%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV154+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% 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 18:04:37 EDT 2024

% Result   : Theorem 0.40s 0.59s
% Output   : Proof 0.43s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem    : SWV154+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% 0.12/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n029.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 26 23:19:39 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.22/0.53  %----Proving TF0_NAR, FOF, or CNF
% 0.40/0.59  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.40/0.59  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.pvtQQeXx8x/cvc5---1.0.5_20552.smt2
% 0.40/0.59  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.pvtQQeXx8x/cvc5---1.0.5_20552.smt2
% 0.40/0.59  (assume a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))))
% 0.40/0.59  (assume a1 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))))
% 0.40/0.59  (assume a2 (forall ((X $$unsorted)) (not (tptp.gt X X))))
% 0.40/0.59  (assume a3 (forall ((X $$unsorted)) (tptp.leq X X)))
% 0.40/0.59  (assume a4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))
% 0.40/0.59  (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))))
% 0.40/0.59  (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))))
% 0.40/0.59  (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))
% 0.40/0.59  (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))))
% 0.40/0.59  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))
% 0.40/0.59  (assume a10 (forall ((X $$unsorted)) (tptp.gt (tptp.succ X) X)))
% 0.40/0.59  (assume a11 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq X Y) (tptp.leq X (tptp.succ Y)))))
% 0.40/0.59  (assume a12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X Y) (tptp.gt (tptp.succ Y) X))))
% 0.40/0.59  (assume a13 (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq (tptp.uniform_int_rnd C X) X))))
% 0.40/0.59  (assume a14 (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq tptp.n0 (tptp.uniform_int_rnd C X)))))
% 0.40/0.59  (assume a15 (forall ((I $$unsorted) (L $$unsorted) (U $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim L U) Val) I) Val))))
% 0.40/0.59  (assume a16 (forall ((I $$unsorted) (L1 $$unsorted) (U1 $$unsorted) (J $$unsorted) (L2 $$unsorted) (U2 $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L1 I) (tptp.leq I U1) (tptp.leq L2 J) (tptp.leq J U2)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim L1 U1) (tptp.dim L2 U2) Val) I J) Val))))
% 0.40/0.59  (assume a17 (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.trans A) I J) (tptp.a_select3 (tptp.trans A) J I)))))))
% 0.40/0.59  (assume a18 (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.inv A) I J) (tptp.a_select3 (tptp.inv A) J I)))))))
% 0.40/0.59  (assume a19 (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted) (VAL $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N) (tptp.leq tptp.n0 K) (tptp.leq K N)) (= (tptp.a_select3 (tptp.tptp_update3 A K K VAL) I J) (tptp.a_select3 (tptp.tptp_update3 A K K VAL) J I)))))))
% 0.40/0.59  (assume a20 (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_madd A B) I J) (tptp.a_select3 (tptp.tptp_madd A B) J I)))))))
% 0.40/0.59  (assume a21 (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_msub A B) I J) (tptp.a_select3 (tptp.tptp_msub A B) J I)))))))
% 0.40/0.59  (assume a22 (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) I J) (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) J I)))))))
% 0.40/0.59  (assume a23 (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) I J) (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) J I)))))))
% 0.40/0.59  (assume a24 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 D I J) (tptp.a_select3 D J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 F I J) (tptp.a_select3 F J I))))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))) I J) (tptp.a_select3 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))) J I)))))))
% 0.40/0.59  (assume a25 (forall ((Body $$unsorted)) (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0)))
% 0.40/0.59  (assume a26 (forall ((Body $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))))
% 0.40/0.59  (assume a27 (= (tptp.succ tptp.tptp_minus_1) tptp.n0))
% 0.40/0.59  (assume a28 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))))
% 0.40/0.59  (assume a29 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))
% 0.40/0.59  (assume a30 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))))
% 0.40/0.59  (assume a31 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))))
% 0.40/0.59  (assume a32 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))))
% 0.40/0.59  (assume a33 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))
% 0.40/0.59  (assume a34 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))
% 0.40/0.59  (assume a35 (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))
% 0.40/0.59  (assume a36 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))
% 0.40/0.59  (assume a37 (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))
% 0.40/0.59  (assume a38 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))
% 0.40/0.59  (assume a39 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))
% 0.40/0.59  (assume a40 (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)))
% 0.40/0.59  (assume a41 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))))
% 0.40/0.59  (assume a42 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.succ X) Y) (tptp.gt Y X))))
% 0.40/0.59  (assume a43 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.minus X Y) X) (tptp.leq tptp.n0 Y))))
% 0.40/0.59  (assume a44 (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) U V) VAL)))
% 0.40/0.59  (assume a45 (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= J V) (= (tptp.a_select3 X U V) VAL)) (= (tptp.a_select3 (tptp.tptp_update3 X I J VAL2) U V) VAL))))
% 0.40/0.59  (assume a46 (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted) (J0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))))
% 0.40/0.59  (assume a47 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)))
% 0.40/0.59  (assume a48 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))))
% 0.40/0.59  (assume a49 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq I0 U)) (= (tptp.a_select2 X I0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) I) VAL))))
% 0.40/0.59  (assume a50 tptp.true)
% 0.40/0.59  (assume a51 (not (= tptp.def tptp.use)))
% 0.40/0.59  (assume a52 (not (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1)))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.pv12)) (=> (= tptp.pv12 C) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))))))
% 0.40/0.59  (assume a53 (tptp.gt tptp.n5 tptp.n4))
% 0.40/0.59  (assume a54 (tptp.gt tptp.n135299 tptp.n4))
% 0.40/0.59  (assume a55 (tptp.gt tptp.n135299 tptp.n5))
% 0.40/0.59  (assume a56 (tptp.gt tptp.n4 tptp.tptp_minus_1))
% 0.40/0.59  (assume a57 (tptp.gt tptp.n5 tptp.tptp_minus_1))
% 0.40/0.59  (assume a58 (tptp.gt tptp.n135299 tptp.tptp_minus_1))
% 0.40/0.59  (assume a59 (tptp.gt tptp.n0 tptp.tptp_minus_1))
% 0.40/0.59  (assume a60 (tptp.gt tptp.n1 tptp.tptp_minus_1))
% 0.40/0.59  (assume a61 (tptp.gt tptp.n2 tptp.tptp_minus_1))
% 0.40/0.59  (assume a62 (tptp.gt tptp.n3 tptp.tptp_minus_1))
% 0.40/0.59  (assume a63 (tptp.gt tptp.n4 tptp.n0))
% 0.40/0.59  (assume a64 (tptp.gt tptp.n5 tptp.n0))
% 0.40/0.59  (assume a65 (tptp.gt tptp.n135299 tptp.n0))
% 0.40/0.59  (assume a66 (tptp.gt tptp.n1 tptp.n0))
% 0.40/0.59  (assume a67 (tptp.gt tptp.n2 tptp.n0))
% 0.40/0.59  (assume a68 (tptp.gt tptp.n3 tptp.n0))
% 0.40/0.59  (assume a69 (tptp.gt tptp.n4 tptp.n1))
% 0.40/0.59  (assume a70 (tptp.gt tptp.n5 tptp.n1))
% 0.40/0.59  (assume a71 (tptp.gt tptp.n135299 tptp.n1))
% 0.40/0.59  (assume a72 (tptp.gt tptp.n2 tptp.n1))
% 0.40/0.59  (assume a73 (tptp.gt tptp.n3 tptp.n1))
% 0.40/0.59  (assume a74 (tptp.gt tptp.n4 tptp.n2))
% 0.40/0.59  (assume a75 (tptp.gt tptp.n5 tptp.n2))
% 0.40/0.59  (assume a76 (tptp.gt tptp.n135299 tptp.n2))
% 0.40/0.59  (assume a77 (tptp.gt tptp.n3 tptp.n2))
% 0.40/0.59  (assume a78 (tptp.gt tptp.n4 tptp.n3))
% 0.40/0.59  (assume a79 (tptp.gt tptp.n5 tptp.n3))
% 0.40/0.59  (assume a80 (tptp.gt tptp.n135299 tptp.n3))
% 0.40/0.59  (assume a81 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))))
% 0.40/0.59  (assume a82 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n5)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5)))))
% 0.40/0.59  (assume a83 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))
% 0.40/0.59  (assume a84 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))))
% 0.40/0.59  (assume a85 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))))
% 0.40/0.59  (assume a86 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n3)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3)))))
% 0.40/0.59  (assume a87 (= (tptp.succ (tptp.succ (tptp.succ (tptp.succ tptp.n0)))) tptp.n4))
% 0.40/0.59  (assume a88 (= (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ tptp.n0))))) tptp.n5))
% 0.40/0.59  (assume a89 (= (tptp.succ tptp.n0) tptp.n1))
% 0.40/0.59  (assume a90 (= (tptp.succ (tptp.succ tptp.n0)) tptp.n2))
% 0.40/0.59  (assume a91 (= (tptp.succ (tptp.succ (tptp.succ tptp.n0))) tptp.n3))
% 0.40/0.59  (assume a92 true)
% 0.40/0.59  (step t1 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) :rule implies_neg1)
% 0.40/0.59  (anchor :step t2)
% 0.40/0.59  (assume t2.a0 (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))
% 0.40/0.59  (step t2.t1 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) :rule implies_neg1)
% 0.40/0.59  (anchor :step t2.t2)
% 0.40/0.59  (assume t2.t2.a0 (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))
% 0.40/0.59  (step t2.t2.t1 (cl (= (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) :rule refl)
% 0.40/0.59  (step t2.t2.t2 (cl (= (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))) tptp.pv70)) :rule symm :premises (t2.t2.a0))
% 0.40/0.59  (step t2.t2.t3 (cl (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) :rule symm :premises (t2.t2.t2))
% 0.40/0.59  (step t2.t2.t4 (cl (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule cong :premises (t2.t2.t1 t2.t2.t3))
% 0.40/0.59  (step t2.t2 (cl (not (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule subproof :discharge (t2.t2.a0))
% 0.40/0.59  (step t2.t3 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule resolution :premises (t2.t1 t2.t2))
% 0.40/0.59  (step t2.t4 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (not (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) :rule implies_neg2)
% 0.40/0.59  (step t2.t5 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) :rule resolution :premises (t2.t3 t2.t4))
% 0.40/0.59  (step t2.t6 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) :rule contraction :premises (t2.t5))
% 0.40/0.59  (step t2.t7 (cl (not (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule implies :premises (t2.t6))
% 0.40/0.59  (step t2.t8 (cl (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule resolution :premises (t2.t7 t2.a0))
% 0.40/0.59  (step t2 (cl (not (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule subproof :discharge (t2.a0))
% 0.40/0.59  (step t3 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule resolution :premises (t1 t2))
% 0.40/0.59  (step t4 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (not (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) :rule implies_neg2)
% 0.40/0.59  (step t5 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) :rule resolution :premises (t3 t4))
% 0.40/0.59  (step t6 (cl (=> (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) :rule contraction :premises (t5))
% 0.40/0.59  (step t7 (cl (not (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule implies :premises (t6))
% 0.40/0.59  (step t8 (cl (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) (not (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule reordering :premises (t7))
% 0.40/0.59  (step t9 (cl (not (= (not (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1)))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.pv12)) (=> (= tptp.pv12 C) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))))) (not (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))))) (not (not (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1)))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.pv12)) (=> (= tptp.pv12 C) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))))))) (not (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))))) :rule equiv_pos2)
% 0.40/0.59  (step t10 (cl (= (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) :rule refl)
% 0.40/0.59  (step t11 (cl (= (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv10))) :rule refl)
% 0.40/0.59  (step t12 (cl (= (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.n0 tptp.pv12))) :rule refl)
% 0.40/0.59  (step t13 (cl (= (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv10 tptp.n135299))) :rule refl)
% 0.40/0.59  (step t14 (cl (= (tptp.leq tptp.pv12 tptp.n4) (tptp.leq tptp.pv12 tptp.n4))) :rule refl)
% 0.40/0.59  (step t15 (cl (= (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))))) :rule all_simplify)
% 0.40/0.59  (anchor :step t16 :args ((B $$unsorted) (:= B B)))
% 0.40/0.59  (step t16.t1 (cl (= B B)) :rule refl)
% 0.40/0.59  (step t16.t2 (cl (= (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))))) :rule refl)
% 0.40/0.59  (step t16.t3 (cl (= (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index))))) :rule all_simplify)
% 0.40/0.59  (step t16.t4 (cl (= (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)))))) :rule cong :premises (t16.t2 t16.t3))
% 0.40/0.59  (step t16 (cl (= (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1))) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index))))))) :rule bind)
% 0.40/0.59  (step t17 (cl (= (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index))))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index))))))) :rule all_simplify)
% 0.40/0.59  (step t18 (cl (= (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index))))))) :rule trans :premises (t16 t17))
% 0.40/0.59  (step t19 (cl (= (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1)))) (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)))))))) :rule cong :premises (t10 t11 t12 t13 t14 t15 t18))
% 0.40/0.59  (step t20 (cl (= (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.pv12)) (=> (= tptp.pv12 C) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.pv12)) (not (= tptp.pv12 C)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))))) :rule all_simplify)
% 0.40/0.59  (step t21 (cl (= (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.pv12)) (not (= tptp.pv12 C)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (not (= tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))) :rule all_simplify)
% 0.40/0.59  (step t22 (cl (= (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.n0 tptp.pv12)))) :rule refl)
% 0.40/0.59  (step t23 (cl (= (not (tptp.leq tptp.pv12 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)))) :rule refl)
% 0.40/0.59  (step t24 (cl (= (= tptp.pv12 tptp.pv12) true)) :rule all_simplify)
% 0.40/0.59  (step t25 (cl (= (not (= tptp.pv12 tptp.pv12)) (not true))) :rule cong :premises (t24))
% 0.40/0.59  (step t26 (cl (= (not true) false)) :rule all_simplify)
% 0.40/0.59  (step t27 (cl (= (not (= tptp.pv12 tptp.pv12)) false)) :rule trans :premises (t25 t26))
% 0.40/0.59  (step t28 (cl (= (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) :rule refl)
% 0.40/0.59  (step t29 (cl (= (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (not (= tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) false (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))) :rule cong :premises (t22 t23 t27 t28))
% 0.40/0.59  (step t30 (cl (= (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) false (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))) :rule all_simplify)
% 0.40/0.59  (step t31 (cl (= (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (not (= tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))) :rule trans :premises (t29 t30))
% 0.40/0.59  (step t32 (cl (= (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.pv12)) (not (= tptp.pv12 C)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))) :rule trans :premises (t21 t31))
% 0.40/0.59  (step t33 (cl (= (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.pv12)) (=> (= tptp.pv12 C) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))) :rule trans :premises (t20 t32))
% 0.40/0.59  (step t34 (cl (= (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1)))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.pv12)) (=> (= tptp.pv12 C) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))))) (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))))) :rule cong :premises (t19 t33))
% 0.40/0.59  (step t35 (cl (= (not (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1)))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.pv12)) (=> (= tptp.pv12 C) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))))) (not (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))))) :rule cong :premises (t34))
% 0.40/0.59  (step t36 (cl (not (=> (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)))))) (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))))) :rule resolution :premises (t9 t35 a52))
% 0.43/0.60  (step t37 (cl (not (or (not (tptp.leq tptp.n0 tptp.pv12)) (not (tptp.leq tptp.pv12 tptp.pv12)) (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))))))) :rule not_implies2 :premises (t36))
% 0.43/0.60  (step t38 (cl (not (= (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) tptp.pv70) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.pv12 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) :rule not_or :premises (t37))
% 0.43/0.60  (step t39 (cl (and (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))))) (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv12) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv12 tptp.n4) (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B (tptp.pred tptp.pv10))) (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index))))))) :rule not_implies1 :premises (t36))
% 0.43/0.60  (step t40 (cl (= tptp.pv70 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)) (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) (tptp.a_select2 tptp.x tptp.pv10))))))) :rule and :premises (t39))
% 0.43/0.60  (step t41 (cl) :rule resolution :premises (t8 t38 t40))
% 0.43/0.60  
% 0.43/0.60  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.pvtQQeXx8x/cvc5---1.0.5_20552.smt2
% 0.43/0.60  % cvc5---1.0.5 exiting
% 0.43/0.60  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------