TSTP Solution File: SWV102+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV102+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n014.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 18:04:30 EDT 2024
% Result : Theorem 0.43s 0.63s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWV102+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% 0.09/0.12 % Command : do_cvc5 %s %d
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 26 23:48:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.46 %----Proving TF0_NAR, FOF, or CNF
% 0.43/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.43/0.63 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.CawmDznP3G/cvc5---1.0.5_15642.smt2
% 0.43/0.63 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.CawmDznP3G/cvc5---1.0.5_15642.smt2
% 0.43/0.63 (assume a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))))
% 0.43/0.63 (assume a1 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))))
% 0.43/0.63 (assume a2 (forall ((X $$unsorted)) (not (tptp.gt X X))))
% 0.43/0.63 (assume a3 (forall ((X $$unsorted)) (tptp.leq X X)))
% 0.43/0.63 (assume a4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))
% 0.43/0.63 (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))))
% 0.43/0.63 (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))))
% 0.43/0.63 (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))
% 0.43/0.63 (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))))
% 0.43/0.63 (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))
% 0.43/0.63 (assume a10 (forall ((X $$unsorted)) (tptp.gt (tptp.succ X) X)))
% 0.43/0.63 (assume a11 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq X Y) (tptp.leq X (tptp.succ Y)))))
% 0.43/0.63 (assume a12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X Y) (tptp.gt (tptp.succ Y) X))))
% 0.43/0.63 (assume a13 (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq (tptp.uniform_int_rnd C X) X))))
% 0.43/0.63 (assume a14 (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq tptp.n0 (tptp.uniform_int_rnd C X)))))
% 0.43/0.63 (assume a15 (forall ((I $$unsorted) (L $$unsorted) (U $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim L U) Val) I) Val))))
% 0.43/0.63 (assume a16 (forall ((I $$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))))
% 0.43/0.63 (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)))))))
% 0.43/0.63 (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)))))))
% 0.43/0.63 (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)))))))
% 0.43/0.63 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_madd A B) I J) (tptp.a_select3 (tptp.tptp_madd A B) J I)))))))
% 0.43/0.63 (assume a21 (forall ((A $$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)))))))
% 0.43/0.63 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) I J) (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) J I)))))))
% 0.43/0.63 (assume a23 (forall ((A $$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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) I J) (tptp.a_select3 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))) J I)))))))
% 0.43/0.63 (assume a24 (forall ((A $$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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))) I J) (tptp.a_select3 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))) J I)))))))
% 0.43/0.63 (assume a25 (forall ((Body $$unsorted)) (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0)))
% 0.43/0.63 (assume a26 (forall ((Body $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))))
% 0.43/0.63 (assume a27 (= (tptp.succ tptp.tptp_minus_1) tptp.n0))
% 0.43/0.63 (assume a28 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))))
% 0.43/0.63 (assume a29 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))
% 0.43/0.63 (assume a30 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))))
% 0.43/0.63 (assume a31 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))))
% 0.43/0.63 (assume a32 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))))
% 0.43/0.63 (assume a33 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))
% 0.43/0.63 (assume a34 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))
% 0.43/0.63 (assume a35 (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))
% 0.43/0.63 (assume a36 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))
% 0.43/0.63 (assume a37 (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))
% 0.43/0.63 (assume a38 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))
% 0.43/0.63 (assume a39 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))
% 0.43/0.63 (assume a40 (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)))
% 0.43/0.63 (assume a41 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))))
% 0.43/0.63 (assume a42 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.succ X) Y) (tptp.gt Y X))))
% 0.43/0.63 (assume a43 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.minus X Y) X) (tptp.leq tptp.n0 Y))))
% 0.43/0.63 (assume a44 (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) U V) VAL)))
% 0.43/0.63 (assume a45 (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= J V) (= (tptp.a_select3 X U V) VAL)) (= (tptp.a_select3 (tptp.tptp_update3 X I J VAL2) U V) VAL))))
% 0.43/0.63 (assume a46 (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted) (J0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))))
% 0.43/0.63 (assume a47 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)))
% 0.43/0.63 (assume a48 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))))
% 0.43/0.63 (assume a49 (forall ((I $$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))))
% 0.43/0.63 (assume a50 tptp.true)
% 0.43/0.63 (assume a51 (not (= tptp.def tptp.use)))
% 0.43/0.63 (assume a52 (not (=> (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use)) (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) tptp.use)))))
% 0.43/0.63 (assume a53 (tptp.gt tptp.n5 tptp.n4))
% 0.43/0.63 (assume a54 (tptp.gt tptp.n4 tptp.tptp_minus_1))
% 0.43/0.63 (assume a55 (tptp.gt tptp.n5 tptp.tptp_minus_1))
% 0.43/0.63 (assume a56 (tptp.gt tptp.n0 tptp.tptp_minus_1))
% 0.43/0.63 (assume a57 (tptp.gt tptp.n1 tptp.tptp_minus_1))
% 0.43/0.63 (assume a58 (tptp.gt tptp.n2 tptp.tptp_minus_1))
% 0.43/0.63 (assume a59 (tptp.gt tptp.n3 tptp.tptp_minus_1))
% 0.43/0.63 (assume a60 (tptp.gt tptp.n4 tptp.n0))
% 0.43/0.63 (assume a61 (tptp.gt tptp.n5 tptp.n0))
% 0.43/0.63 (assume a62 (tptp.gt tptp.n1 tptp.n0))
% 0.43/0.63 (assume a63 (tptp.gt tptp.n2 tptp.n0))
% 0.43/0.63 (assume a64 (tptp.gt tptp.n3 tptp.n0))
% 0.43/0.63 (assume a65 (tptp.gt tptp.n4 tptp.n1))
% 0.43/0.63 (assume a66 (tptp.gt tptp.n5 tptp.n1))
% 0.43/0.63 (assume a67 (tptp.gt tptp.n2 tptp.n1))
% 0.43/0.63 (assume a68 (tptp.gt tptp.n3 tptp.n1))
% 0.43/0.63 (assume a69 (tptp.gt tptp.n4 tptp.n2))
% 0.43/0.63 (assume a70 (tptp.gt tptp.n5 tptp.n2))
% 0.43/0.63 (assume a71 (tptp.gt tptp.n3 tptp.n2))
% 0.43/0.63 (assume a72 (tptp.gt tptp.n4 tptp.n3))
% 0.43/0.63 (assume a73 (tptp.gt tptp.n5 tptp.n3))
% 0.43/0.63 (assume a74 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))))
% 0.43/0.63 (assume a75 (forall ((X $$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)))))
% 0.43/0.63 (assume a76 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))
% 0.43/0.63 (assume a77 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))))
% 0.43/0.63 (assume a78 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))))
% 0.43/0.63 (assume a79 (forall ((X $$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)))))
% 0.43/0.63 (assume a80 (= (tptp.succ (tptp.succ (tptp.succ (tptp.succ tptp.n0)))) tptp.n4))
% 0.43/0.63 (assume a81 (= (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ tptp.n0))))) tptp.n5))
% 0.43/0.63 (assume a82 (= (tptp.succ tptp.n0) tptp.n1))
% 0.43/0.63 (assume a83 (= (tptp.succ (tptp.succ tptp.n0)) tptp.n2))
% 0.43/0.63 (assume a84 (= (tptp.succ (tptp.succ (tptp.succ tptp.n0))) tptp.n3))
% 0.43/0.63 (assume a85 true)
% 0.43/0.63 (step t1 (cl (not (= (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.n0 tptp.n2) (not (= tptp.n0 tptp.n1))))) (not (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1)))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.n0 tptp.n2) (not (= tptp.n0 tptp.n1)))) :rule equiv_pos2)
% 0.43/0.63 (step t2 (cl (= (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))))) :rule refl)
% 0.43/0.63 (step t3 (cl (= (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n1 (tptp.succ tptp.n0))))) :rule refl)
% 0.43/0.63 (step t4 (cl (= (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))))) :rule refl)
% 0.43/0.63 (step t5 (cl (= (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))))) :rule refl)
% 0.43/0.63 (step t6 (cl (= (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))))) :rule refl)
% 0.43/0.63 (step t7 (cl (= (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))))) :rule refl)
% 0.43/0.63 (step t8 (cl (= (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))))) :rule refl)
% 0.43/0.63 (step t9 (cl (= (= (= (not (not (= tptp.n0 tptp.n2))) (= tptp.n0 tptp.n2)) true) (= (not (not (= tptp.n0 tptp.n2))) (= tptp.n0 tptp.n2)))) :rule equiv_simplify)
% 0.43/0.63 (step t10 (cl (not (= (= (not (not (= tptp.n0 tptp.n2))) (= tptp.n0 tptp.n2)) true)) (= (not (not (= tptp.n0 tptp.n2))) (= tptp.n0 tptp.n2))) :rule equiv1 :premises (t9))
% 0.43/0.63 (step t11 (cl (= (= (not (not (= tptp.n0 tptp.n2))) (= tptp.n0 tptp.n2)) (= (= tptp.n0 tptp.n2) (not (not (= tptp.n0 tptp.n2)))))) :rule all_simplify)
% 0.43/0.63 (step t12 (cl (= (= tptp.n0 tptp.n2) (= tptp.n0 tptp.n2))) :rule refl)
% 0.43/0.63 (step t13 (cl (= (not (not (= tptp.n0 tptp.n2))) (= tptp.n0 tptp.n2))) :rule all_simplify)
% 0.43/0.63 (step t14 (cl (= (= (= tptp.n0 tptp.n2) (not (not (= tptp.n0 tptp.n2)))) (= (= tptp.n0 tptp.n2) (= tptp.n0 tptp.n2)))) :rule cong :premises (t12 t13))
% 0.43/0.63 (step t15 (cl (= (= (= tptp.n0 tptp.n2) (= tptp.n0 tptp.n2)) true)) :rule all_simplify)
% 0.43/0.63 (step t16 (cl (= (= (= tptp.n0 tptp.n2) (not (not (= tptp.n0 tptp.n2)))) true)) :rule trans :premises (t14 t15))
% 0.43/0.63 (step t17 (cl (= (= (not (not (= tptp.n0 tptp.n2))) (= tptp.n0 tptp.n2)) true)) :rule trans :premises (t11 t16))
% 0.43/0.63 (step t18 (cl (= (not (not (= tptp.n0 tptp.n2))) (= tptp.n0 tptp.n2))) :rule resolution :premises (t10 t17))
% 0.43/0.63 (step t19 (cl (= (not (= tptp.n0 tptp.n1)) (not (= tptp.n0 tptp.n1)))) :rule refl)
% 0.43/0.63 (step t20 (cl (= (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.n0 tptp.n2) (not (= tptp.n0 tptp.n1))))) :rule cong :premises (t2 t3 t4 t5 t6 t7 t8 t18 t19))
% 0.43/0.63 (step t21 (cl (not (= (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))))) (not (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)))) :rule equiv_pos2)
% 0.43/0.63 (step t22 (cl (= (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)))) :rule refl)
% 0.43/0.63 (step t23 (cl (= (= (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))))) :rule equiv_simplify)
% 0.43/0.63 (step t24 (cl (= (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false) (not (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))))) :rule equiv2 :premises (t23))
% 0.43/0.63 (step t25 (cl (not (not (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))))) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) :rule not_not)
% 0.43/0.63 (step t26 (cl (= (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) :rule resolution :premises (t24 t25))
% 0.43/0.63 (step t27 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) :rule implies_neg1)
% 0.43/0.63 (anchor :step t28)
% 0.43/0.63 (assume t28.a0 (= tptp.n0 (tptp.succ tptp.tptp_minus_1)))
% 0.43/0.63 (assume t28.a1 (= tptp.n0 tptp.n1))
% 0.43/0.63 (assume t28.a2 (= tptp.tptp_minus_1 tptp.n1))
% 0.43/0.63 (assume t28.a3 (= tptp.tptp_minus_1 tptp.n2))
% 0.43/0.63 (assume t28.a4 (not (= tptp.n0 tptp.n2)))
% 0.43/0.63 (step t28.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 0.43/0.63 (step t28.t2 (cl (= (= false true) false)) :rule all_simplify)
% 0.43/0.63 (step t28.t3 (cl (= (= (= tptp.n0 tptp.n2) false) (not (= tptp.n0 tptp.n2)))) :rule equiv_simplify)
% 0.43/0.63 (step t28.t4 (cl (= (= tptp.n0 tptp.n2) false) (not (not (= tptp.n0 tptp.n2)))) :rule equiv2 :premises (t28.t3))
% 0.43/0.63 (step t28.t5 (cl (not (not (not (= tptp.n0 tptp.n2)))) (= tptp.n0 tptp.n2)) :rule not_not)
% 0.43/0.63 (step t28.t6 (cl (= (= tptp.n0 tptp.n2) false) (= tptp.n0 tptp.n2)) :rule resolution :premises (t28.t4 t28.t5))
% 0.43/0.63 (step t28.t7 (cl (= (= tptp.n0 tptp.n2) false)) :rule resolution :premises (t28.t6 t28.a4))
% 0.43/0.63 (step t28.t8 (cl (= false (= tptp.n0 tptp.n2))) :rule symm :premises (t28.t7))
% 0.43/0.63 (step t28.t9 (cl (= (= (= tptp.n0 tptp.n2) true) (= tptp.n0 tptp.n2))) :rule equiv_simplify)
% 0.43/0.63 (step t28.t10 (cl (= (= tptp.n0 tptp.n2) true) (not (= tptp.n0 tptp.n2))) :rule equiv2 :premises (t28.t9))
% 0.43/0.63 (step t28.t11 (cl (= (tptp.succ tptp.tptp_minus_1) tptp.n0)) :rule symm :premises (t28.a0))
% 0.43/0.63 (step t28.t12 (cl (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) :rule symm :premises (t28.t11))
% 0.43/0.63 (step t28.t13 (cl (= tptp.n2 tptp.tptp_minus_1)) :rule symm :premises (t28.a3))
% 0.43/0.63 (step t28.t14 (cl (= tptp.n1 tptp.tptp_minus_1)) :rule symm :premises (t28.a2))
% 0.43/0.63 (step t28.t15 (cl (= tptp.tptp_minus_1 tptp.n1)) :rule symm :premises (t28.t14))
% 0.43/0.63 (step t28.t16 (cl (= tptp.n1 tptp.n0)) :rule symm :premises (t28.a1))
% 0.43/0.63 (step t28.t17 (cl (= tptp.n2 (tptp.succ tptp.tptp_minus_1))) :rule trans :premises (t28.t13 t28.t15 t28.t16 t28.t12))
% 0.43/0.63 (step t28.t18 (cl (= (tptp.succ tptp.tptp_minus_1) tptp.n2)) :rule symm :premises (t28.t17))
% 0.43/0.63 (step t28.t19 (cl (= tptp.n0 tptp.n2)) :rule trans :premises (t28.t12 t28.t18))
% 0.43/0.63 (step t28.t20 (cl (= (= tptp.n0 tptp.n2) true)) :rule resolution :premises (t28.t10 t28.t19))
% 0.43/0.63 (step t28.t21 (cl (= false true)) :rule trans :premises (t28.t8 t28.t20))
% 0.43/0.63 (step t28.t22 (cl false) :rule resolution :premises (t28.t1 t28.t2 t28.t21))
% 0.43/0.63 (step t28 (cl (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n1)) (not (= tptp.tptp_minus_1 tptp.n1)) (not (= tptp.tptp_minus_1 tptp.n2)) (not (not (= tptp.n0 tptp.n2))) false) :rule subproof :discharge (t28.a0 t28.a1 t28.a2 t28.a3 t28.a4))
% 0.43/0.63 (step t29 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) :rule and_pos)
% 0.43/0.63 (step t30 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (= tptp.n0 tptp.n1)) :rule and_pos)
% 0.43/0.63 (step t31 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (= tptp.tptp_minus_1 tptp.n1)) :rule and_pos)
% 0.43/0.63 (step t32 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (= tptp.tptp_minus_1 tptp.n2)) :rule and_pos)
% 0.43/0.63 (step t33 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (= tptp.n0 tptp.n2))) :rule and_pos)
% 0.43/0.63 (step t34 (cl false (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))))) :rule resolution :premises (t28 t29 t30 t31 t32 t33))
% 0.43/0.63 (step t35 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) false) :rule reordering :premises (t34))
% 0.43/0.63 (step t36 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) false) :rule contraction :premises (t35))
% 0.43/0.63 (step t37 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false) false) :rule resolution :premises (t27 t36))
% 0.43/0.63 (step t38 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false) (not false)) :rule implies_neg2)
% 0.43/0.63 (step t39 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false) (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false)) :rule resolution :premises (t37 t38))
% 0.43/0.63 (step t40 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false)) :rule contraction :premises (t39))
% 0.43/0.63 (step t41 (cl (= (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))))) :rule implies_simplify)
% 0.43/0.63 (step t42 (cl (not (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false)) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))))) :rule equiv1 :premises (t41))
% 0.43/0.63 (step t43 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))))) :rule resolution :premises (t40 t42))
% 0.43/0.63 (step t44 (cl (= (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) false)) :rule resolution :premises (t26 t43))
% 0.43/0.63 (step t45 (cl (= (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) false))) :rule cong :premises (t22 t44))
% 0.43/0.63 (step t46 (cl (= (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) false) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))))) :rule all_simplify)
% 0.43/0.63 (step t47 (cl (= (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))))) :rule trans :premises (t45 t46))
% 0.43/0.63 (step t48 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) :rule implies_neg1)
% 0.43/0.63 (anchor :step t49)
% 0.43/0.63 (assume t49.a0 (= tptp.n0 (tptp.succ tptp.tptp_minus_1)))
% 0.43/0.63 (assume t49.a1 (= tptp.n1 (tptp.succ tptp.n0)))
% 0.43/0.63 (assume t49.a2 (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))))
% 0.43/0.63 (assume t49.a3 (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)))
% 0.43/0.63 (assume t49.a4 (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)))
% 0.43/0.63 (assume t49.a5 (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))))
% 0.43/0.63 (assume t49.a6 (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))
% 0.43/0.63 (assume t49.a7 (not (= tptp.n0 tptp.n2)))
% 0.43/0.63 (assume t49.a8 (= tptp.n0 tptp.n1))
% 0.43/0.63 (step t49.t1 (cl (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n1)) (not (= tptp.tptp_minus_1 tptp.n1)) (not (= tptp.tptp_minus_1 tptp.n2)) (not (not (= tptp.n0 tptp.n2)))) :rule and_neg)
% 0.43/0.63 (step t49.t2 (cl (=> (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n1)) (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule implies_neg1)
% 0.43/0.63 (anchor :step t49.t3)
% 0.43/0.63 (assume t49.t3.a0 (= tptp.n0 tptp.n1))
% 0.43/0.63 (assume t49.t3.a1 (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))))
% 0.43/0.63 (assume t49.t3.a2 (= tptp.n1 (tptp.succ tptp.n0)))
% 0.43/0.63 (assume t49.t3.a3 (= tptp.n0 (tptp.succ tptp.tptp_minus_1)))
% 0.43/0.63 (assume t49.t3.a4 (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))
% 0.43/0.63 (step t49.t3.t1 (cl (= (tptp.pred (tptp.succ tptp.tptp_minus_1)) tptp.tptp_minus_1)) :rule symm :premises (t49.t3.a4))
% 0.43/0.63 (step t49.t3.t2 (cl (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule symm :premises (t49.t3.t1))
% 0.43/0.63 (step t49.t3.t3 (cl (= (tptp.succ tptp.tptp_minus_1) tptp.n0)) :rule symm :premises (t49.t3.a3))
% 0.43/0.63 (step t49.t3.t4 (cl (= (tptp.pred (tptp.succ tptp.tptp_minus_1)) (tptp.pred tptp.n0))) :rule cong :premises (t49.t3.t3))
% 0.43/0.63 (step t49.t3.t5 (cl (= tptp.n1 tptp.n0)) :rule symm :premises (t49.t3.a0))
% 0.43/0.63 (step t49.t3.t6 (cl (= tptp.n0 tptp.n1)) :rule symm :premises (t49.t3.t5))
% 0.43/0.63 (step t49.t3.t7 (cl (= (tptp.succ tptp.n0) tptp.n1)) :rule symm :premises (t49.t3.a2))
% 0.43/0.63 (step t49.t3.t8 (cl (= tptp.n1 (tptp.succ tptp.n0))) :rule symm :premises (t49.t3.t7))
% 0.43/0.63 (step t49.t3.t9 (cl (= tptp.n0 (tptp.succ tptp.n0))) :rule trans :premises (t49.t3.t6 t49.t3.t8))
% 0.43/0.63 (step t49.t3.t10 (cl (= (tptp.pred tptp.n0) (tptp.pred (tptp.succ tptp.n0)))) :rule cong :premises (t49.t3.t9))
% 0.43/0.63 (step t49.t3.t11 (cl (= (tptp.pred (tptp.succ tptp.n0)) tptp.n0)) :rule symm :premises (t49.t3.a1))
% 0.43/0.63 (step t49.t3.t12 (cl (= tptp.tptp_minus_1 tptp.n1)) :rule trans :premises (t49.t3.t2 t49.t3.t4 t49.t3.t10 t49.t3.t11 t49.t3.t6))
% 0.43/0.63 (step t49.t3 (cl (not (= tptp.n0 tptp.n1)) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n1)) :rule subproof :discharge (t49.t3.a0 t49.t3.a1 t49.t3.a2 t49.t3.a3 t49.t3.a4))
% 0.43/0.63 (step t49.t4 (cl (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.n0 tptp.n1)) :rule and_pos)
% 0.43/0.63 (step t49.t5 (cl (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) :rule and_pos)
% 0.43/0.63 (step t49.t6 (cl (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.n1 (tptp.succ tptp.n0))) :rule and_pos)
% 0.43/0.63 (step t49.t7 (cl (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) :rule and_pos)
% 0.43/0.63 (step t49.t8 (cl (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule and_pos)
% 0.43/0.63 (step t49.t9 (cl (= tptp.tptp_minus_1 tptp.n1) (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))))) :rule resolution :premises (t49.t3 t49.t4 t49.t5 t49.t6 t49.t7 t49.t8))
% 0.43/0.63 (step t49.t10 (cl (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.tptp_minus_1 tptp.n1)) :rule reordering :premises (t49.t9))
% 0.43/0.63 (step t49.t11 (cl (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.tptp_minus_1 tptp.n1)) :rule contraction :premises (t49.t10))
% 0.43/0.63 (step t49.t12 (cl (=> (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n1)) (= tptp.tptp_minus_1 tptp.n1)) :rule resolution :premises (t49.t2 t49.t11))
% 0.43/0.63 (step t49.t13 (cl (=> (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n1)) (not (= tptp.tptp_minus_1 tptp.n1))) :rule implies_neg2)
% 0.43/0.63 (step t49.t14 (cl (=> (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n1)) (=> (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n1))) :rule resolution :premises (t49.t12 t49.t13))
% 0.43/0.63 (step t49.t15 (cl (=> (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n1))) :rule contraction :premises (t49.t14))
% 0.43/0.63 (step t49.t16 (cl (not (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.tptp_minus_1 tptp.n1)) :rule implies :premises (t49.t15))
% 0.43/0.63 (step t49.t17 (cl (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (= tptp.n0 tptp.n1)) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule and_neg)
% 0.43/0.63 (step t49.t18 (cl (and (= tptp.n0 tptp.n1) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule resolution :premises (t49.t17 t49.a8 t49.a5 t49.a1 t49.a0 t49.a6))
% 0.43/0.63 (step t49.t19 (cl (= tptp.tptp_minus_1 tptp.n1)) :rule resolution :premises (t49.t16 t49.t18))
% 0.43/0.63 (step t49.t20 (cl (=> (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n2)) (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule implies_neg1)
% 0.43/0.63 (anchor :step t49.t21)
% 0.43/0.63 (assume t49.t21.a0 (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))))
% 0.43/0.63 (assume t49.t21.a1 (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)))
% 0.43/0.63 (assume t49.t21.a2 (= tptp.n1 (tptp.succ tptp.n0)))
% 0.43/0.63 (assume t49.t21.a3 (= tptp.n0 tptp.n1))
% 0.43/0.63 (assume t49.t21.a4 (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)))
% 0.43/0.63 (assume t49.t21.a5 (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))))
% 0.43/0.63 (assume t49.t21.a6 (= tptp.n0 (tptp.succ tptp.tptp_minus_1)))
% 0.43/0.63 (assume t49.t21.a7 (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))
% 0.43/0.63 (step t49.t21.t1 (cl (= (tptp.pred (tptp.succ tptp.tptp_minus_1)) tptp.tptp_minus_1)) :rule symm :premises (t49.t21.a7))
% 0.43/0.63 (step t49.t21.t2 (cl (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule symm :premises (t49.t21.t1))
% 0.43/0.63 (step t49.t21.t3 (cl (= (tptp.succ tptp.tptp_minus_1) tptp.n0)) :rule symm :premises (t49.t21.a6))
% 0.43/0.63 (step t49.t21.t4 (cl (= (tptp.pred (tptp.succ tptp.tptp_minus_1)) (tptp.pred tptp.n0))) :rule cong :premises (t49.t21.t3))
% 0.43/0.63 (step t49.t21.t5 (cl (= tptp.n1 tptp.n0)) :rule symm :premises (t49.t21.a3))
% 0.43/0.63 (step t49.t21.t6 (cl (= tptp.n0 tptp.n1)) :rule symm :premises (t49.t21.t5))
% 0.43/0.63 (step t49.t21.t7 (cl (= (tptp.succ tptp.n0) tptp.n1)) :rule symm :premises (t49.t21.a2))
% 0.43/0.63 (step t49.t21.t8 (cl (= tptp.n1 (tptp.succ tptp.n0))) :rule symm :premises (t49.t21.t7))
% 0.43/0.63 (step t49.t21.t9 (cl (= tptp.n0 (tptp.succ tptp.n0))) :rule trans :premises (t49.t21.t6 t49.t21.t8))
% 0.43/0.63 (step t49.t21.t10 (cl (= (tptp.pred tptp.n0) (tptp.pred (tptp.succ tptp.n0)))) :rule cong :premises (t49.t21.t9))
% 0.43/0.63 (step t49.t21.t11 (cl (= (tptp.pred (tptp.succ tptp.n0)) tptp.n0)) :rule symm :premises (t49.t21.a5))
% 0.43/0.63 (step t49.t21.t12 (cl (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) :rule symm :premises (t49.t21.a4))
% 0.43/0.63 (step t49.t21.t13 (cl (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) :rule symm :premises (t49.t21.t12))
% 0.43/0.63 (step t49.t21.t14 (cl (= tptp.n1 tptp.n1)) :rule refl)
% 0.43/0.63 (step t49.t21.t15 (cl (= (tptp.plus tptp.n1 tptp.n0) (tptp.plus tptp.n1 (tptp.succ tptp.n0)))) :rule cong :premises (t49.t21.t14 t49.t21.t9))
% 0.43/0.63 (step t49.t21.t16 (cl (= (tptp.succ tptp.n0) tptp.n1)) :rule symm :premises (t49.t21.t8))
% 0.43/0.63 (step t49.t21.t17 (cl (= (tptp.plus tptp.n1 (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) :rule cong :premises (t49.t21.t8 t49.t21.t16))
% 0.43/0.63 (step t49.t21.t18 (cl (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) :rule symm :premises (t49.t21.a1))
% 0.43/0.63 (step t49.t21.t19 (cl (= (tptp.succ (tptp.succ tptp.n0)) tptp.n2)) :rule symm :premises (t49.t21.a0))
% 0.43/0.63 (step t49.t21.t20 (cl (= tptp.tptp_minus_1 tptp.n2)) :rule trans :premises (t49.t21.t2 t49.t21.t4 t49.t21.t10 t49.t21.t11 t49.t21.t6 t49.t21.t8 t49.t21.t13 t49.t21.t15 t49.t21.t17 t49.t21.t18 t49.t21.t19))
% 0.43/0.63 (step t49.t21 (cl (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n0 tptp.n1)) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n2)) :rule subproof :discharge (t49.t21.a0 t49.t21.a1 t49.t21.a2 t49.t21.a3 t49.t21.a4 t49.t21.a5 t49.t21.a6 t49.t21.a7))
% 0.43/0.63 (step t49.t22 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) :rule and_pos)
% 0.43/0.63 (step t49.t23 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) :rule and_pos)
% 0.43/0.63 (step t49.t24 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.n1 (tptp.succ tptp.n0))) :rule and_pos)
% 0.43/0.63 (step t49.t25 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.n0 tptp.n1)) :rule and_pos)
% 0.43/0.63 (step t49.t26 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) :rule and_pos)
% 0.43/0.63 (step t49.t27 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) :rule and_pos)
% 0.43/0.63 (step t49.t28 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) :rule and_pos)
% 0.43/0.63 (step t49.t29 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule and_pos)
% 0.43/0.63 (step t49.t30 (cl (= tptp.tptp_minus_1 tptp.n2) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))))) :rule resolution :premises (t49.t21 t49.t22 t49.t23 t49.t24 t49.t25 t49.t26 t49.t27 t49.t28 t49.t29))
% 0.43/0.63 (step t49.t31 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.tptp_minus_1 tptp.n2)) :rule reordering :premises (t49.t30))
% 0.43/0.63 (step t49.t32 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.tptp_minus_1 tptp.n2)) :rule contraction :premises (t49.t31))
% 0.43/0.63 (step t49.t33 (cl (=> (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n2)) (= tptp.tptp_minus_1 tptp.n2)) :rule resolution :premises (t49.t20 t49.t32))
% 0.43/0.63 (step t49.t34 (cl (=> (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n2)) (not (= tptp.tptp_minus_1 tptp.n2))) :rule implies_neg2)
% 0.43/0.63 (step t49.t35 (cl (=> (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n2)) (=> (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n2))) :rule resolution :premises (t49.t33 t49.t34))
% 0.43/0.63 (step t49.t36 (cl (=> (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 tptp.n2))) :rule contraction :premises (t49.t35))
% 0.43/0.63 (step t49.t37 (cl (not (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) (= tptp.tptp_minus_1 tptp.n2)) :rule implies :premises (t49.t36))
% 0.43/0.63 (step t49.t38 (cl (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n0 tptp.n1)) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule and_neg)
% 0.43/0.63 (step t49.t39 (cl (and (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n0 tptp.n1) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule resolution :premises (t49.t38 t49.a2 t49.a3 t49.a1 t49.a8 t49.a4 t49.a5 t49.a0 t49.a6))
% 0.43/0.63 (step t49.t40 (cl (= tptp.tptp_minus_1 tptp.n2)) :rule resolution :premises (t49.t37 t49.t39))
% 0.43/0.63 (step t49.t41 (cl (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) :rule resolution :premises (t49.t1 t49.a0 t49.a8 t49.t19 t49.t40 t49.a7))
% 0.43/0.63 (step t49 (cl (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) :rule subproof :discharge (t49.a0 t49.a1 t49.a2 t49.a3 t49.a4 t49.a5 t49.a6 t49.a7 t49.a8))
% 0.45/0.63 (step t50 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) :rule and_pos)
% 0.45/0.63 (step t51 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (= tptp.n1 (tptp.succ tptp.n0))) :rule and_pos)
% 0.45/0.63 (step t52 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) :rule and_pos)
% 0.45/0.63 (step t53 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) :rule and_pos)
% 0.45/0.63 (step t54 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) :rule and_pos)
% 0.45/0.63 (step t55 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) :rule and_pos)
% 0.45/0.63 (step t56 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule and_pos)
% 0.45/0.63 (step t57 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (= tptp.n0 tptp.n2))) :rule and_pos)
% 0.45/0.63 (step t58 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (= tptp.n0 tptp.n1)) :rule and_pos)
% 0.45/0.63 (step t59 (cl (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)))) :rule resolution :premises (t49 t50 t51 t52 t53 t54 t55 t56 t57 t58))
% 0.45/0.63 (step t60 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) :rule reordering :premises (t59))
% 0.45/0.63 (step t61 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1))) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) :rule contraction :premises (t60))
% 0.45/0.63 (step t62 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) :rule resolution :premises (t48 t61))
% 0.45/0.63 (step t63 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))))) :rule implies_neg2)
% 0.45/0.63 (step t64 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2)))) (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))))) :rule resolution :premises (t62 t63))
% 0.45/0.63 (step t65 (cl (=> (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)) (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n0 tptp.n1) (= tptp.tptp_minus_1 tptp.n1) (= tptp.tptp_minus_1 tptp.n2) (not (= tptp.n0 tptp.n2))))) :rule contraction :premises (t64))
% 0.45/0.63 (step t66 (cl (not (and (= tptp.n0 (tptp.succ tptp.tptp_minus_1)) (= tptp.n1 (tptp.succ tptp.n0)) (= tptp.n2 (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n0 tptp.n2)) (= tptp.n0 tptp.n1)))) :rule resolution :premises (t21 t47 t65))
% 0.45/0.63 (step t67 (cl (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) :rule not_and :premises (t66))
% 0.45/0.63 (step t68 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (not (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))))) :rule or_neg)
% 0.45/0.63 (step t69 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (not (not (= tptp.n1 (tptp.succ tptp.n0))))) :rule or_neg)
% 0.45/0.63 (step t70 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (not (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))))) :rule or_neg)
% 0.45/0.63 (step t71 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (not (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))))) :rule or_neg)
% 0.45/0.63 (step t72 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (not (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))))) :rule or_neg)
% 0.45/0.63 (step t73 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (not (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))))) :rule or_neg)
% 0.45/0.63 (step t74 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (not (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))))) :rule or_neg)
% 0.45/0.63 (step t75 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (not (not (not (= tptp.n0 tptp.n2))))) :rule or_neg)
% 0.45/0.63 (step t76 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (not (not (= tptp.n0 tptp.n1)))) :rule or_neg)
% 0.45/0.63 (step t77 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1))) (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1)))) :rule resolution :premises (t67 t68 t69 t70 t71 t72 t73 t74 t75 t76))
% 0.45/0.63 (step t78 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (not (= tptp.n0 tptp.n2))) (not (= tptp.n0 tptp.n1)))) :rule contraction :premises (t77))
% 0.45/0.63 (step t79 (cl (or (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.n0 tptp.n2) (not (= tptp.n0 tptp.n1)))) :rule resolution :premises (t1 t20 t78))
% 0.45/0.63 (step t80 (cl (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.n0 tptp.n2) (not (= tptp.n0 tptp.n1))) :rule or :premises (t79))
% 0.45/0.63 (step t81 (cl (not (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) (not (= tptp.n1 (tptp.succ tptp.n0))) (not (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) (= tptp.n0 tptp.n2) (not (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) (not (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (= tptp.n0 tptp.n1))) :rule reordering :premises (t80))
% 0.45/0.63 (step t82 (cl (not (or (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) :rule or_pos)
% 0.45/0.63 (step t83 (cl (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)) (= tptp.n0 tptp.n1) (not (or (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule reordering :premises (t82))
% 0.45/0.63 (step t84 (cl (not (= (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (or (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))))) (not (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) (or (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule equiv_pos2)
% 0.45/0.63 (step t85 (cl (= (= (= (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) true) (= (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) :rule equiv_simplify)
% 0.45/0.63 (step t86 (cl (not (= (= (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) true)) (= (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule equiv1 :premises (t85))
% 0.45/0.63 (step t87 (cl (= (= (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))))) :rule all_simplify)
% 0.45/0.63 (step t88 (cl (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule refl)
% 0.45/0.63 (step t89 (cl (= (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule all_simplify)
% 0.45/0.63 (step t90 (cl (= (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) :rule cong :premises (t88 t89))
% 0.45/0.63 (step t91 (cl (= (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) true)) :rule all_simplify)
% 0.45/0.63 (step t92 (cl (= (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) true)) :rule trans :premises (t90 t91))
% 0.45/0.63 (step t93 (cl (= (= (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) true)) :rule trans :premises (t87 t92))
% 0.45/0.63 (step t94 (cl (= (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule resolution :premises (t86 t93))
% 0.45/0.63 (step t95 (cl (= (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))))) :rule refl)
% 0.45/0.63 (step t96 (cl (= (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule refl)
% 0.45/0.63 (step t97 (cl (= (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule refl)
% 0.45/0.63 (step t98 (cl (= (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (or (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))))) :rule cong :premises (t94 t95 t96 t97))
% 0.45/0.63 (step t99 (cl (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule and_neg)
% 0.45/0.63 (step t100 (cl (=> (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t101)
% 0.45/0.63 (assume t101.a0 (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))
% 0.45/0.63 (assume t101.a1 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)))
% 0.45/0.63 (assume t101.a2 (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))
% 0.45/0.63 (step t101.t1 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t101.t2)
% 0.45/0.63 (assume t101.t2.a0 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)))
% 0.45/0.63 (assume t101.t2.a1 (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))
% 0.45/0.63 (assume t101.t2.a2 (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))
% 0.45/0.63 (step t101.t2.t1 (cl (= (= (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)) false) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule equiv_simplify)
% 0.45/0.63 (step t101.t2.t2 (cl (not (= (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)) false)) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule equiv1 :premises (t101.t2.t1))
% 0.45/0.63 (step t101.t2.t3 (cl (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) tptp.use)) :rule symm :premises (t101.t2.a0))
% 0.45/0.63 (step t101.t2.t4 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule symm :premises (t101.t2.a2))
% 0.45/0.63 (step t101.t2.t5 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule cong :premises (t101.t2.t3 t101.t2.t4))
% 0.45/0.63 (step t101.t2.t6 (cl (= (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) false) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) :rule equiv_simplify)
% 0.45/0.63 (step t101.t2.t7 (cl (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) false) (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) :rule equiv2 :premises (t101.t2.t6))
% 0.45/0.63 (step t101.t2.t8 (cl (not (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule not_not)
% 0.45/0.63 (step t101.t2.t9 (cl (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) false) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule resolution :premises (t101.t2.t7 t101.t2.t8))
% 0.45/0.63 (step t101.t2.t10 (cl (= (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) false)) :rule resolution :premises (t101.t2.t9 t101.t2.a1))
% 0.45/0.63 (step t101.t2.t11 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)) false)) :rule trans :premises (t101.t2.t5 t101.t2.t10))
% 0.45/0.63 (step t101.t2.t12 (cl (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t101.t2.t2 t101.t2.t11))
% 0.45/0.63 (step t101.t2 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule subproof :discharge (t101.t2.a0 t101.t2.a1 t101.t2.a2))
% 0.45/0.63 (step t101.t3 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) :rule and_pos)
% 0.45/0.63 (step t101.t4 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule and_pos)
% 0.45/0.63 (step t101.t5 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) :rule and_pos)
% 0.45/0.63 (step t101.t6 (cl (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule resolution :premises (t101.t2 t101.t3 t101.t4 t101.t5))
% 0.45/0.63 (step t101.t7 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule reordering :premises (t101.t6))
% 0.45/0.63 (step t101.t8 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule contraction :premises (t101.t7))
% 0.45/0.63 (step t101.t9 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t101.t1 t101.t8))
% 0.45/0.63 (step t101.t10 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule implies_neg2)
% 0.45/0.63 (step t101.t11 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule resolution :premises (t101.t9 t101.t10))
% 0.45/0.63 (step t101.t12 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule contraction :premises (t101.t11))
% 0.45/0.63 (step t101.t13 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule implies :premises (t101.t12))
% 0.45/0.63 (step t101.t14 (cl (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule and_neg)
% 0.45/0.63 (step t101.t15 (cl (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t101.t14 t101.a1 t101.a0 t101.a2))
% 0.45/0.63 (step t101.t16 (cl (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t101.t13 t101.t15))
% 0.45/0.63 (step t101 (cl (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule subproof :discharge (t101.a0 t101.a1 t101.a2))
% 0.45/0.63 (step t102 (cl (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule and_pos)
% 0.45/0.63 (step t103 (cl (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) :rule and_pos)
% 0.45/0.63 (step t104 (cl (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) :rule and_pos)
% 0.45/0.63 (step t105 (cl (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule resolution :premises (t101 t102 t103 t104))
% 0.45/0.63 (step t106 (cl (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule reordering :premises (t105))
% 0.45/0.63 (step t107 (cl (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule contraction :premises (t106))
% 0.45/0.63 (step t108 (cl (=> (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t100 t107))
% 0.45/0.63 (step t109 (cl (=> (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule implies_neg2)
% 0.45/0.63 (step t110 (cl (=> (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (=> (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule resolution :premises (t108 t109))
% 0.45/0.63 (step t111 (cl (=> (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule contraction :premises (t110))
% 0.45/0.63 (step t112 (cl (not (and (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule implies :premises (t111))
% 0.45/0.63 (step t113 (cl (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t99 t112))
% 0.45/0.63 (step t114 (cl (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))))) :rule or_neg)
% 0.45/0.63 (step t115 (cl (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))))) :rule or_neg)
% 0.45/0.63 (step t116 (cl (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule or_neg)
% 0.45/0.63 (step t117 (cl (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule or_neg)
% 0.45/0.63 (step t118 (cl (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule resolution :premises (t113 t114 t115 t116 t117))
% 0.45/0.63 (step t119 (cl (or (not (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule contraction :premises (t118))
% 0.45/0.63 (step t120 (cl (or (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule resolution :premises (t84 t98 t119))
% 0.45/0.63 (step t121 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule or :premises (t120))
% 0.45/0.63 (step t122 (cl (not (= (not (=> (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use)) (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) tptp.use)))) (not (=> (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5))) (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))))))) (not (not (=> (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use)) (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) tptp.use))))) (not (=> (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5))) (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))))) :rule equiv_pos2)
% 0.45/0.63 (step t123 (cl (= (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)))) :rule all_simplify)
% 0.45/0.63 (step t124 (cl (= (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)))) :rule all_simplify)
% 0.45/0.63 (step t125 (cl (= (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)))) :rule all_simplify)
% 0.45/0.63 (step t126 (cl (= (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)))) :rule all_simplify)
% 0.45/0.63 (step t127 (cl (= (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)))) :rule all_simplify)
% 0.45/0.63 (step t128 (cl (= (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)))) :rule all_simplify)
% 0.45/0.63 (step t129 (cl (= (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)))) :rule all_simplify)
% 0.45/0.63 (step t130 (cl (= (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)))) :rule all_simplify)
% 0.45/0.63 (step t131 (cl (= (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)))) :rule all_simplify)
% 0.45/0.63 (step t132 (cl (= (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)))) :rule all_simplify)
% 0.45/0.63 (step t133 (cl (= (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)))) :rule all_simplify)
% 0.45/0.63 (step t134 (cl (= (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5)))) :rule all_simplify)
% 0.45/0.63 (step t135 (cl (= (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use)) (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5))))) :rule cong :premises (t123 t124 t125 t126 t127 t128 t129 t130 t131 t132 t133 t134))
% 0.45/0.63 (step t136 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) tptp.use) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule all_simplify)
% 0.45/0.63 (step t137 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) tptp.use) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule all_simplify)
% 0.45/0.63 (step t138 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) tptp.use) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) :rule all_simplify)
% 0.45/0.63 (step t139 (cl (= (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) tptp.use)) (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))))) :rule cong :premises (t123 t124 t125 t126 t127 t128 t129 t130 t131 t132 t133 t134 t136 t137 t138))
% 0.45/0.63 (step t140 (cl (= (=> (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use)) (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) tptp.use))) (=> (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5))) (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))))) :rule cong :premises (t135 t139))
% 0.45/0.63 (step t141 (cl (= (not (=> (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use)) (and (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) tptp.use) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) tptp.use)))) (not (=> (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5))) (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))))))) :rule cong :premises (t140))
% 0.45/0.63 (step t142 (cl (not (=> (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5))) (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))))) :rule resolution :premises (t122 t141 a52))
% 0.45/0.63 (step t143 (cl (not (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))))) :rule not_implies2 :premises (t142))
% 0.45/0.63 (step t144 (cl (not (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0))) (not (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1))) (not (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2))) (not (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3))) (not (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4))) (not (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5))) (not (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0))) (not (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0))) (not (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0))) (not (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3))) (not (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4))) (not (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) :rule not_and :premises (t143))
% 0.45/0.63 (step t145 (cl (and (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4)) (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5)))) :rule not_implies1 :premises (t142))
% 0.45/0.63 (step t146 (cl (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n0))) :rule and :premises (t145))
% 0.45/0.63 (step t147 (cl (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n1))) :rule and :premises (t145))
% 0.45/0.63 (step t148 (cl (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n2))) :rule and :premises (t145))
% 0.45/0.63 (step t149 (cl (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n3))) :rule and :premises (t145))
% 0.45/0.63 (step t150 (cl (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n4))) :rule and :premises (t145))
% 0.45/0.63 (step t151 (cl (= tptp.use (tptp.a_select2 tptp.sigma_defuse tptp.n5))) :rule and :premises (t145))
% 0.45/0.63 (step t152 (cl (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0))) :rule and :premises (t145))
% 0.45/0.63 (step t153 (cl (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0))) :rule and :premises (t145))
% 0.45/0.63 (step t154 (cl (= tptp.use (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0))) :rule and :premises (t145))
% 0.45/0.63 (step t155 (cl (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n3))) :rule and :premises (t145))
% 0.45/0.63 (step t156 (cl (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n4))) :rule and :premises (t145))
% 0.45/0.63 (step t157 (cl (= tptp.use (tptp.a_select2 tptp.xinit_defuse tptp.n5))) :rule and :premises (t145))
% 0.45/0.63 (step t158 (cl (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule and_neg)
% 0.45/0.63 (step t159 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t160)
% 0.45/0.63 (assume t160.a0 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))
% 0.45/0.63 (assume t160.a1 (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))
% 0.45/0.63 (step t160.t1 (cl (=> (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t160.t2)
% 0.45/0.63 (assume t160.t2.a0 (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))
% 0.45/0.63 (assume t160.t2.a1 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))
% 0.45/0.63 (step t160.t2.t1 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) tptp.use)) :rule symm :premises (t160.t2.a1))
% 0.45/0.63 (step t160.t2.t2 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule symm :premises (t160.t2.t1))
% 0.45/0.63 (step t160.t2.t3 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule symm :premises (t160.t2.a0))
% 0.45/0.63 (step t160.t2.t4 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule trans :premises (t160.t2.t2 t160.t2.t3))
% 0.45/0.63 (step t160.t2 (cl (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule subproof :discharge (t160.t2.a0 t160.t2.a1))
% 0.45/0.63 (step t160.t3 (cl (not (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule and_pos)
% 0.45/0.63 (step t160.t4 (cl (not (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule and_pos)
% 0.45/0.63 (step t160.t5 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (not (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (not (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))))) :rule resolution :premises (t160.t2 t160.t3 t160.t4))
% 0.45/0.63 (step t160.t6 (cl (not (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (not (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule reordering :premises (t160.t5))
% 0.45/0.63 (step t160.t7 (cl (not (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule contraction :premises (t160.t6))
% 0.45/0.63 (step t160.t8 (cl (=> (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule resolution :premises (t160.t1 t160.t7))
% 0.45/0.63 (step t160.t9 (cl (=> (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule implies_neg2)
% 0.45/0.63 (step t160.t10 (cl (=> (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (=> (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule resolution :premises (t160.t8 t160.t9))
% 0.45/0.63 (step t160.t11 (cl (=> (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule contraction :premises (t160.t10))
% 0.45/0.63 (step t160.t12 (cl (not (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule implies :premises (t160.t11))
% 0.45/0.63 (step t160.t13 (cl (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule and_neg)
% 0.45/0.63 (step t160.t14 (cl (and (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule resolution :premises (t160.t13 t160.a1 t160.a0))
% 0.45/0.63 (step t160.t15 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule resolution :premises (t160.t12 t160.t14))
% 0.45/0.63 (step t160 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule subproof :discharge (t160.a0 t160.a1))
% 0.45/0.63 (step t161 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule and_pos)
% 0.45/0.63 (step t162 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule and_pos)
% 0.45/0.63 (step t163 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))))) :rule resolution :premises (t160 t161 t162))
% 0.45/0.63 (step t164 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule reordering :premises (t163))
% 0.45/0.63 (step t165 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule contraction :premises (t164))
% 0.45/0.63 (step t166 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule resolution :premises (t159 t165))
% 0.45/0.63 (step t167 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule implies_neg2)
% 0.45/0.63 (step t168 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule resolution :premises (t166 t167))
% 0.45/0.63 (step t169 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule contraction :premises (t168))
% 0.45/0.63 (step t170 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule implies :premises (t169))
% 0.45/0.63 (step t171 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule resolution :premises (t158 t170))
% 0.45/0.63 (step t172 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule reordering :premises (t171))
% 0.45/0.63 (step t173 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t174)
% 0.45/0.63 (assume t174.a0 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))))
% 0.45/0.63 (step t174.t1 (cl (or (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule forall_inst :args ((:= X (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use)) (:= U tptp.n1) (:= VAL tptp.use)))
% 0.45/0.63 (step t174.t2 (cl (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule or :premises (t174.t1))
% 0.45/0.63 (step t174.t3 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule resolution :premises (t174.t2 t174.a0))
% 0.45/0.63 (step t174 (cl (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule subproof :discharge (t174.a0))
% 0.45/0.63 (step t175 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule resolution :premises (t173 t174))
% 0.45/0.63 (step t176 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule implies_neg2)
% 0.45/0.63 (step t177 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule resolution :premises (t175 t176))
% 0.45/0.63 (step t178 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule contraction :premises (t177))
% 0.45/0.63 (step t179 (cl (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule implies :premises (t178))
% 0.45/0.63 (step t180 (cl (not (= (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))))) (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL))) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) :rule equiv_pos2)
% 0.45/0.63 (anchor :step t181 :args ((X $$unsorted) (:= X X) (U $$unsorted) (:= U U) (VAL $$unsorted) (:= VAL VAL)))
% 0.45/0.63 (step t181.t1 (cl (= X X)) :rule refl)
% 0.45/0.63 (step t181.t2 (cl (= U U)) :rule refl)
% 0.45/0.63 (step t181.t3 (cl (= VAL VAL)) :rule refl)
% 0.45/0.63 (step t181.t4 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) :rule all_simplify)
% 0.45/0.63 (step t181 (cl (= (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))))) :rule bind)
% 0.45/0.63 (step t182 (cl (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) :rule resolution :premises (t180 t181 a47))
% 0.45/0.63 (step t183 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule resolution :premises (t179 t182))
% 0.45/0.63 (step t184 (cl (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.n1 tptp.n2))) :rule and_neg)
% 0.45/0.63 (step t185 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t186)
% 0.45/0.63 (assume t186.a0 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))
% 0.45/0.63 (assume t186.a1 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))
% 0.45/0.63 (assume t186.a2 (= tptp.n1 tptp.n2))
% 0.45/0.63 (step t186.t1 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t186.t2)
% 0.45/0.63 (assume t186.t2.a0 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))
% 0.45/0.63 (assume t186.t2.a1 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))
% 0.45/0.63 (assume t186.t2.a2 (= tptp.n1 tptp.n2))
% 0.45/0.63 (step t186.t2.t1 (cl (= (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use))) :rule refl)
% 0.45/0.63 (step t186.t2.t2 (cl (= tptp.n2 tptp.n1)) :rule symm :premises (t186.t2.a2))
% 0.45/0.63 (step t186.t2.t3 (cl (= tptp.n1 tptp.n2)) :rule symm :premises (t186.t2.t2))
% 0.45/0.63 (step t186.t2.t4 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule cong :premises (t186.t2.t1 t186.t2.t3))
% 0.45/0.63 (step t186.t2.t5 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) tptp.use)) :rule symm :premises (t186.t2.a1))
% 0.45/0.63 (step t186.t2.t6 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) tptp.use)) :rule symm :premises (t186.t2.a0))
% 0.45/0.63 (step t186.t2.t7 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule symm :premises (t186.t2.t6))
% 0.45/0.63 (step t186.t2.t8 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule trans :premises (t186.t2.t4 t186.t2.t5 t186.t2.t7))
% 0.45/0.63 (step t186.t2 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule subproof :discharge (t186.t2.a0 t186.t2.a1 t186.t2.a2))
% 0.45/0.63 (step t186.t3 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule and_pos)
% 0.45/0.63 (step t186.t4 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule and_pos)
% 0.45/0.63 (step t186.t5 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (= tptp.n1 tptp.n2)) :rule and_pos)
% 0.45/0.63 (step t186.t6 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2)))) :rule resolution :premises (t186.t2 t186.t3 t186.t4 t186.t5))
% 0.45/0.63 (step t186.t7 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule reordering :premises (t186.t6))
% 0.45/0.63 (step t186.t8 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule contraction :premises (t186.t7))
% 0.45/0.63 (step t186.t9 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule resolution :premises (t186.t1 t186.t8))
% 0.45/0.63 (step t186.t10 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule implies_neg2)
% 0.45/0.63 (step t186.t11 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule resolution :premises (t186.t9 t186.t10))
% 0.45/0.63 (step t186.t12 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule contraction :premises (t186.t11))
% 0.45/0.63 (step t186.t13 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule implies :premises (t186.t12))
% 0.45/0.63 (step t186.t14 (cl (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.n1 tptp.n2))) :rule and_neg)
% 0.45/0.63 (step t186.t15 (cl (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n1 tptp.n2))) :rule resolution :premises (t186.t14 t186.a1 t186.a0 t186.a2))
% 0.45/0.63 (step t186.t16 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule resolution :premises (t186.t13 t186.t15))
% 0.45/0.63 (step t186 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule subproof :discharge (t186.a0 t186.a1 t186.a2))
% 0.45/0.63 (step t187 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule and_pos)
% 0.45/0.63 (step t188 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule and_pos)
% 0.45/0.63 (step t189 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (= tptp.n1 tptp.n2)) :rule and_pos)
% 0.45/0.63 (step t190 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2)))) :rule resolution :premises (t186 t187 t188 t189))
% 0.45/0.63 (step t191 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule reordering :premises (t190))
% 0.45/0.63 (step t192 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule contraction :premises (t191))
% 0.45/0.63 (step t193 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule resolution :premises (t185 t192))
% 0.45/0.63 (step t194 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule implies_neg2)
% 0.45/0.63 (step t195 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule resolution :premises (t193 t194))
% 0.45/0.63 (step t196 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule contraction :premises (t195))
% 0.45/0.63 (step t197 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= tptp.n1 tptp.n2))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule implies :premises (t196))
% 0.45/0.63 (step t198 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.n1 tptp.n2)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule resolution :premises (t184 t197))
% 0.45/0.63 (step t199 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) (not (= tptp.n1 tptp.n2))) :rule reordering :premises (t198))
% 0.45/0.63 (step t200 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t201)
% 0.45/0.63 (assume t201.a0 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))))
% 0.45/0.63 (step t201.t1 (cl (or (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) :rule forall_inst :args ((:= X (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use)) (:= U tptp.n2) (:= VAL tptp.use)))
% 0.45/0.63 (step t201.t2 (cl (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule or :premises (t201.t1))
% 0.45/0.63 (step t201.t3 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule resolution :premises (t201.t2 t201.a0))
% 0.45/0.63 (step t201 (cl (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule subproof :discharge (t201.a0))
% 0.45/0.63 (step t202 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule resolution :premises (t200 t201))
% 0.45/0.63 (step t203 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) :rule implies_neg2)
% 0.45/0.63 (step t204 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) :rule resolution :premises (t202 t203))
% 0.45/0.63 (step t205 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) :rule contraction :premises (t204))
% 0.45/0.63 (step t206 (cl (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule implies :premises (t205))
% 0.45/0.63 (step t207 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))))) :rule reordering :premises (t206))
% 0.45/0.63 (step t208 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule resolution :premises (t207 t182))
% 0.45/0.63 (step t209 (cl (not (or (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule or_pos)
% 0.45/0.63 (step t210 (cl (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (not (or (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))))) :rule reordering :premises (t209))
% 0.45/0.63 (step t211 (cl (not (= (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))))) (not (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))))) :rule equiv_pos2)
% 0.45/0.63 (step t212 (cl (= (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) :rule refl)
% 0.45/0.63 (step t213 (cl (= (= tptp.n2 tptp.n1) (= tptp.n1 tptp.n2))) :rule all_simplify)
% 0.45/0.63 (step t214 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule all_simplify)
% 0.45/0.63 (step t215 (cl (= (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) (or (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))))) :rule cong :premises (t213 t214))
% 0.45/0.63 (step t216 (cl (= (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))))) :rule cong :premises (t212 t215))
% 0.45/0.63 (step t217 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t218)
% 0.45/0.63 (assume t218.a0 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))
% 0.45/0.63 (step t218.t1 (cl (or (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))))) :rule forall_inst :args ((:= I tptp.n2) (:= U tptp.n1) (:= X (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use)) (:= VAL2 tptp.use)))
% 0.45/0.63 (step t218.t2 (cl (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule or :premises (t218.t1))
% 0.45/0.63 (step t218.t3 (cl (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule resolution :premises (t218.t2 t218.a0))
% 0.45/0.63 (step t218 (cl (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule subproof :discharge (t218.a0))
% 0.45/0.63 (step t219 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) :rule resolution :premises (t217 t218))
% 0.45/0.63 (step t220 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) (not (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))))) :rule implies_neg2)
% 0.45/0.63 (step t221 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1)))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))))) :rule resolution :premises (t219 t220))
% 0.45/0.63 (step t222 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))))) :rule contraction :premises (t221))
% 0.45/0.63 (step t223 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))))) :rule resolution :premises (t211 t216 t222))
% 0.45/0.63 (step t224 (cl (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule implies :premises (t223))
% 0.45/0.63 (step t225 (cl (not (= (forall ((I $$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))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) :rule equiv_pos2)
% 0.45/0.63 (anchor :step t226 :args ((I $$unsorted) (:= I I) (U $$unsorted) (:= U U) (X $$unsorted) (:= X X) (VAL $$unsorted) (:= VAL VAL) (VAL2 $$unsorted) (:= VAL2 VAL2)))
% 0.45/0.63 (step t226.t1 (cl (= I I)) :rule refl)
% 0.45/0.63 (step t226.t2 (cl (= U U)) :rule refl)
% 0.45/0.63 (step t226.t3 (cl (= X X)) :rule refl)
% 0.45/0.63 (step t226.t4 (cl (= VAL VAL)) :rule refl)
% 0.45/0.63 (step t226.t5 (cl (= VAL2 VAL2)) :rule refl)
% 0.45/0.63 (step t226.t6 (cl (= (not (= I U)) (not (= I U)))) :rule refl)
% 0.45/0.63 (step t226.t7 (cl (= (= (tptp.a_select2 X U) VAL) (= VAL (tptp.a_select2 X U)))) :rule all_simplify)
% 0.45/0.63 (step t226.t8 (cl (= (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (and (not (= I U)) (= VAL (tptp.a_select2 X U))))) :rule cong :premises (t226.t6 t226.t7))
% 0.45/0.63 (step t226.t9 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL) (= VAL (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) :rule all_simplify)
% 0.45/0.63 (step t226.t10 (cl (= (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL)) (=> (and (not (= I U)) (= VAL (tptp.a_select2 X U))) (= VAL (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) :rule cong :premises (t226.t8 t226.t9))
% 0.45/0.63 (step t226 (cl (= (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= VAL (tptp.a_select2 X U))) (= VAL (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) :rule bind)
% 0.45/0.63 (step t227 (cl (= (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= VAL (tptp.a_select2 X U))) (= VAL (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (or (= I U) (not (= VAL (tptp.a_select2 X U))) (= VAL (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) :rule all_simplify)
% 0.45/0.63 (step t228 (cl (= (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (or (= I U) (not (= VAL (tptp.a_select2 X U))) (= VAL (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (not (= (tptp.a_select2 X U) (tptp.a_select2 X U))) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) :rule all_simplify)
% 0.45/0.63 (anchor :step t229 :args ((I $$unsorted) (:= I I) (U $$unsorted) (:= U U) (X $$unsorted) (:= X X) (VAL2 $$unsorted) (:= VAL2 VAL2)))
% 0.45/0.63 (step t229.t1 (cl (= I I)) :rule refl)
% 0.45/0.63 (step t229.t2 (cl (= U U)) :rule refl)
% 0.45/0.63 (step t229.t3 (cl (= X X)) :rule refl)
% 0.45/0.63 (step t229.t4 (cl (= VAL2 VAL2)) :rule refl)
% 0.45/0.63 (step t229.t5 (cl (= (= I U) (= I U))) :rule refl)
% 0.45/0.63 (step t229.t6 (cl (= (= (tptp.a_select2 X U) (tptp.a_select2 X U)) true)) :rule all_simplify)
% 0.45/0.63 (step t229.t7 (cl (= (not (= (tptp.a_select2 X U) (tptp.a_select2 X U))) (not true))) :rule cong :premises (t229.t6))
% 0.45/0.63 (step t229.t8 (cl (= (not true) false)) :rule all_simplify)
% 0.45/0.63 (step t229.t9 (cl (= (not (= (tptp.a_select2 X U) (tptp.a_select2 X U))) false)) :rule trans :premises (t229.t7 t229.t8))
% 0.45/0.63 (step t229.t10 (cl (= (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) :rule refl)
% 0.45/0.63 (step t229.t11 (cl (= (or (= I U) (not (= (tptp.a_select2 X U) (tptp.a_select2 X U))) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))) (or (= I U) false (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) :rule cong :premises (t229.t5 t229.t9 t229.t10))
% 0.45/0.63 (step t229.t12 (cl (= (or (= I U) false (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) :rule all_simplify)
% 0.45/0.63 (step t229.t13 (cl (= (or (= I U) (not (= (tptp.a_select2 X U) (tptp.a_select2 X U))) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) :rule trans :premises (t229.t11 t229.t12))
% 0.45/0.63 (step t229 (cl (= (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (not (= (tptp.a_select2 X U) (tptp.a_select2 X U))) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) :rule bind)
% 0.45/0.63 (step t230 (cl (= (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (or (= I U) (not (= VAL (tptp.a_select2 X U))) (= VAL (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) :rule trans :premises (t228 t229))
% 0.45/0.63 (step t231 (cl (= (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= VAL (tptp.a_select2 X U))) (= VAL (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) :rule trans :premises (t227 t230))
% 0.45/0.63 (step t232 (cl (= (forall ((I $$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))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) :rule trans :premises (t226 t231))
% 0.45/0.63 (step t233 (cl (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) :rule resolution :premises (t225 t232 a48))
% 0.45/0.63 (step t234 (cl (or (= tptp.n1 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)))) :rule resolution :premises (t224 t233))
% 0.45/0.63 (step t235 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule resolution :premises (t199 t208 t183 t210 t234))
% 0.45/0.63 (step t236 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n1))) :rule contraction :premises (t235))
% 0.45/0.63 (step t237 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n1))) :rule resolution :premises (t172 t183 t236))
% 0.45/0.63 (step t238 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule resolution :premises (t144 t146 t147 t148 t149 t150 t151 t152 t153 t154 t155 t156 t157 t237 t208))
% 0.45/0.63 (step t239 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t240)
% 0.45/0.63 (assume t240.a0 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))))
% 0.45/0.63 (step t240.t1 (cl (or (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)))) :rule forall_inst :args ((:= X tptp.rho_defuse) (:= U tptp.n0) (:= VAL tptp.use)))
% 0.45/0.63 (step t240.t2 (cl (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) :rule or :premises (t240.t1))
% 0.45/0.63 (step t240.t3 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) :rule resolution :premises (t240.t2 t240.a0))
% 0.45/0.63 (step t240 (cl (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) :rule subproof :discharge (t240.a0))
% 0.45/0.63 (step t241 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) :rule resolution :premises (t239 t240))
% 0.45/0.63 (step t242 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)))) :rule implies_neg2)
% 0.45/0.63 (step t243 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)))) :rule resolution :premises (t241 t242))
% 0.45/0.63 (step t244 (cl (=> (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0)))) :rule contraction :premises (t243))
% 0.45/0.63 (step t245 (cl (not (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) :rule implies :premises (t244))
% 0.45/0.63 (step t246 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0))) :rule resolution :premises (t245 t182))
% 0.45/0.63 (step t247 (cl (not (or (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) :rule or_pos)
% 0.45/0.63 (step t248 (cl (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)) (not (or (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule reordering :premises (t247))
% 0.45/0.63 (step t249 (cl (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.n0 tptp.n2))) :rule and_neg)
% 0.45/0.63 (step t250 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t251)
% 0.45/0.63 (assume t251.a0 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))
% 0.45/0.63 (assume t251.a1 (= tptp.n0 tptp.n2))
% 0.45/0.63 (step t251.t1 (cl (=> (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t251.t2)
% 0.45/0.63 (assume t251.t2.a0 (= tptp.n0 tptp.n2))
% 0.45/0.63 (assume t251.t2.a1 (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))
% 0.45/0.63 (step t251.t2.t1 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) tptp.use)) :rule symm :premises (t251.t2.a1))
% 0.45/0.63 (step t251.t2.t2 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule symm :premises (t251.t2.t1))
% 0.45/0.63 (step t251.t2.t3 (cl (= (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use))) :rule refl)
% 0.45/0.63 (step t251.t2.t4 (cl (= tptp.n2 tptp.n0)) :rule symm :premises (t251.t2.a0))
% 0.45/0.63 (step t251.t2.t5 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule cong :premises (t251.t2.t3 t251.t2.t4))
% 0.45/0.63 (step t251.t2.t6 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule trans :premises (t251.t2.t2 t251.t2.t5))
% 0.45/0.63 (step t251.t2 (cl (not (= tptp.n0 tptp.n2)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule subproof :discharge (t251.t2.a0 t251.t2.a1))
% 0.45/0.63 (step t251.t3 (cl (not (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) (= tptp.n0 tptp.n2)) :rule and_pos)
% 0.45/0.63 (step t251.t4 (cl (not (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule and_pos)
% 0.45/0.63 (step t251.t5 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) (not (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))))) :rule resolution :premises (t251.t2 t251.t3 t251.t4))
% 0.45/0.63 (step t251.t6 (cl (not (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) (not (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule reordering :premises (t251.t5))
% 0.45/0.63 (step t251.t7 (cl (not (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule contraction :premises (t251.t6))
% 0.45/0.63 (step t251.t8 (cl (=> (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule resolution :premises (t251.t1 t251.t7))
% 0.45/0.63 (step t251.t9 (cl (=> (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule implies_neg2)
% 0.45/0.63 (step t251.t10 (cl (=> (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (=> (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule resolution :premises (t251.t8 t251.t9))
% 0.45/0.63 (step t251.t11 (cl (=> (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule contraction :premises (t251.t10))
% 0.45/0.63 (step t251.t12 (cl (not (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule implies :premises (t251.t11))
% 0.45/0.63 (step t251.t13 (cl (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.n0 tptp.n2)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) :rule and_neg)
% 0.45/0.63 (step t251.t14 (cl (and (= tptp.n0 tptp.n2) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)))) :rule resolution :premises (t251.t13 t251.a1 t251.a0))
% 0.45/0.63 (step t251.t15 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule resolution :premises (t251.t12 t251.t14))
% 0.45/0.63 (step t251 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.n0 tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule subproof :discharge (t251.a0 t251.a1))
% 0.45/0.63 (step t252 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) :rule and_pos)
% 0.45/0.63 (step t253 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2))) (= tptp.n0 tptp.n2)) :rule and_pos)
% 0.45/0.63 (step t254 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2)))) :rule resolution :premises (t251 t252 t253))
% 0.45/0.63 (step t255 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2))) (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule reordering :premises (t254))
% 0.45/0.63 (step t256 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule contraction :premises (t255))
% 0.45/0.63 (step t257 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule resolution :premises (t250 t256))
% 0.45/0.63 (step t258 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule implies_neg2)
% 0.45/0.63 (step t259 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule resolution :premises (t257 t258))
% 0.45/0.63 (step t260 (cl (=> (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule contraction :premises (t259))
% 0.45/0.63 (step t261 (cl (not (and (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2)) (= tptp.n0 tptp.n2))) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule implies :premises (t260))
% 0.45/0.63 (step t262 (cl (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.n0 tptp.n2)) (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) :rule resolution :premises (t249 t261))
% 0.45/0.63 (step t263 (cl (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (not (= tptp.use (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n2))) (not (= tptp.n0 tptp.n2))) :rule reordering :premises (t262))
% 0.45/0.63 (step t264 (cl (not (= tptp.n0 tptp.n2))) :rule resolution :premises (t263 t238 t208))
% 0.45/0.63 (step t265 (cl (not (= (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))))) (not (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule equiv_pos2)
% 0.45/0.63 (step t266 (cl (= (= tptp.n2 tptp.n0) (= tptp.n0 tptp.n2))) :rule all_simplify)
% 0.45/0.63 (step t267 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule all_simplify)
% 0.45/0.63 (step t268 (cl (= (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))) (or (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule cong :premises (t266 t267))
% 0.45/0.63 (step t269 (cl (= (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))))) :rule cong :premises (t212 t268))
% 0.45/0.63 (step t270 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t271)
% 0.45/0.63 (assume t271.a0 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))
% 0.45/0.63 (step t271.t1 (cl (or (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) :rule forall_inst :args ((:= I tptp.n2) (:= U tptp.n0) (:= X (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use)) (:= VAL2 tptp.use)))
% 0.45/0.63 (step t271.t2 (cl (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule or :premises (t271.t1))
% 0.45/0.63 (step t271.t3 (cl (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule resolution :premises (t271.t2 t271.a0))
% 0.45/0.63 (step t271 (cl (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule subproof :discharge (t271.a0))
% 0.45/0.63 (step t272 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) :rule resolution :premises (t270 t271))
% 0.45/0.63 (step t273 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (not (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) :rule implies_neg2)
% 0.45/0.63 (step t274 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0)))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) :rule resolution :premises (t272 t273))
% 0.45/0.63 (step t275 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n2 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0))))) :rule contraction :premises (t274))
% 0.45/0.63 (step t276 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule resolution :premises (t265 t269 t275))
% 0.45/0.63 (step t277 (cl (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule implies :premises (t276))
% 0.45/0.63 (step t278 (cl (or (= tptp.n0 tptp.n2) (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t277 t233))
% 0.45/0.63 (step t279 (cl (= (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n2 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) :rule resolution :premises (t248 t264 t278))
% 0.45/0.63 (step t280 (cl (not (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t121 t238 t246 t279))
% 0.45/0.63 (step t281 (cl (not (= (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))))) (not (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule equiv_pos2)
% 0.45/0.63 (step t282 (cl (= (= tptp.n1 tptp.n0) (= tptp.n0 tptp.n1))) :rule all_simplify)
% 0.45/0.63 (step t283 (cl (= (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule refl)
% 0.45/0.63 (step t284 (cl (= (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))) (or (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule cong :premises (t282 t283))
% 0.45/0.63 (step t285 (cl (= (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))))) :rule cong :premises (t212 t284))
% 0.45/0.63 (step t286 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t287)
% 0.45/0.63 (assume t287.a0 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))
% 0.45/0.63 (step t287.t1 (cl (or (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule forall_inst :args ((:= I tptp.n1) (:= U tptp.n0) (:= X (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use)) (:= VAL2 tptp.use)))
% 0.45/0.63 (step t287.t2 (cl (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule or :premises (t287.t1))
% 0.45/0.63 (step t287.t3 (cl (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t287.t2 t287.a0))
% 0.45/0.63 (step t287 (cl (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule subproof :discharge (t287.a0))
% 0.45/0.63 (step t288 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t286 t287))
% 0.45/0.63 (step t289 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (not (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule implies_neg2)
% 0.45/0.63 (step t290 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule resolution :premises (t288 t289))
% 0.45/0.63 (step t291 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n1 tptp.n0) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule contraction :premises (t290))
% 0.45/0.63 (step t292 (cl (=> (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (or (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0))))) :rule resolution :premises (t281 t285 t291))
% 0.45/0.63 (step t293 (cl (not (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U))))) (or (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule implies :premises (t292))
% 0.45/0.63 (step t294 (cl (or (= tptp.n0 tptp.n1) (= (tptp.a_select2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n0) (tptp.a_select2 (tptp.tptp_update2 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use) tptp.n1 tptp.use) tptp.n0)))) :rule resolution :premises (t293 t233))
% 0.45/0.63 (step t295 (cl (= tptp.n0 tptp.n1)) :rule resolution :premises (t83 t280 t294))
% 0.45/0.63 (step t296 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t297)
% 0.45/0.63 (assume t297.a0 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))
% 0.45/0.63 (step t297.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule forall_inst :args ((:= X tptp.tptp_minus_1)))
% 0.45/0.63 (step t297.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule or :premises (t297.t1))
% 0.45/0.63 (step t297.t3 (cl (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule resolution :premises (t297.t2 t297.a0))
% 0.45/0.63 (step t297 (cl (not (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule subproof :discharge (t297.a0))
% 0.45/0.63 (step t298 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule resolution :premises (t296 t297))
% 0.45/0.63 (step t299 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (not (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule implies_neg2)
% 0.45/0.63 (step t300 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule resolution :premises (t298 t299))
% 0.45/0.63 (step t301 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1))))) :rule contraction :premises (t300))
% 0.45/0.63 (step t302 (cl (not (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule implies :premises (t301))
% 0.45/0.63 (step t303 (cl (not (= (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)) (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (not (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X))) (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) :rule equiv_pos2)
% 0.45/0.63 (anchor :step t304 :args ((X $$unsorted) (:= X X)))
% 0.45/0.63 (step t304.t1 (cl (= X X)) :rule refl)
% 0.45/0.63 (step t304.t2 (cl (= (= (tptp.pred (tptp.succ X)) X) (= X (tptp.pred (tptp.succ X))))) :rule all_simplify)
% 0.45/0.63 (step t304 (cl (= (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)) (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) :rule bind)
% 0.45/0.63 (step t305 (cl (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) :rule resolution :premises (t303 t304 a39))
% 0.45/0.63 (step t306 (cl (= tptp.tptp_minus_1 (tptp.pred (tptp.succ tptp.tptp_minus_1)))) :rule resolution :premises (t302 t305))
% 0.45/0.63 (step t307 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t308)
% 0.45/0.63 (assume t308.a0 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))
% 0.45/0.63 (step t308.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))))) :rule forall_inst :args ((:= X tptp.n0)))
% 0.45/0.63 (step t308.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) :rule or :premises (t308.t1))
% 0.45/0.63 (step t308.t3 (cl (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) :rule resolution :premises (t308.t2 t308.a0))
% 0.45/0.63 (step t308 (cl (not (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) :rule subproof :discharge (t308.a0))
% 0.45/0.63 (step t309 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) :rule resolution :premises (t307 t308))
% 0.45/0.63 (step t310 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (not (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))))) :rule implies_neg2)
% 0.45/0.63 (step t311 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))))) :rule resolution :premises (t309 t310))
% 0.45/0.63 (step t312 (cl (=> (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0))))) :rule contraction :premises (t311))
% 0.45/0.63 (step t313 (cl (not (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X))))) (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) :rule implies :premises (t312))
% 0.45/0.63 (step t314 (cl (= tptp.n0 (tptp.pred (tptp.succ tptp.n0)))) :rule resolution :premises (t313 t305))
% 0.45/0.63 (step t315 (cl (not (= (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))))) (not (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0)))) (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)))) :rule equiv_pos2)
% 0.45/0.63 (step t316 (cl (= (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) :rule refl)
% 0.45/0.63 (step t317 (cl (= (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0)) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)))) :rule all_simplify)
% 0.45/0.63 (step t318 (cl (= (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))))) :rule cong :premises (t316 t317))
% 0.45/0.63 (step t319 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t320)
% 0.45/0.63 (assume t320.a0 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))
% 0.45/0.63 (step t320.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X)))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0)))) :rule forall_inst :args ((:= X tptp.n0)))
% 0.45/0.63 (step t320.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X)))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) :rule or :premises (t320.t1))
% 0.45/0.63 (step t320.t3 (cl (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) :rule resolution :premises (t320.t2 t320.a0))
% 0.45/0.63 (step t320 (cl (not (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X)))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) :rule subproof :discharge (t320.a0))
% 0.45/0.63 (step t321 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) :rule resolution :premises (t319 t320))
% 0.45/0.63 (step t322 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) (not (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0)))) :rule implies_neg2)
% 0.45/0.63 (step t323 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0))) (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0)))) :rule resolution :premises (t321 t322))
% 0.45/0.63 (step t324 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.plus tptp.n1 tptp.n0) (tptp.succ tptp.n0)))) :rule contraction :premises (t323))
% 0.45/0.63 (step t325 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0)))) :rule resolution :premises (t315 t318 t324))
% 0.45/0.63 (step t326 (cl (not (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X)))) (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) :rule implies :premises (t325))
% 0.45/0.63 (step t327 (cl (= (tptp.succ tptp.n0) (tptp.plus tptp.n1 tptp.n0))) :rule resolution :premises (t326 a29))
% 0.45/0.63 (step t328 (cl (not (= (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))))) (not (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0))))) (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)))) :rule equiv_pos2)
% 0.45/0.63 (step t329 (cl (= (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))))) :rule refl)
% 0.45/0.63 (step t330 (cl (= (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)))) :rule all_simplify)
% 0.45/0.63 (step t331 (cl (= (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))))) :rule cong :premises (t329 t330))
% 0.45/0.63 (step t332 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X)))) :rule implies_neg1)
% 0.45/0.63 (anchor :step t333)
% 0.45/0.63 (assume t333.a0 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))))
% 0.45/0.63 (step t333.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X)))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0))))) :rule forall_inst :args ((:= X (tptp.succ tptp.n0))))
% 0.45/0.63 (step t333.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X)))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) :rule or :premises (t333.t1))
% 0.45/0.63 (step t333.t3 (cl (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) :rule resolution :premises (t333.t2 t333.a0))
% 0.45/0.63 (step t333 (cl (not (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X)))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) :rule subproof :discharge (t333.a0))
% 0.45/0.63 (step t334 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) :rule resolution :premises (t332 t333))
% 0.45/0.63 (step t335 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) (not (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0))))) :rule implies_neg2)
% 0.45/0.63 (step t336 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0)))) (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0))))) :rule resolution :premises (t334 t335))
% 0.45/0.63 (step t337 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.plus (tptp.succ tptp.n0) tptp.n1) (tptp.succ (tptp.succ tptp.n0))))) :rule contraction :premises (t336))
% 0.45/0.63 (step t338 (cl (=> (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1)))) :rule resolution :premises (t328 t331 t337))
% 0.45/0.63 (step t339 (cl (not (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X)))) (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) :rule implies :premises (t338))
% 0.45/0.63 (step t340 (cl (= (tptp.succ (tptp.succ tptp.n0)) (tptp.plus (tptp.succ tptp.n0) tptp.n1))) :rule resolution :premises (t339 a28))
% 0.45/0.63 (step t341 (cl (= tptp.n2 (tptp.succ (tptp.succ tptp.n0)))) :rule symm :premises (a83))
% 0.45/0.63 (step t342 (cl (= tptp.n1 (tptp.succ tptp.n0))) :rule symm :premises (a82))
% 0.45/0.63 (step t343 (cl (= tptp.n0 (tptp.succ tptp.tptp_minus_1))) :rule symm :premises (a27))
% 0.45/0.63 (step t344 (cl) :rule resolution :premises (t81 t295 t264 t306 t314 t327 t340 t341 t342 t343))
% 0.45/0.63
% 0.45/0.63 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.CawmDznP3G/cvc5---1.0.5_15642.smt2
% 0.45/0.63 % cvc5---1.0.5 exiting
% 0.45/0.64 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------