TSTP Solution File: SWV170+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV170+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n021.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 18:04:39 EDT 2024
% Result : Theorem 0.38s 0.58s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SWV170+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% 0.06/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 26 23:42:09 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.35/0.53 %----Proving TF0_NAR, FOF, or CNF
% 0.38/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.38/0.58 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.SjzuhNWLUW/cvc5---1.0.5_5778.smt2
% 0.38/0.58 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.SjzuhNWLUW/cvc5---1.0.5_5778.smt2
% 0.38/0.58 (assume a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))))
% 0.38/0.58 (assume a1 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))))
% 0.38/0.58 (assume a2 (forall ((X $$unsorted)) (not (tptp.gt X X))))
% 0.38/0.58 (assume a3 (forall ((X $$unsorted)) (tptp.leq X X)))
% 0.38/0.58 (assume a4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))
% 0.38/0.58 (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))))
% 0.38/0.58 (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))))
% 0.38/0.58 (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))
% 0.38/0.58 (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))))
% 0.38/0.58 (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))
% 0.38/0.58 (assume a10 (forall ((X $$unsorted)) (tptp.gt (tptp.succ X) X)))
% 0.38/0.58 (assume a11 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq X Y) (tptp.leq X (tptp.succ Y)))))
% 0.38/0.58 (assume a12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X Y) (tptp.gt (tptp.succ Y) X))))
% 0.38/0.58 (assume a13 (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq (tptp.uniform_int_rnd C X) X))))
% 0.38/0.58 (assume a14 (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq tptp.n0 (tptp.uniform_int_rnd C X)))))
% 0.38/0.58 (assume a15 (forall ((I $$unsorted) (L $$unsorted) (U $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim L U) Val) I) Val))))
% 0.38/0.58 (assume a16 (forall ((I $$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))))
% 0.38/0.58 (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)))))))
% 0.38/0.58 (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)))))))
% 0.38/0.58 (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)))))))
% 0.38/0.58 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_madd A B) I J) (tptp.a_select3 (tptp.tptp_madd A B) J I)))))))
% 0.38/0.58 (assume a21 (forall ((A $$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)))))))
% 0.38/0.58 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) I J) (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) J I)))))))
% 0.38/0.58 (assume a23 (forall ((A $$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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) I J) (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) J I)))))))
% 0.38/0.58 (assume a24 (forall ((A $$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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))) I J) (tptp.a_select3 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))) J I)))))))
% 0.38/0.58 (assume a25 (forall ((Body $$unsorted)) (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0)))
% 0.38/0.58 (assume a26 (forall ((Body $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))))
% 0.38/0.58 (assume a27 (= (tptp.succ tptp.tptp_minus_1) tptp.n0))
% 0.38/0.58 (assume a28 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))))
% 0.38/0.58 (assume a29 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))
% 0.38/0.58 (assume a30 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))))
% 0.38/0.58 (assume a31 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))))
% 0.38/0.58 (assume a32 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))))
% 0.38/0.58 (assume a33 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))
% 0.38/0.58 (assume a34 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))
% 0.38/0.58 (assume a35 (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))
% 0.38/0.58 (assume a36 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))
% 0.38/0.58 (assume a37 (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))
% 0.38/0.58 (assume a38 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))
% 0.38/0.58 (assume a39 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))
% 0.38/0.58 (assume a40 (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)))
% 0.38/0.58 (assume a41 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))))
% 0.38/0.58 (assume a42 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.succ X) Y) (tptp.gt Y X))))
% 0.38/0.58 (assume a43 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.minus X Y) X) (tptp.leq tptp.n0 Y))))
% 0.38/0.58 (assume a44 (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) U V) VAL)))
% 0.38/0.58 (assume a45 (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= J V) (= (tptp.a_select3 X U V) VAL)) (= (tptp.a_select3 (tptp.tptp_update3 X I J VAL2) U V) VAL))))
% 0.38/0.58 (assume a46 (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted) (J0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))))
% 0.38/0.58 (assume a47 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)))
% 0.38/0.58 (assume a48 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))))
% 0.38/0.58 (assume a49 (forall ((I $$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))))
% 0.38/0.58 (assume a50 tptp.true)
% 0.38/0.58 (assume a51 (not (= tptp.def tptp.use)))
% 0.38/0.58 (assume a52 (not (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init))) (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init))) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.sigma_init E) tptp.init))) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init))))) (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= (tptp.a_select2 tptp.muold_init J) tptp.init))))))
% 0.38/0.58 (assume a53 (tptp.gt tptp.n5 tptp.n4))
% 0.38/0.58 (assume a54 (tptp.gt tptp.n135299 tptp.n4))
% 0.38/0.58 (assume a55 (tptp.gt tptp.n135299 tptp.n5))
% 0.38/0.58 (assume a56 (tptp.gt tptp.n4 tptp.tptp_minus_1))
% 0.38/0.58 (assume a57 (tptp.gt tptp.n5 tptp.tptp_minus_1))
% 0.38/0.58 (assume a58 (tptp.gt tptp.n135299 tptp.tptp_minus_1))
% 0.38/0.58 (assume a59 (tptp.gt tptp.n0 tptp.tptp_minus_1))
% 0.38/0.58 (assume a60 (tptp.gt tptp.n1 tptp.tptp_minus_1))
% 0.38/0.58 (assume a61 (tptp.gt tptp.n2 tptp.tptp_minus_1))
% 0.38/0.58 (assume a62 (tptp.gt tptp.n3 tptp.tptp_minus_1))
% 0.38/0.58 (assume a63 (tptp.gt tptp.n4 tptp.n0))
% 0.38/0.58 (assume a64 (tptp.gt tptp.n5 tptp.n0))
% 0.38/0.58 (assume a65 (tptp.gt tptp.n135299 tptp.n0))
% 0.38/0.58 (assume a66 (tptp.gt tptp.n1 tptp.n0))
% 0.38/0.58 (assume a67 (tptp.gt tptp.n2 tptp.n0))
% 0.38/0.58 (assume a68 (tptp.gt tptp.n3 tptp.n0))
% 0.38/0.58 (assume a69 (tptp.gt tptp.n4 tptp.n1))
% 0.38/0.58 (assume a70 (tptp.gt tptp.n5 tptp.n1))
% 0.38/0.58 (assume a71 (tptp.gt tptp.n135299 tptp.n1))
% 0.38/0.58 (assume a72 (tptp.gt tptp.n2 tptp.n1))
% 0.38/0.58 (assume a73 (tptp.gt tptp.n3 tptp.n1))
% 0.38/0.58 (assume a74 (tptp.gt tptp.n4 tptp.n2))
% 0.38/0.58 (assume a75 (tptp.gt tptp.n5 tptp.n2))
% 0.38/0.58 (assume a76 (tptp.gt tptp.n135299 tptp.n2))
% 0.38/0.58 (assume a77 (tptp.gt tptp.n3 tptp.n2))
% 0.38/0.58 (assume a78 (tptp.gt tptp.n4 tptp.n3))
% 0.38/0.58 (assume a79 (tptp.gt tptp.n5 tptp.n3))
% 0.38/0.58 (assume a80 (tptp.gt tptp.n135299 tptp.n3))
% 0.38/0.58 (assume a81 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))))
% 0.38/0.58 (assume a82 (forall ((X $$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)))))
% 0.38/0.58 (assume a83 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))
% 0.38/0.58 (assume a84 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))))
% 0.38/0.58 (assume a85 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))))
% 0.38/0.58 (assume a86 (forall ((X $$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)))))
% 0.38/0.58 (assume a87 (= (tptp.succ (tptp.succ (tptp.succ (tptp.succ tptp.n0)))) tptp.n4))
% 0.38/0.58 (assume a88 (= (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ tptp.n0))))) tptp.n5))
% 0.38/0.58 (assume a89 (= (tptp.succ tptp.n0) tptp.n1))
% 0.38/0.58 (assume a90 (= (tptp.succ (tptp.succ tptp.n0)) tptp.n2))
% 0.38/0.58 (assume a91 (= (tptp.succ (tptp.succ (tptp.succ tptp.n0))) tptp.n3))
% 0.38/0.58 (assume a92 true)
% 0.38/0.58 (step t1 (cl (not (= (not (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init))) (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init))) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.sigma_init E) tptp.init))) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init))))) (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= (tptp.a_select2 tptp.muold_init J) tptp.init))))) (not (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))) (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))) (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))) (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))))) (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J)))))))) (not (not (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init))) (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init))) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.sigma_init E) tptp.init))) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init))))) (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= (tptp.a_select2 tptp.muold_init J) tptp.init)))))) (not (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))) (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))) (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))) (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))))) (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J))))))) :rule equiv_pos2)
% 0.38/0.58 (step t2 (cl (= (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv10))) :rule refl)
% 0.38/0.58 (step t3 (cl (= (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv52))) :rule refl)
% 0.38/0.58 (step t4 (cl (= (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.n0 tptp.pv54))) :rule refl)
% 0.38/0.58 (step t5 (cl (= (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv10 tptp.n135299))) :rule refl)
% 0.38/0.58 (step t6 (cl (= (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv52 tptp.n4))) :rule refl)
% 0.38/0.58 (step t7 (cl (= (tptp.leq tptp.pv54 tptp.n4) (tptp.leq tptp.pv54 tptp.n4))) :rule refl)
% 0.38/0.58 (step t8 (cl (= (tptp.gt tptp.loopcounter tptp.n1) (tptp.gt tptp.loopcounter tptp.n1))) :rule refl)
% 0.38/0.58 (anchor :step t9 :args ((A $$unsorted) (:= A A)))
% 0.38/0.58 (step t9.t1 (cl (= A A)) :rule refl)
% 0.38/0.58 (step t9.t2 (cl (= (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)))) :rule refl)
% 0.38/0.58 (anchor :step t9.t3 :args ((B $$unsorted) (:= B B)))
% 0.38/0.58 (step t9.t3.t1 (cl (= B B)) :rule refl)
% 0.38/0.58 (step t9.t3.t2 (cl (= (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)))) :rule refl)
% 0.38/0.58 (step t9.t3.t3 (cl (= (= (tptp.a_select3 tptp.q_init A B) tptp.init) (= tptp.init (tptp.a_select3 tptp.q_init A B)))) :rule all_simplify)
% 0.38/0.58 (step t9.t3.t4 (cl (= (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B))))) :rule cong :premises (t9.t3.t2 t9.t3.t3))
% 0.38/0.58 (step t9.t3 (cl (= (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))))) :rule bind)
% 0.38/0.58 (step t9.t4 (cl (= (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))))) :rule all_simplify)
% 0.38/0.58 (step t9.t5 (cl (= (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))))) :rule trans :premises (t9.t3 t9.t4))
% 0.38/0.58 (step t9.t6 (cl (= (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init)))) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B))))))) :rule cong :premises (t9.t2 t9.t5))
% 0.38/0.58 (step t9 (cl (= (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))))))) :rule bind)
% 0.38/0.58 (step t10 (cl (= (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))))) (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))))))) :rule all_simplify)
% 0.38/0.58 (step t11 (cl (= (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))))) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (or (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155))))))) :rule all_simplify)
% 0.38/0.58 (anchor :step t12 :args ((A $$unsorted) (:= A A) (BOUND_VARIABLE_2155 $$unsorted) (:= BOUND_VARIABLE_2155 BOUND_VARIABLE_2155)))
% 0.38/0.58 (step t12.t1 (cl (= A A)) :rule refl)
% 0.38/0.58 (step t12.t2 (cl (= BOUND_VARIABLE_2155 BOUND_VARIABLE_2155)) :rule refl)
% 0.38/0.58 (step t12.t3 (cl (= (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (or (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155))))) :rule all_simplify)
% 0.38/0.58 (step t12 (cl (= (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (or (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155))))) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))))) :rule bind)
% 0.38/0.58 (step t13 (cl (= (forall ((A $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))))) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))))) :rule trans :premises (t11 t12))
% 0.38/0.58 (step t14 (cl (= (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A B)))))) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))))) :rule trans :premises (t10 t13))
% 0.38/0.58 (step t15 (cl (= (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))))) :rule trans :premises (t9 t14))
% 0.38/0.58 (anchor :step t16 :args ((C $$unsorted) (:= C C)))
% 0.38/0.58 (step t16.t1 (cl (= C C)) :rule refl)
% 0.38/0.58 (step t16.t2 (cl (= (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)))) :rule refl)
% 0.38/0.58 (step t16.t3 (cl (= (= (tptp.a_select2 tptp.rho_init C) tptp.init) (= tptp.init (tptp.a_select2 tptp.rho_init C)))) :rule all_simplify)
% 0.38/0.58 (step t16.t4 (cl (= (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C))))) :rule cong :premises (t16.t2 t16.t3))
% 0.38/0.58 (step t16 (cl (= (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))))) :rule bind)
% 0.38/0.58 (step t17 (cl (= (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))))) :rule all_simplify)
% 0.38/0.58 (step t18 (cl (= (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))))) :rule trans :premises (t16 t17))
% 0.38/0.58 (anchor :step t19 :args ((D $$unsorted) (:= D D)))
% 0.38/0.58 (step t19.t1 (cl (= D D)) :rule refl)
% 0.38/0.58 (step t19.t2 (cl (= (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)))) :rule refl)
% 0.38/0.58 (step t19.t3 (cl (= (= (tptp.a_select2 tptp.mu_init D) tptp.init) (= tptp.init (tptp.a_select2 tptp.mu_init D)))) :rule all_simplify)
% 0.38/0.58 (step t19.t4 (cl (= (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D))))) :rule cong :premises (t19.t2 t19.t3))
% 0.38/0.58 (step t19 (cl (= (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init))) (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))))) :rule bind)
% 0.38/0.58 (step t20 (cl (= (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))) (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))))) :rule all_simplify)
% 0.38/0.58 (step t21 (cl (= (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init))) (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))))) :rule trans :premises (t19 t20))
% 0.38/0.58 (anchor :step t22 :args ((E $$unsorted) (:= E E)))
% 0.38/0.58 (step t22.t1 (cl (= E E)) :rule refl)
% 0.38/0.58 (step t22.t2 (cl (= (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)))) :rule refl)
% 0.38/0.58 (step t22.t3 (cl (= (= (tptp.a_select2 tptp.sigma_init E) tptp.init) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))) :rule all_simplify)
% 0.38/0.58 (step t22.t4 (cl (= (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.sigma_init E) tptp.init)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E))))) :rule cong :premises (t22.t2 t22.t3))
% 0.38/0.58 (step t22 (cl (= (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.sigma_init E) tptp.init))) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))))) :rule bind)
% 0.38/0.58 (step t23 (cl (= (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))) (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))))) :rule all_simplify)
% 0.38/0.58 (step t24 (cl (= (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.sigma_init E) tptp.init))) (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))))) :rule trans :premises (t22 t23))
% 0.38/0.58 (anchor :step t25 :args ((F $$unsorted) (:= F F)))
% 0.38/0.58 (step t25.t1 (cl (= F F)) :rule refl)
% 0.38/0.58 (step t25.t2 (cl (= (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)))) :rule refl)
% 0.38/0.58 (step t25.t3 (cl (= (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))) :rule all_simplify)
% 0.38/0.58 (step t25.t4 (cl (= (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0))))) :rule cong :premises (t25.t2 t25.t3))
% 0.38/0.58 (step t25 (cl (= (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init))) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))))) :rule bind)
% 0.38/0.58 (step t26 (cl (= (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))) (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))))) :rule all_simplify)
% 0.38/0.58 (step t27 (cl (= (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init))) (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))))) :rule trans :premises (t25 t26))
% 0.38/0.58 (anchor :step t28 :args ((G $$unsorted) (:= G G)))
% 0.38/0.58 (step t28.t1 (cl (= G G)) :rule refl)
% 0.38/0.58 (step t28.t2 (cl (= (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)))) :rule refl)
% 0.38/0.58 (step t28.t3 (cl (= (= (tptp.a_select2 tptp.muold_init G) tptp.init) (= tptp.init (tptp.a_select2 tptp.muold_init G)))) :rule all_simplify)
% 0.38/0.58 (step t28.t4 (cl (= (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) :rule cong :premises (t28.t2 t28.t3))
% 0.38/0.58 (step t28 (cl (= (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init))) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))))) :rule bind)
% 0.38/0.58 (step t29 (cl (= (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))))) :rule all_simplify)
% 0.38/0.58 (step t30 (cl (= (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init))) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))))) :rule trans :premises (t28 t29))
% 0.38/0.58 (step t31 (cl (= (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))))) :rule cong :premises (t8 t30))
% 0.38/0.58 (anchor :step t32 :args ((H $$unsorted) (:= H H)))
% 0.38/0.58 (step t32.t1 (cl (= H H)) :rule refl)
% 0.38/0.58 (step t32.t2 (cl (= (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)))) :rule refl)
% 0.38/0.58 (step t32.t3 (cl (= (= (tptp.a_select2 tptp.rhoold_init H) tptp.init) (= tptp.init (tptp.a_select2 tptp.rhoold_init H)))) :rule all_simplify)
% 0.38/0.58 (step t32.t4 (cl (= (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H))))) :rule cong :premises (t32.t2 t32.t3))
% 0.38/0.58 (step t32 (cl (= (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init))) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H)))))) :rule bind)
% 0.38/0.58 (step t33 (cl (= (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H)))) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H)))))) :rule all_simplify)
% 0.38/0.58 (step t34 (cl (= (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init))) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H)))))) :rule trans :premises (t32 t33))
% 0.38/0.58 (step t35 (cl (= (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H))))))) :rule cong :premises (t8 t34))
% 0.38/0.58 (anchor :step t36 :args ((I $$unsorted) (:= I I)))
% 0.38/0.58 (step t36.t1 (cl (= I I)) :rule refl)
% 0.38/0.58 (step t36.t2 (cl (= (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)))) :rule refl)
% 0.38/0.58 (step t36.t3 (cl (= (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))) :rule all_simplify)
% 0.38/0.58 (step t36.t4 (cl (= (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I))))) :rule cong :premises (t36.t2 t36.t3))
% 0.38/0.58 (step t36 (cl (= (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init))) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))))) :rule bind)
% 0.38/0.58 (step t37 (cl (= (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))))) :rule all_simplify)
% 0.38/0.58 (step t38 (cl (= (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init))) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))))) :rule trans :premises (t36 t37))
% 0.38/0.58 (step t39 (cl (= (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I))))))) :rule cong :premises (t8 t38))
% 0.38/0.58 (step t40 (cl (= (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init))) (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init))) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.sigma_init E) tptp.init))) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init))))) (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))) (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))) (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))) (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))))))) :rule cong :premises (t2 t3 t4 t5 t6 t7 t8 t15 t18 t21 t24 t27 t31 t35 t39))
% 0.38/0.58 (anchor :step t41 :args ((J $$unsorted) (:= J J)))
% 0.38/0.58 (step t41.t1 (cl (= J J)) :rule refl)
% 0.38/0.58 (step t41.t2 (cl (= (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)))) :rule refl)
% 0.38/0.58 (step t41.t3 (cl (= (= (tptp.a_select2 tptp.muold_init J) tptp.init) (= tptp.init (tptp.a_select2 tptp.muold_init J)))) :rule all_simplify)
% 0.38/0.58 (step t41.t4 (cl (= (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= (tptp.a_select2 tptp.muold_init J) tptp.init)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J))))) :rule cong :premises (t41.t2 t41.t3))
% 0.38/0.58 (step t41 (cl (= (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= (tptp.a_select2 tptp.muold_init J) tptp.init))) (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J)))))) :rule bind)
% 0.38/0.58 (step t42 (cl (= (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J)))) (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J)))))) :rule all_simplify)
% 0.38/0.58 (step t43 (cl (= (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= (tptp.a_select2 tptp.muold_init J) tptp.init))) (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J)))))) :rule trans :premises (t41 t42))
% 0.38/0.58 (step t44 (cl (= (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init))) (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init))) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.sigma_init E) tptp.init))) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init))))) (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= (tptp.a_select2 tptp.muold_init J) tptp.init)))) (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))) (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))) (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))) (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))))) (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J))))))) :rule cong :premises (t40 t43))
% 0.38/0.58 (step t45 (cl (= (not (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init))) (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init))) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.sigma_init E) tptp.init))) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init))))) (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.n4)) (= (tptp.a_select2 tptp.muold_init J) tptp.init))))) (not (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))) (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))) (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))) (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))))) (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J)))))))) :rule cong :premises (t44))
% 0.38/0.58 (step t46 (cl (not (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))) (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))) (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))) (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I)))))) (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J))))))) :rule resolution :premises (t1 t45 a52))
% 0.38/0.58 (step t47 (cl (not (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J)))))) :rule not_implies2 :premises (t46))
% 0.38/0.58 (step t48 (cl (= (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))) (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J)))))) :rule hole :args ((forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))) (= G J)))
% 0.38/0.58 (step t49 (cl (not (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J))))) :rule equiv1 :premises (t48))
% 0.38/0.58 (step t50 (cl (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J)))) (not (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))))) :rule reordering :premises (t49))
% 0.38/0.58 (step t51 (cl (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.n0 tptp.pv52) (tptp.leq tptp.n0 tptp.pv54) (tptp.leq tptp.pv10 tptp.n135299) (tptp.leq tptp.pv52 tptp.n4) (tptp.leq tptp.pv54 tptp.n4) (tptp.gt tptp.loopcounter tptp.n1) (forall ((A $$unsorted) (BOUND_VARIABLE_2155 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n135299)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2155)) (not (tptp.leq BOUND_VARIABLE_2155 tptp.n4)) (= tptp.init (tptp.a_select3 tptp.q_init A BOUND_VARIABLE_2155)))) (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rho_init C)))) (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n4)) (= tptp.init (tptp.a_select2 tptp.mu_init D)))) (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigma_init E)))) (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F tptp.n4)) (= tptp.init (tptp.a_select3 tptp.center_init F tptp.n0)))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n4)) (= tptp.init (tptp.a_select2 tptp.rhoold_init H))))) (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((I $$unsorted)) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I tptp.n4)) (= tptp.init (tptp.a_select2 tptp.sigmaold_init I))))))) :rule not_implies1 :premises (t46))
% 0.38/0.58 (step t52 (cl (=> (tptp.gt tptp.loopcounter tptp.n1) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))))) :rule and :premises (t51))
% 0.38/0.58 (step t53 (cl (not (tptp.gt tptp.loopcounter tptp.n1)) (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) :rule implies :premises (t52))
% 0.38/0.58 (step t54 (cl (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))) (not (tptp.gt tptp.loopcounter tptp.n1))) :rule reordering :premises (t53))
% 0.38/0.58 (step t55 (cl (tptp.gt tptp.loopcounter tptp.n1)) :rule and :premises (t51))
% 0.38/0.58 (step t56 (cl (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G))))) :rule resolution :premises (t54 t55))
% 0.38/0.59 (step t57 (cl (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init J))))) :rule resolution :premises (t50 t56))
% 0.38/0.59 (step t58 (cl) :rule resolution :premises (t47 t57))
% 0.38/0.59
% 0.38/0.59 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.SjzuhNWLUW/cvc5---1.0.5_5778.smt2
% 0.38/0.59 % cvc5---1.0.5 exiting
% 0.38/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------