.37/0.90 (step t81.t2.t17 (cl (= (tptp.segmentP tptp.sk2 tptp.sk1) false) (tptp.segmentP tptp.sk2 tptp.sk1)) :rule resolution :premises (t81.t2.t15 t81.t2.t16))
% 0.37/0.90 (step t81.t2.t18 (cl (= (tptp.segmentP tptp.sk2 tptp.sk1) false)) :rule resolution :premises (t81.t2.t17 t81.t2.a0))
% 0.37/0.90 (step t81.t2.t19 (cl (= (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1) false)) :rule trans :premises (t81.t2.t13 t81.t2.t18))
% 0.37/0.90 (step t81.t2.t20 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule resolution :premises (t81.t2.t2 t81.t2.t19))
% 0.37/0.90 (step t81.t2 (cl (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule subproof :discharge (t81.t2.a0 t81.t2.a1 t81.t2.a2 t81.t2.a3 t81.t2.a4))
% 0.37/0.90 (step t81.t3 (cl (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (tptp.segmentP tptp.sk2 tptp.sk1))) :rule and_pos)
% 0.37/0.90 (step t81.t4 (cl (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 0.37/0.90 (step t81.t5 (cl (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) :rule and_pos)
% 0.37/0.90 (step t81.t6 (cl (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk1 tptp.sk3)) :rule and_pos)
% 0.37/0.90 (step t81.t7 (cl (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) :rule and_pos)
% 0.37/0.90 (step t81.t8 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)) (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule resolution :premises (t81.t2 t81.t3 t81.t4 t81.t5 t81.t6 t81.t7))
% 0.37/0.90 (step t81.t9 (cl (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule reordering :premises (t81.t8))
% 0.37/0.90 (step t81.t10 (cl (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule contraction :premises (t81.t9))
% 0.37/0.90 (step t81.t11 (cl (=> (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule resolution :premises (t81.t1 t81.t10))
% 0.37/0.90 (step t81.t12 (cl (=> (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule implies_neg2)
% 0.37/0.90 (step t81.t13 (cl (=> (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (=> (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule resolution :premises (t81.t11 t81.t12))
% 0.37/0.90 (step t81.t14 (cl (=> (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule contraction :premises (t81.t13))
% 0.37/0.90 (step t81.t15 (cl (not (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule implies :premises (t81.t14))
% 0.37/0.90 (step t81.t16 (cl (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule and_neg)
% 0.37/0.90 (step t81.t17 (cl (and (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk2 tptp.sk4) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 tptp.sk3) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) :rule resolution :premises (t81.t16 t81.a2 t81.a0 t81.a3 t81.a1 t81.a4))
% 0.37/0.90 (step t81.t18 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule resolution :premises (t81.t15 t81.t17))
% 0.37/0.90 (step t81 (cl (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule subproof :discharge (t81.a0 t81.a1 t81.a2 t81.a3 t81.a4))
% 0.37/0.90 (step t82 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk2 tptp.sk4)) :rule and_pos)
% 0.37/0.90 (step t83 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk1 tptp.sk3)) :rule and_pos)
% 0.37/0.90 (step t84 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (tptp.segmentP tptp.sk2 tptp.sk1))) :rule and_pos)
% 0.37/0.90 (step t85 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) :rule and_pos)
% 0.37/0.90 (step t86 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) :rule and_pos)
% 0.37/0.90 (step t87 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule resolution :premises (t81 t82 t83 t84 t85 t86))
% 0.37/0.90 (step t88 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule reordering :premises (t87))
% 0.37/0.90 (step t89 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule contraction :premises (t88))
% 0.37/0.90 (step t90 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule resolution :premises (t80 t89))
% 0.37/0.90 (step t91 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule implies_neg2)
% 0.37/0.90 (step t92 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule resolution :premises (t90 t91))
% 0.37/0.90 (step t93 (cl (=> (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule contraction :premises (t92))
% 0.37/0.90 (step t94 (cl (not (and (= tptp.sk2 tptp.sk4) (= tptp.sk1 tptp.sk3) (not (tptp.segmentP tptp.sk2 tptp.sk1)) (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil))) (= tptp.sk1 (tptp.app tptp.nil tptp.sk1)))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule implies :premises (t93))
% 0.37/0.90 (step t95 (cl (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule resolution :premises (t79 t94))
% 0.37/0.90 (step t96 (cl (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (not (= tptp.sk2 tptp.sk4)))) :rule or_neg)
% 0.37/0.90 (step t97 (cl (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (not (= tptp.sk1 tptp.sk3)))) :rule or_neg)
% 0.37/0.90 (step t98 (cl (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (not (not (tptp.segmentP tptp.sk2 tptp.sk1))))) :rule or_neg)
% 0.37/0.90 (step t99 (cl (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))))) :rule or_neg)
% 0.37/0.90 (step t100 (cl (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))))) :rule or_neg)
% 0.37/0.90 (step t101 (cl (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule or_neg)
% 0.37/0.90 (step t102 (cl (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule resolution :premises (t95 t96 t97 t98 t99 t100 t101))
% 0.37/0.90 (step t103 (cl (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (not (tptp.segmentP tptp.sk2 tptp.sk1))) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule contraction :premises (t102))
% 0.37/0.90 (step t104 (cl (or (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (tptp.segmentP tptp.sk2 tptp.sk1) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule resolution :premises (t62 t78 t103))
% 0.37/0.90 (step t105 (cl (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (tptp.segmentP tptp.sk2 tptp.sk1) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule or :premises (t104))
% 0.37/0.90 (step t106 (cl (tptp.segmentP tptp.sk2 tptp.sk1) (not (= tptp.sk2 tptp.sk4)) (not (= tptp.sk1 tptp.sk3)) (not (= tptp.sk4 (tptp.app tptp.sk3 (tptp.cons tptp.sk5 tptp.nil)))) (not (= tptp.sk1 (tptp.app tptp.nil tptp.sk1))) (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule reordering :premises (t105))
% 0.37/0.90 (step t107 (cl (not (tptp.segmentP tptp.sk2 tptp.sk1)) (not (tptp.neq tptp.sk4 tptp.nil))) :rule or :premises (a198))
% 0.37/0.90 (step t108 (cl (not (tptp.neq tptp.sk4 tptp.nil)) (not (tptp.segmentP tptp.sk2 tptp.sk1))) :rule reordering :premises (t107))
% 0.37/0.90 (step t109 (cl (not (tptp.segmentP tptp.sk2 tptp.sk1))) :rule resolution :premises (t108 t45))
% 0.37/0.90 (step t110 (cl (not (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule resolution :premises (t106 t109 a189 a190 t46 t60))
% 0.37/0.90 (step t111 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule implies_neg1)
% 0.37/0.90 (anchor :step t112)
% 0.37/0.90 (assume t112.a0 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))
% 0.37/0.90 (step t112.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule forall_inst :args ((:= U tptp.nil) (:= V tptp.sk1) (:= W (tptp.cons tptp.sk5 tptp.nil))))
% 0.37/0.90 (step t112.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule or :premises (t112.t1))
% 0.37/0.90 (step t112.t3 (cl (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule resolution :premises (t112.t2 t112.a0))
% 0.37/0.90 (step t112 (cl (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule subproof :discharge (t112.a0))
% 0.37/0.90 (step t113 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule resolution :premises (t111 t112))
% 0.37/0.90 (step t114 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (not (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule implies_neg2)
% 0.37/0.90 (step t115 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule resolution :premises (t113 t114))
% 0.37/0.90 (step t116 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1)))) :rule contraction :premises (t115))
% 0.37/0.90 (step t117 (cl (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule implies :premises (t116))
% 0.37/0.90 (step t118 (cl (not (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule equiv_pos2)
% 0.37/0.90 (anchor :step t119 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V) (W $$unsorted) (:= W W) (X $$unsorted) (:= X X)))
% 0.37/0.90 (step t119.t1 (cl (= U U)) :rule refl)
% 0.37/0.90 (step t119.t2 (cl (= V V)) :rule refl)
% 0.37/0.90 (step t119.t3 (cl (= W W)) :rule refl)
% 0.37/0.90 (step t119.t4 (cl (= X X)) :rule refl)
% 0.37/0.90 (step t119.t5 (cl (= (= (tptp.app (tptp.app U V) W) X) (= X (tptp.app (tptp.app U V) W)))) :rule all_simplify)
% 0.37/0.90 (step t119.t6 (cl (= (not (= (tptp.app (tptp.app U V) W) X)) (not (= X (tptp.app (tptp.app U V) W))))) :rule cong :premises (t119.t5))
% 0.37/0.90 (step t119.t7 (cl (= (not (tptp.ssList W)) (not (tptp.ssList W)))) :rule refl)
% 0.37/0.90 (step t119.t8 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 0.37/0.90 (step t119.t9 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 0.37/0.90 (step t119.t10 (cl (= (not (tptp.ssList X)) (not (tptp.ssList X)))) :rule refl)
% 0.37/0.90 (step t119.t11 (cl (= (tptp.segmentP X V) (tptp.segmentP X V))) :rule refl)
% 0.37/0.90 (step t119.t12 (cl (= (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V)) (or (not (= X (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V)))) :rule cong :premises (t119.t6 t119.t7 t119.t8 t119.t9 t119.t10 t119.t11))
% 0.37/0.90 (step t119 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= X (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))))) :rule bind)
% 0.37/0.90 (step t120 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= X (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) :rule all_simplify)
% 0.37/0.90 (anchor :step t121 :args ((U $$unsorted) (:= U U) (V $$unsorted) (:= V V) (W $$unsorted) (:= W W)))
% 0.37/0.90 (step t121.t1 (cl (= U U)) :rule refl)
% 0.37/0.90 (step t121.t2 (cl (= V V)) :rule refl)
% 0.37/0.90 (step t121.t3 (cl (= W W)) :rule refl)
% 0.37/0.90 (step t121.t4 (cl (= (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W)) true)) :rule all_simplify)
% 0.37/0.90 (step t121.t5 (cl (= (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not true))) :rule cong :premises (t121.t4))
% 0.37/0.90 (step t121.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.37/0.90 (step t121.t7 (cl (= (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) false)) :rule trans :premises (t121.t5 t121.t6))
% 0.37/0.90 (step t121.t8 (cl (= (not (tptp.ssList W)) (not (tptp.ssList W)))) :rule refl)
% 0.37/0.90 (step t121.t9 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 0.37/0.90 (step t121.t10 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 0.37/0.90 (step t121.t11 (cl (= (not (tptp.ssList (tptp.app (tptp.app U V) W))) (not (tptp.ssList (tptp.app (tptp.app U V) W))))) :rule refl)
% 0.37/0.90 (step t121.t12 (cl (= (tptp.segmentP (tptp.app (tptp.app U V) W) V) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) :rule refl)
% 0.37/0.90 (step t121.t13 (cl (= (or (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)) (or false (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule cong :premises (t121.t7 t121.t8 t121.t9 t121.t10 t121.t11 t121.t12))
% 0.37/0.90 (step t121.t14 (cl (= (or false (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule all_simplify)
% 0.37/0.90 (step t121.t15 (cl (= (or (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule trans :premises (t121.t13 t121.t14))
% 0.37/0.90 (step t121 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) :rule bind)
% 0.37/0.90 (step t122 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= X (tptp.app (tptp.app U V) W))) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) :rule trans :premises (t120 t121))
% 0.37/0.90 (step t123 (cl (= (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V))))) :rule trans :premises (t119 t122))
% 0.37/0.90 (step t124 (cl (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList (tptp.app (tptp.app U V) W))) (tptp.segmentP (tptp.app (tptp.app U V) W) V)))) :rule resolution :premises (t118 t123 a172))
% 0.37/0.90 (step t125 (cl (or (not (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) (not (tptp.ssList tptp.nil)) (not (tptp.ssList tptp.sk1)) (not (tptp.ssList (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)))) (tptp.segmentP (tptp.app (tptp.app tptp.nil tptp.sk1) (tptp.cons tptp.sk5 tptp.nil)) tptp.sk1))) :rule resolution :premises (t117 t124))
% 0.37/0.90 (step t126 (cl (not (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) :rule or_pos)
% 0.37/0.90 (step t127 (cl (not (tptp.ssList tptp.nil)) (not (tptp.ssItem tptp.sk5)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)) (not (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))))) :rule reordering :premises (t126))
% 0.37/0.90 (step t128 (cl (tptp.ssItem tptp.sk5) (not (tptp.neq tptp.sk4 tptp.nil))) :rule or :premises (a196))
% 0.37/0.90 (step t129 (cl (not (tptp.neq tptp.sk4 tptp.nil)) (tptp.ssItem tptp.sk5)) :rule reordering :premises (t128))
% 0.37/0.90 (step t130 (cl (tptp.ssItem tptp.sk5)) :rule resolution :premises (t129 t45))
% 0.37/0.90 (step t131 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) :rule implies_neg1)
% 0.37/0.90 (anchor :step t132)
% 0.37/0.90 (assume t132.a0 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))))
% 0.37/0.90 (step t132.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))))) :rule forall_inst :args ((:= U tptp.sk5) (:= V tptp.nil)))
% 0.37/0.90 (step t132.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) :rule or :premises (t132.t1))
% 0.37/0.90 (step t132.t3 (cl (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t132.t2 t132.a0))
% 0.37/0.90 (step t132 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) :rule subproof :discharge (t132.a0))
% 0.37/0.90 (step t133 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t131 t132))
% 0.37/0.90 (step t134 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) (not (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))))) :rule implies_neg2)
% 0.37/0.90 (step t135 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))))) :rule resolution :premises (t133 t134))
% 0.37/0.90 (step t136 (cl (=> (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))))) :rule contraction :premises (t135))
% 0.37/0.90 (step t137 (cl (not (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V))))) (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) :rule implies :premises (t136))
% 0.37/0.90 (step t138 (cl (or (not (tptp.ssItem tptp.sk5)) (not (tptp.ssList tptp.nil)) (tptp.ssList (tptp.cons tptp.sk5 tptp.nil)))) :rule resolution :premises (t137 a85))
% 0.37/0.90 (step t139 (cl (tptp.ssList (tptp.cons tptp.sk5 tptp.nil))) :rule resolution :premises (t127 a7 t130 t138))
% 0.37/0.90 (step t140 (cl) :rule resolution :premises (t2 t61 t110 t125 t139 a185 a7))
% 0.37/0.90
% 0.37/0.91 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.jbNoZnJxgB/cvc5---1.0.5_4304.smt2
% 0.37/0.91 % cvc5---1.0.5 exiting
% 0.37/0.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------