TSTP Solution File: SWC360+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC360+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n029.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 18:01:43 EDT 2024
% Result : Theorem 0.38s 0.63s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWC360+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n029.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 26 16:36:09 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.37/0.54 %----Proving TF0_NAR, FOF, or CNF
% 0.38/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.38/0.63 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.6ffHEf1MDb/cvc5---1.0.5_8711.smt2
% 0.38/0.63 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.6ffHEf1MDb/cvc5---1.0.5_8711.smt2
% 0.38/0.63 (assume a0 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))))
% 0.38/0.63 (assume a1 (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))))
% 0.38/0.63 (assume a2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))
% 0.38/0.63 (assume a3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))
% 0.38/0.63 (assume a4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))))
% 0.38/0.63 (assume a5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))))
% 0.38/0.63 (assume a6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))))
% 0.38/0.63 (assume a7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))))
% 0.38/0.63 (assume a8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))))
% 0.38/0.63 (assume a9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))))
% 0.38/0.63 (assume a10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))))
% 0.38/0.63 (assume a11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))))
% 0.38/0.63 (assume a12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))))
% 0.38/0.63 (assume a13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))))
% 0.38/0.63 (assume a14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))
% 0.38/0.63 (assume a15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))
% 0.38/0.63 (assume a16 (tptp.ssList tptp.nil))
% 0.38/0.63 (assume a17 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))
% 0.38/0.63 (assume a18 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))))
% 0.38/0.63 (assume a19 (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))))
% 0.38/0.63 (assume a20 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))))
% 0.38/0.63 (assume a21 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))
% 0.38/0.63 (assume a22 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))))
% 0.38/0.63 (assume a23 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))))
% 0.38/0.63 (assume a24 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))
% 0.38/0.63 (assume a25 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))
% 0.38/0.63 (assume a26 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))))
% 0.38/0.63 (assume a27 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))
% 0.38/0.63 (assume a28 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))))
% 0.38/0.63 (assume a29 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))))
% 0.38/0.63 (assume a30 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))))
% 0.38/0.63 (assume a31 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))))
% 0.38/0.63 (assume a32 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))))
% 0.38/0.63 (assume a33 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))))
% 0.38/0.63 (assume a34 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))))
% 0.38/0.63 (assume a35 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))))
% 0.38/0.63 (assume a36 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))))
% 0.38/0.63 (assume a37 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))))
% 0.38/0.63 (assume a38 (not (tptp.singletonP tptp.nil)))
% 0.38/0.63 (assume a39 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))))
% 0.38/0.63 (assume a40 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))))
% 0.38/0.63 (assume a41 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))))
% 0.38/0.63 (assume a42 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))))
% 0.38/0.63 (assume a43 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))))
% 0.38/0.63 (assume a44 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))))
% 0.38/0.63 (assume a45 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))))
% 0.38/0.63 (assume a46 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))))
% 0.38/0.63 (assume a47 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))))
% 0.38/0.63 (assume a48 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))))
% 0.38/0.63 (assume a49 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))))
% 0.38/0.63 (assume a50 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))))
% 0.38/0.63 (assume a51 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))))
% 0.38/0.63 (assume a52 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))))
% 0.38/0.63 (assume a53 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))))
% 0.38/0.63 (assume a54 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))
% 0.38/0.63 (assume a55 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))
% 0.38/0.63 (assume a56 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))))
% 0.38/0.63 (assume a57 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))))
% 0.38/0.63 (assume a58 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))))
% 0.38/0.63 (assume a59 (tptp.cyclefreeP tptp.nil))
% 0.38/0.63 (assume a60 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))))
% 0.38/0.63 (assume a61 (tptp.totalorderP tptp.nil))
% 0.38/0.63 (assume a62 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))))
% 0.38/0.63 (assume a63 (tptp.strictorderP tptp.nil))
% 0.38/0.63 (assume a64 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))))
% 0.38/0.63 (assume a65 (tptp.totalorderedP tptp.nil))
% 0.38/0.63 (assume a66 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or (= tptp.nil V) (and (not (= tptp.nil V)) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V))))))))))
% 0.38/0.63 (assume a67 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))))
% 0.38/0.63 (assume a68 (tptp.strictorderedP tptp.nil))
% 0.38/0.63 (assume a69 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or (= tptp.nil V) (and (not (= tptp.nil V)) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V))))))))))
% 0.38/0.63 (assume a70 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))))
% 0.38/0.63 (assume a71 (tptp.duplicatefreeP tptp.nil))
% 0.38/0.63 (assume a72 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))))
% 0.38/0.63 (assume a73 (tptp.equalelemsP tptp.nil))
% 0.38/0.63 (assume a74 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))))
% 0.38/0.63 (assume a75 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))))
% 0.38/0.63 (assume a76 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))))
% 0.38/0.63 (assume a77 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))
% 0.38/0.63 (assume a78 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))))
% 0.38/0.63 (assume a79 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))))
% 0.38/0.63 (assume a80 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))
% 0.38/0.63 (assume a81 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))
% 0.38/0.63 (assume a82 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))
% 0.38/0.63 (assume a83 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))
% 0.38/0.63 (assume a84 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))))
% 0.38/0.63 (assume a85 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))))
% 0.38/0.63 (assume a86 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))))
% 0.38/0.63 (assume a87 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))))
% 0.38/0.63 (assume a88 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))))
% 0.38/0.63 (assume a89 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))))
% 0.38/0.63 (assume a90 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))))
% 0.38/0.63 (assume a91 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))))
% 0.38/0.63 (assume a92 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))))
% 0.38/0.63 (assume a93 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))))
% 0.38/0.63 (assume a94 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))))
% 0.38/0.63 (assume a95 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U))))))))))))
% 0.38/0.63 (assume a96 true)
% 0.38/0.63 (step t1 (cl (not (= (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U))))))))))) false)) (not (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)))))))))))) false) :rule equiv_pos2)
% 0.38/0.63 (anchor :step t2 :args ((U $$unsorted) (:= U U)))
% 0.38/0.63 (step t2.t1 (cl (= U U)) :rule refl)
% 0.38/0.63 (step t2.t2 (cl (= (tptp.ssList U) (tptp.ssList U))) :rule refl)
% 0.38/0.63 (anchor :step t2.t3 :args ((V $$unsorted) (:= V V)))
% 0.38/0.63 (step t2.t3.t1 (cl (= V V)) :rule refl)
% 0.38/0.63 (step t2.t3.t2 (cl (= (tptp.ssList V) (tptp.ssList V))) :rule refl)
% 0.38/0.63 (anchor :step t2.t3.t3 :args ((W $$unsorted) (:= W W)))
% 0.38/0.63 (step t2.t3.t3.t1 (cl (= W W)) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t2 (cl (= (tptp.ssList W) (tptp.ssList W))) :rule refl)
% 0.38/0.63 (anchor :step t2.t3.t3.t3 :args ((X $$unsorted) (:= X X)))
% 0.38/0.63 (step t2.t3.t3.t3.t1 (cl (= X X)) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t3.t2 (cl (= (tptp.ssList X) (tptp.ssList X))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t3.t3 (cl (= (not (= V X)) (not (= V X)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t3.t4 (cl (= (not (= U W)) (not (= U W)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t3.t5 (cl (= (not (tptp.neq V tptp.nil)) (not (tptp.neq V tptp.nil)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t3.t6 (cl (= (not (tptp.segmentP X W)) (not (tptp.segmentP X W)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t3.t7 (cl (= (not (tptp.totalorderedP W)) (not (tptp.totalorderedP W)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t3.t8 (cl (= (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (not (forall ((Y $$unsorted)) (not (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t3.t3.t9 (cl (= (forall ((Y $$unsorted)) (not (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y)))) (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t3.t3.t10 (cl (= (not (forall ((Y $$unsorted)) (not (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))))) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) :rule cong :premises (t2.t3.t3.t3.t9))
% 0.38/0.63 (step t2.t3.t3.t3.t11 (cl (= (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) :rule trans :premises (t2.t3.t3.t3.t8 t2.t3.t3.t3.t10))
% 0.38/0.63 (step t2.t3.t3.t3.t12 (cl (= (tptp.segmentP V U) (tptp.segmentP V U))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t3.t13 (cl (= (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))) (tptp.segmentP V U)))) :rule cong :premises (t2.t3.t3.t3.t3 t2.t3.t3.t3.t4 t2.t3.t3.t3.t5 t2.t3.t3.t3.t6 t2.t3.t3.t3.t7 t2.t3.t3.t3.t11 t2.t3.t3.t3.t12))
% 0.38/0.63 (step t2.t3.t3.t3.t14 (cl (= (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U))) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))) (tptp.segmentP V U))))) :rule cong :premises (t2.t3.t3.t3.t2 t2.t3.t3.t3.t13))
% 0.38/0.63 (step t2.t3.t3.t3 (cl (= (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)))) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))) (tptp.segmentP V U)))))) :rule bind)
% 0.38/0.63 (step t2.t3.t3.t4 (cl (= (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))) (tptp.segmentP V U)))) (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))) (tptp.segmentP V U))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t3.t5 (cl (= (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))) (tptp.segmentP V U))) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (tptp.segmentP X W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t3.t6 (cl (= (not (= U W)) (not (= U W)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t7 (cl (= (not (tptp.neq V tptp.nil)) (not (tptp.neq V tptp.nil)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t8 (cl (= (not (tptp.totalorderedP W)) (not (tptp.totalorderedP W)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t9 (cl (= (tptp.segmentP V U) (tptp.segmentP V U))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t10 (cl (= (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (tptp.segmentP X W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) (or (not (tptp.ssList V)) (not (= V V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t3.t11 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t12 (cl (= (= V V) true)) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t3.t13 (cl (= (not (= V V)) (not true))) :rule cong :premises (t2.t3.t3.t12))
% 0.38/0.63 (step t2.t3.t3.t14 (cl (= (not true) false)) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t3.t15 (cl (= (not (= V V)) false)) :rule trans :premises (t2.t3.t3.t13 t2.t3.t3.t14))
% 0.38/0.63 (step t2.t3.t3.t16 (cl (= (not (tptp.segmentP V W)) (not (tptp.segmentP V W)))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t17 (cl (= (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) :rule refl)
% 0.38/0.63 (step t2.t3.t3.t18 (cl (= (or (not (tptp.ssList V)) (not (= V V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))) (or (not (tptp.ssList V)) false (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule cong :premises (t2.t3.t3.t11 t2.t3.t3.t15 t2.t3.t3.t16 t2.t3.t3.t17))
% 0.38/0.63 (step t2.t3.t3.t19 (cl (= (or (not (tptp.ssList V)) false (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))) (or (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t3.t20 (cl (= (or (not (tptp.ssList V)) (not (= V V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))) (or (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t3.t18 t2.t3.t3.t19))
% 0.38/0.63 (step t2.t3.t3.t21 (cl (= (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (tptp.segmentP X W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) (or (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t3.t10 t2.t3.t3.t20))
% 0.38/0.63 (step t2.t3.t3.t22 (cl (= (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (tptp.segmentP X W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (or (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))))) :rule cong :premises (t2.t3.t3.t6 t2.t3.t3.t7 t2.t3.t3.t8 t2.t3.t3.t9 t2.t3.t3.t21))
% 0.38/0.63 (step t2.t3.t3.t23 (cl (= (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (or (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t3.t24 (cl (= (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (tptp.segmentP X W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t3.t22 t2.t3.t3.t23))
% 0.38/0.63 (step t2.t3.t3.t25 (cl (= (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))) (tptp.segmentP V U))) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t3.t5 t2.t3.t3.t24))
% 0.38/0.63 (step t2.t3.t3.t26 (cl (= (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP X Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))) (tptp.segmentP V U)))) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t3.t4 t2.t3.t3.t25))
% 0.38/0.63 (step t2.t3.t3.t27 (cl (= (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)))) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t3.t3 t2.t3.t3.t26))
% 0.38/0.63 (step t2.t3.t3.t28 (cl (= (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U))))) (=> (tptp.ssList W) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))))) :rule cong :premises (t2.t3.t3.t2 t2.t3.t3.t27))
% 0.38/0.63 (step t2.t3.t3 (cl (= (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)))))) (forall ((W $$unsorted)) (=> (tptp.ssList W) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))))) :rule bind)
% 0.38/0.63 (step t2.t3.t4 (cl (= (forall ((W $$unsorted)) (=> (tptp.ssList W) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t5 (cl (= (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U W)) (not (tptp.totalorderedP W)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t6 (cl (= (not (tptp.neq V tptp.nil)) (not (tptp.neq V tptp.nil)))) :rule refl)
% 0.38/0.63 (step t2.t3.t7 (cl (= (tptp.segmentP V U) (tptp.segmentP V U))) :rule refl)
% 0.38/0.63 (step t2.t3.t8 (cl (= (not (tptp.ssList V)) (not (tptp.ssList V)))) :rule refl)
% 0.38/0.63 (step t2.t3.t9 (cl (= (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U W)) (not (tptp.totalorderedP W)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) (or (not (tptp.ssList U)) (not (= U U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t10 (cl (= (not (tptp.ssList U)) (not (tptp.ssList U)))) :rule refl)
% 0.38/0.63 (step t2.t3.t11 (cl (= (= U U) true)) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t12 (cl (= (not (= U U)) (not true))) :rule cong :premises (t2.t3.t11))
% 0.38/0.63 (step t2.t3.t13 (cl (= (not true) false)) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t14 (cl (= (not (= U U)) false)) :rule trans :premises (t2.t3.t12 t2.t3.t13))
% 0.38/0.63 (step t2.t3.t15 (cl (= (not (tptp.totalorderedP U)) (not (tptp.totalorderedP U)))) :rule refl)
% 0.38/0.63 (step t2.t3.t16 (cl (= (not (tptp.segmentP V U)) (not (tptp.segmentP V U)))) :rule refl)
% 0.38/0.63 (step t2.t3.t17 (cl (= (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y))))) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y))))))) :rule refl)
% 0.38/0.63 (step t2.t3.t18 (cl (= (or (not (tptp.ssList U)) (not (= U U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))) (or (not (tptp.ssList U)) false (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule cong :premises (t2.t3.t10 t2.t3.t14 t2.t3.t15 t2.t3.t16 t2.t3.t17))
% 0.38/0.63 (step t2.t3.t19 (cl (= (or (not (tptp.ssList U)) false (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))) (or (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t20 (cl (= (or (not (tptp.ssList U)) (not (= U U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))) (or (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t18 t2.t3.t19))
% 0.38/0.63 (step t2.t3.t21 (cl (= (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U W)) (not (tptp.totalorderedP W)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) (or (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t9 t2.t3.t20))
% 0.38/0.63 (step t2.t3.t22 (cl (= (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U W)) (not (tptp.totalorderedP W)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (or (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y))))))))) :rule cong :premises (t2.t3.t6 t2.t3.t7 t2.t3.t8 t2.t3.t21))
% 0.38/0.63 (step t2.t3.t23 (cl (= (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (or (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y))))))) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule all_simplify)
% 0.38/0.63 (step t2.t3.t24 (cl (= (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U W)) (not (tptp.totalorderedP W)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t22 t2.t3.t23))
% 0.38/0.63 (step t2.t3.t25 (cl (= (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y))))))) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t5 t2.t3.t24))
% 0.38/0.63 (step t2.t3.t26 (cl (= (forall ((W $$unsorted)) (=> (tptp.ssList W) (or (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.totalorderedP W)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.segmentP V W)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq W Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y W)) (not (tptp.totalorderedP Y)))))))) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t4 t2.t3.t25))
% 0.38/0.63 (step t2.t3.t27 (cl (= (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)))))) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) :rule trans :premises (t2.t3.t3 t2.t3.t26))
% 0.38/0.63 (step t2.t3.t28 (cl (= (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U))))))) (=> (tptp.ssList V) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y))))))))) :rule cong :premises (t2.t3.t2 t2.t3.t27))
% 0.38/0.63 (step t2.t3 (cl (= (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)))))))) (forall ((V $$unsorted)) (=> (tptp.ssList V) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))))) :rule bind)
% 0.38/0.63 (step t2.t4 (cl (= (forall ((V $$unsorted)) (=> (tptp.ssList V) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) (forall ((V $$unsorted)) (or (not (tptp.ssList V)) true)))) :rule all_simplify)
% 0.38/0.63 (anchor :step t2.t5 :args ((V $$unsorted) (:= V V)))
% 0.38/0.63 (step t2.t5.t1 (cl (= V V)) :rule refl)
% 0.38/0.63 (step t2.t5.t2 (cl (= (or (not (tptp.ssList V)) true) true)) :rule all_simplify)
% 0.38/0.63 (step t2.t5 (cl (= (forall ((V $$unsorted)) (or (not (tptp.ssList V)) true)) (forall ((V $$unsorted)) true))) :rule bind)
% 0.38/0.63 (step t2.t6 (cl (= (forall ((V $$unsorted)) true) true)) :rule all_simplify)
% 0.38/0.63 (step t2.t7 (cl (= (forall ((V $$unsorted)) (or (not (tptp.ssList V)) true)) true)) :rule trans :premises (t2.t5 t2.t6))
% 0.38/0.63 (step t2.t8 (cl (= (forall ((V $$unsorted)) (=> (tptp.ssList V) (or (not (tptp.neq V tptp.nil)) (tptp.segmentP V U) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.segmentP V U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP V Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y)))))))) true)) :rule trans :premises (t2.t4 t2.t7))
% 0.38/0.63 (step t2.t9 (cl (= (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)))))))) true)) :rule trans :premises (t2.t3 t2.t8))
% 0.38/0.63 (step t2.t10 (cl (= (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U))))))))) (=> (tptp.ssList U) true))) :rule cong :premises (t2.t2 t2.t9))
% 0.38/0.63 (step t2.t11 (cl (= (=> (tptp.ssList U) true) true)) :rule all_simplify)
% 0.38/0.63 (step t2.t12 (cl (= (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U))))))))) true)) :rule trans :premises (t2.t10 t2.t11))
% 0.38/0.63 (step t2 (cl (= (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)))))))))) (forall ((U $$unsorted)) true))) :rule bind)
% 0.38/0.63 (step t3 (cl (= (forall ((U $$unsorted)) true) true)) :rule all_simplify)
% 0.38/0.63 (step t4 (cl (= (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U)))))))))) true)) :rule trans :premises (t2 t3))
% 0.38/0.63 (step t5 (cl (= (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U))))))))))) (not true))) :rule cong :premises (t4))
% 0.38/0.63 (step t6 (cl (= (not true) false)) :rule all_simplify)
% 0.38/0.63 (step t7 (cl (= (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (tptp.segmentP V U))))))))))) false)) :rule trans :premises (t5 t6))
% 0.38/0.63 (step t8 (cl false) :rule resolution :premises (t1 t7 a95))
% 0.38/0.63 (step t9 (cl (not false)) :rule false)
% 0.38/0.63 (step t10 (cl) :rule resolution :premises (t8 t9))
% 0.38/0.63
% 0.38/0.63 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.6ffHEf1MDb/cvc5---1.0.5_8711.smt2
% 0.38/0.64 % cvc5---1.0.5 exiting
% 0.38/0.64 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------