%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV053+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n025.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 21:49:06 EDT 2023

% Result   : Theorem 0.22s 0.65s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWV053+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n025.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Aug 29 11:05:10 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.65  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.TEFnk3qNDY/cvc5---1.0.5_11494.p...
% 0.22/0.65  ------- get file name : TPTP file name is SWV053+1
% 0.22/0.65  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11494.smt2...
% 0.22/0.65  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.65  % SZS status Theorem for SWV053+1
% 0.22/0.65  % SZS output start Proof for SWV053+1
% 0.22/0.65  (
% 0.22/0.65  (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.leq tptp.pv12 (tptp.minus tptp.n5 tptp.n1)))) (let ((_let_6 (tptp.leq tptp.pv10 (tptp.minus tptp.n135300 tptp.n1)))) (let ((_let_7 (tptp.leq tptp.n0 tptp.pv12))) (let ((_let_8 (tptp.leq tptp.n0 tptp.pv10))) (let ((_let_9 (tptp.minus (tptp.a_select3 tptp.center tptp.pv71 tptp.n0) (tptp.a_select2 tptp.x tptp.pv10)))) (let ((_let_10 (tptp.sqrt (tptp.times _let_9 _let_9)))) (let ((_let_11 (tptp.minus tptp.n0 tptp.n1))) (let ((_let_12 (= tptp.n0 (tptp.sum tptp.n0 _let_11 _let_10)))) (let ((_let_13 (not (=> (and _let_8 _let_7 _let_6 _let_5 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center B tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) _let_1))) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.minus tptp.pv12 tptp.n1))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 (tptp.minus tptp.n5 tptp.n1) (tptp.sqrt (tptp.times _let_2 _let_2)))))))))) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C (tptp.minus tptp.pv10 tptp.n1))) (= (tptp.sum tptp.n0 (tptp.minus tptp.n5 tptp.n1) (tptp.a_select3 tptp.q C D)) tptp.n1)))) (and _let_12 _let_8 _let_7 _let_6 _let_5 (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center F tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center E tptp.n0) _let_1))) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E (tptp.minus tptp.pv12 tptp.n1))) (= (tptp.a_select3 tptp.q tptp.pv10 E) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 (tptp.minus tptp.n5 tptp.n1) (tptp.sqrt (tptp.times _let_2 _let_2)))))))))) (forall ((G $$unsorted) (H $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G (tptp.minus tptp.pv10 tptp.n1))) (= (tptp.sum tptp.n0 (tptp.minus tptp.n5 tptp.n1) (tptp.a_select3 tptp.q G H)) tptp.n1)))))))) (let ((_let_14 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_15 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))) (let ((_let_16 (tptp.succ tptp.tptp_minus_1))) (let ((_let_17 (= _let_16 tptp.n0))) (let ((_let_18 (forall ((Body $$unsorted)) (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0)))) (let ((_let_19 (= tptp.n0 _let_16))) (let ((_let_20 (= _let_11 (tptp.pred tptp.n0)))) (let ((_let_21 (= tptp.tptp_minus_1 (tptp.pred _let_16)))) (let ((_let_22 (= tptp.n0 (tptp.sum tptp.n0 tptp.tptp_minus_1 _let_10)))) (let ((_let_23 (SYMM (ASSUME :args (_let_17))))) (let ((_let_24 (forall ((G $$unsorted) (H $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G (tptp.minus tptp.pv10 tptp.n1))) (= tptp.n1 (tptp.sum tptp.n0 (tptp.minus tptp.n5 tptp.n1) (tptp.a_select3 tptp.q G H))))))) (let ((_let_25 (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center F tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center E tptp.n0) _let_1))) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E (tptp.minus tptp.pv12 tptp.n1))) (= (tptp.a_select3 tptp.q tptp.pv10 E) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 (tptp.minus tptp.n5 tptp.n1) (tptp.sqrt (tptp.times _let_2 _let_2)))))))))))) (let ((_let_26 (not _let_12))) (let ((_let_27 (forall ((C $$unsorted) (D $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C (tptp.minus tptp.pv10 tptp.n1))) (= tptp.n1 (tptp.sum tptp.n0 (tptp.minus tptp.n5 tptp.n1) (tptp.a_select3 tptp.q C D))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (NOT_IMPLIES_ELIM1 _let_28))) (let ((_let_30 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center B tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) _let_1))) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.minus tptp.pv12 tptp.n1))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 (tptp.minus tptp.n5 tptp.n1) (tptp.sqrt (tptp.times _let_2 _let_2)))))))))))) (let ((_let_31 (_let_15))) (let ((_let_32 (ASSUME :args _let_31))) (let ((_let_33 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (forall ((Body $$unsorted)) (= tptp.n0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (not _let_22))) (let ((_let_38 (not _let_21))) (let ((_let_39 (not _let_20))) (let ((_let_40 (not _let_19))) (let ((_let_41 (_let_37))) (let ((_let_42 (ASSUME :args (_let_22)))) (let ((_let_43 (ASSUME :args (_let_26)))) (let ((_let_44 (ASSUME :args (_let_20)))) (let ((_let_45 (ASSUME :args (_let_21)))) (let ((_let_46 (REFL :args (tptp.n0)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_43 _let_44 _let_23 _let_45) (SCOPE (FALSE_ELIM (TRANS (CONG _let_46 (CONG _let_46 (TRANS (SYMM (SYMM _let_45)) (CONG (SYMM _let_23) :args (APPLY_UF tptp.pred)) (SYMM _let_44)) (REFL :args (_let_10)) :args (APPLY_UF tptp.sum)) :args (=)) (FALSE_INTRO _let_43))) :args (_let_26 _let_20 _let_19 _let_21))) _let_42) :args (_let_19 _let_26 _let_20 _let_21 _let_22)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_41))) (TRUE_INTRO _let_42))) :args (_let_37 _let_22)) :args ((not (and _let_19 _let_26 _let_20 _let_21 _let_22)) SB_LITERAL))) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_12))) (REFL :args (_let_39)) (REFL :args (_let_38)) (REFL :args _let_41) :args (or))) :args ((or _let_12 _let_40 _let_39 _let_38 _let_37))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0))))) :args (_let_35))) _let_36 :args (_let_22 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args (_let_33))) _let_34 :args (_let_21 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.minus X tptp.n1)))) :args _let_31)) _let_32 :args (_let_20 false _let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (NOT_AND (NOT_IMPLIES_ELIM2 _let_28)) :args ((or (not _let_8) (not _let_7) (not _let_6) (not _let_5) _let_26 (not _let_25) (not _let_24)))) (AND_ELIM _let_29 :args (0)) (AND_ELIM _let_29 :args (1)) (AND_ELIM _let_29 :args (2)) (AND_ELIM _let_29 :args (3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_30 (= A E) (= B F)))) :args ((or _let_25 (not _let_30)))) (AND_ELIM _let_29 :args (4)) :args (_let_25 false _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_27 (= C G) (= D H)))) :args ((or _let_24 (not _let_27)))) (AND_ELIM _let_29 :args (5)) :args (_let_24 false _let_27)) :args (_let_26 false _let_8 false _let_7 false _let_6 false _let_5 false _let_25 false _let_24)) _let_23 :args (false false _let_22 false _let_21 false _let_20 true _let_12 false _let_19)) :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))))))) _let_18 (forall ((Body $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) _let_17 (forall ((X $$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 $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) _let_15 _let_14 (forall ((X $$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_13 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n135300 tptp.n4) (tptp.gt tptp.n135300 tptp.n5) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n135300 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.n135300 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.n135300 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.n135300 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n135300 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 $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))) (forall ((X $$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) (= (tptp.succ _let_4) tptp.n5) (= _let_1 tptp.n1) (= _let_2 tptp.n2) (= _let_3 tptp.n3) true)))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.65  )
% 0.22/0.65  % SZS output end Proof for SWV053+1
% 0.22/0.65  % cvc5---1.0.5 exiting
% 0.22/0.65  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------