TSTP Solution File: SWV115+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV115+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 : Thu Aug 31 21:49:22 EDT 2023
% Result : Theorem 0.22s 0.58s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : SWV115+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.11/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 06:41:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.58 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Q87eB5MkqN/cvc5---1.0.5_5473.p...
% 0.22/0.58 ------- get file name : TPTP file name is SWV115+1
% 0.22/0.58 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_5473.smt2...
% 0.22/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.58 % SZS status Theorem for SWV115+1
% 0.22/0.58 % SZS output start Proof for SWV115+1
% 0.22/0.58 (
% 0.22/0.58 (let ((_let_1 (tptp.succ tptp.n0))) (let ((_let_2 (tptp.succ _let_1))) (let ((_let_3 (tptp.succ _let_2))) (let ((_let_4 (tptp.succ _let_3))) (let ((_let_5 (tptp.succ _let_4))) (let ((_let_6 (tptp.leq tptp.pv5 (tptp.minus tptp.n999 tptp.n1)))) (let ((_let_7 (tptp.leq tptp.n0 tptp.pv5))) (let ((_let_8 (not (=> (and _let_7 _let_6 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 A) (tptp.leq tptp.n0 B) (tptp.leq A _let_1) (tptp.leq B _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter A B) (tptp.a_select3 tptp.q_ds1_filter B A))))) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (=> (and (tptp.leq tptp.n0 C) (tptp.leq tptp.n0 D) (tptp.leq C _let_1) (tptp.leq D _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter C D) (tptp.a_select3 tptp.r_ds1_filter D C))))) (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 E) (tptp.leq tptp.n0 F) (tptp.leq E _let_1) (tptp.leq F _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter E F) (tptp.a_select3 tptp.pminus_ds1_filter F E))))) (forall ((G $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 G) (tptp.leq tptp.n0 H) (tptp.leq G _let_1) (tptp.leq H _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter G H) (tptp.a_select3 tptp.pminus_ds1_filter H G))))) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I (tptp.minus tptp.n6 tptp.n1))) (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter I J) (tptp.a_select3 tptp.id_ds1_filter J I))))))) (and _let_7 _let_6 (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 K) (tptp.leq tptp.n0 L) (tptp.leq K _let_1) (tptp.leq L _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter K L) (tptp.a_select3 tptp.q_ds1_filter L K))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (=> (and (tptp.leq tptp.n0 M) (tptp.leq tptp.n0 N) (tptp.leq M _let_1) (tptp.leq N _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter M N) (tptp.a_select3 tptp.r_ds1_filter N M))))) (forall ((O $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 O) (tptp.leq tptp.n0 P) (tptp.leq O _let_1) (tptp.leq P _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter O P) (tptp.a_select3 tptp.pminus_ds1_filter P O))))) (forall ((Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 Q) (tptp.leq tptp.n0 R) (tptp.leq Q _let_1) (tptp.leq R _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter Q R) (tptp.a_select3 tptp.pminus_ds1_filter R Q))))) (forall ((S $$unsorted)) (=> (and (tptp.leq tptp.n0 S) (tptp.leq S (tptp.minus tptp.n6 tptp.n1))) (forall ((T $$unsorted)) (=> (and (tptp.leq tptp.n0 T) (tptp.leq T (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter S T) (tptp.a_select3 tptp.id_ds1_filter T S))))))))))) (let ((_let_9 (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 K)) (not (tptp.leq tptp.n0 L)) (not (tptp.leq K _let_1)) (not (tptp.leq L _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter K L) (tptp.a_select3 tptp.q_ds1_filter L K))))))) (let ((_let_10 (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (or (not (tptp.leq tptp.n0 M)) (not (tptp.leq tptp.n0 N)) (not (tptp.leq M _let_1)) (not (tptp.leq N _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter M N) (tptp.a_select3 tptp.r_ds1_filter N M))))))) (let ((_let_11 (forall ((O $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 O)) (not (tptp.leq tptp.n0 P)) (not (tptp.leq O _let_1)) (not (tptp.leq P _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter O P) (tptp.a_select3 tptp.pminus_ds1_filter P O))))))) (let ((_let_12 (forall ((Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 Q)) (not (tptp.leq tptp.n0 R)) (not (tptp.leq Q _let_1)) (not (tptp.leq R _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter Q R) (tptp.a_select3 tptp.pminus_ds1_filter R Q))))))) (let ((_let_13 (forall ((S $$unsorted) (BOUND_VARIABLE_2310 $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 S)) (not (tptp.leq S _let_1)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2310)) (not (tptp.leq BOUND_VARIABLE_2310 _let_1)) (= (tptp.a_select3 tptp.id_ds1_filter S BOUND_VARIABLE_2310) (tptp.a_select3 tptp.id_ds1_filter BOUND_VARIABLE_2310 S))))))) (let ((_let_14 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_15 (NOT_IMPLIES_ELIM1 _let_14))) (let ((_let_16 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq tptp.n0 B)) (not (tptp.leq A _let_1)) (not (tptp.leq B _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter A B) (tptp.a_select3 tptp.q_ds1_filter B A))))))) (let ((_let_17 (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq tptp.n0 D)) (not (tptp.leq C _let_1)) (not (tptp.leq D _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter C D) (tptp.a_select3 tptp.r_ds1_filter D C))))))) (let ((_let_18 (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq tptp.n0 F)) (not (tptp.leq E _let_1)) (not (tptp.leq F _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter E F) (tptp.a_select3 tptp.pminus_ds1_filter F E))))))) (let ((_let_19 (AND_ELIM _let_15 :args (4)))) (let ((_let_20 (not _let_18))) (let ((_let_21 (forall ((I $$unsorted) (BOUND_VARIABLE_2248 $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq I _let_1)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2248)) (not (tptp.leq BOUND_VARIABLE_2248 _let_1)) (= (tptp.a_select3 tptp.id_ds1_filter I BOUND_VARIABLE_2248) (tptp.a_select3 tptp.id_ds1_filter BOUND_VARIABLE_2248 I))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_AND (NOT_IMPLIES_ELIM2 _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_21 (= I S) (= BOUND_VARIABLE_2248 BOUND_VARIABLE_2310)))) :args ((or _let_13 (not _let_21)))) (AND_ELIM _let_15 :args (6)) :args (_let_13 false _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_18 (= E Q) (= F R)))) :args ((or _let_12 _let_20))) _let_19 :args (_let_12 false _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_18 (= E O) (= F P)))) :args ((or _let_11 _let_20))) _let_19 :args (_let_11 false _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_17 (= C M) (= D N)))) :args ((or _let_10 (not _let_17)))) (AND_ELIM _let_15 :args (3)) :args (_let_10 false _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_16 (= A K) (= B L)))) :args ((or _let_9 (not _let_16)))) (AND_ELIM _let_15 :args (2)) :args (_let_9 false _let_16)) (AND_ELIM _let_15 :args (1)) (AND_ELIM _let_15 :args (0)) :args (false false _let_13 false _let_12 false _let_11 false _let_10 false _let_9 false _let_6 false _let_7)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))) (forall ((X $$unsorted)) (not (tptp.gt X X))) (forall ((X $$unsorted)) (tptp.leq X X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))) (forall ((X $$unsorted)) (tptp.gt (tptp.succ X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq X Y) (tptp.leq X (tptp.succ Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X Y) (tptp.gt (tptp.succ Y) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq (tptp.uniform_int_rnd C X) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq tptp.n0 (tptp.uniform_int_rnd C X)))) (forall ((I $$unsorted) (L $$unsorted) (U $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim L U) Val) I) Val))) (forall ((I $$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))) (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)) (let ((_let_1 (tptp.trans A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (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)) (let ((_let_1 (tptp.inv A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (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)) (let ((_let_1 (tptp.tptp_update3 A K K VAL))) (=> (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 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (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 $$unsorted)) (let ((_let_1 (tptp.tptp_madd A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$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)) (let ((_let_1 (tptp.tptp_msub A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (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 $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((Body $$unsorted)) (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0)) (forall ((Body $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) (= (tptp.succ tptp.tptp_minus_1) tptp.n0) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)) (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.succ X) Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.minus X Y) X) (tptp.leq tptp.n0 Y))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) U V) VAL)) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= J V) (= (tptp.a_select3 X U V) VAL)) (= (tptp.a_select3 (tptp.tptp_update3 X I J VAL2) U V) VAL))) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted) (J0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)) (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 $$unsorted)) (=> (and (forall ((I0 $$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))) tptp.true (not (= tptp.def tptp.use)) _let_8 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n6 tptp.n4) (tptp.gt tptp.n999 tptp.n4) (tptp.gt tptp.n6 tptp.n5) (tptp.gt tptp.n999 tptp.n5) (tptp.gt tptp.n999 tptp.n6) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n6 tptp.tptp_minus_1) (tptp.gt tptp.n999 tptp.tptp_minus_1) (tptp.gt tptp.n0 tptp.tptp_minus_1) (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) (tptp.gt tptp.n4 tptp.n0) (tptp.gt tptp.n5 tptp.n0) (tptp.gt tptp.n6 tptp.n0) (tptp.gt tptp.n999 tptp.n0) (tptp.gt tptp.n1 tptp.n0) (tptp.gt tptp.n2 tptp.n0) (tptp.gt tptp.n3 tptp.n0) (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n6 tptp.n1) (tptp.gt tptp.n999 tptp.n1) (tptp.gt tptp.n2 tptp.n1) (tptp.gt tptp.n3 tptp.n1) (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n6 tptp.n2) (tptp.gt tptp.n999 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n6 tptp.n3) (tptp.gt tptp.n999 tptp.n3) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))) (forall ((X $$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)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n6)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5) (= X tptp.n6)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))) (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)))) (= _let_4 tptp.n4) (= _let_5 tptp.n5) (= (tptp.succ _let_5) tptp.n6) (= _let_1 tptp.n1) (= _let_2 tptp.n2) (= _let_3 tptp.n3) true))))))))))))))))))))))))
% 0.22/0.59 )
% 0.22/0.59 % SZS output end Proof for SWV115+1
% 0.22/0.59 % cvc5---1.0.5 exiting
% 0.22/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------