TSTP Solution File: SWV203+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV203+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 21:49:42 EDT 2023
% Result : Theorem 0.21s 0.66s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV203+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 04:40:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.66 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.lJ5NRRWHdC/cvc5---1.0.5_7950.p...
% 0.21/0.66 ------- get file name : TPTP file name is SWV203+1
% 0.21/0.66 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7950.smt2...
% 0.21/0.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.66 % SZS status Theorem for SWV203+1
% 0.21/0.66 % SZS output start Proof for SWV203+1
% 0.21/0.66 (
% 0.21/0.66 (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 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))))) (let ((_let_6 (not (=> (and (= (tptp.a_select2 tptp.rho_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.rho_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.rho_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n5) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n5) tptp.use) (tptp.leq tptp.n0 tptp.pv5) (tptp.leq tptp.pv5 tptp.n998) (tptp.gt tptp.pv5 tptp.n0) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq tptp.n0 B) (tptp.leq A tptp.n2) (tptp.leq B (tptp.pred tptp.pv5))) (= (tptp.a_select3 tptp.u_defuse A B) tptp.use))) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq tptp.n0 D) (tptp.leq C tptp.n2) (tptp.leq D (tptp.pred tptp.pv5))) (= (tptp.a_select3 tptp.z_defuse C D) tptp.use)))) (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (= tptp.pv5 F))) (=> (and (tptp.leq tptp.n0 E) (tptp.leq tptp.n0 F) (tptp.leq E tptp.n2) (tptp.leq F tptp.pv5)) (=> (and (not (and (= tptp.n0 E) _let_1)) (not (and (= tptp.n1 E) _let_1)) (not (and (= tptp.n2 E) _let_1))) (= (tptp.a_select3 tptp.z_defuse E F) tptp.use))))))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))))) (let ((_let_9 (= tptp.pv5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (tptp.gt tptp.pv5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.pv5))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_9 _let_11))) (let ((_let_15 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.leq X Y)) (= X Y) (tptp.gt Y X))))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_17 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.pred tptp.pv5)))) (let ((_let_18 (= _let_11 _let_17))) (let ((_let_19 (not _let_11))) (let ((_let_20 (_let_7))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (= tptp.use (tptp.a_select3 tptp.z_defuse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_23 (not _let_17))) (let ((_let_24 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n2))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27 _let_25 _let_23 _let_22))) (let ((_let_31 (forall ((C $$unsorted) (D $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq tptp.n0 D)) (not (tptp.leq C tptp.n2)) (not (tptp.leq D (tptp.pred tptp.pv5))) (= tptp.use (tptp.a_select3 tptp.z_defuse C D)))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (_let_31))) (let ((_let_34 (= tptp.n2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (and _let_34 _let_9))) (let ((_let_36 (= tptp.n1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (and _let_36 _let_9))) (let ((_let_38 (and _let_10 _let_9))) (let ((_let_39 (or _let_29 _let_27 _let_25 _let_13 _let_38 _let_37 _let_35 _let_22))) (let ((_let_40 (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (= tptp.pv5 F))) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq tptp.n0 F)) (not (tptp.leq E tptp.n2)) (not (tptp.leq F tptp.pv5)) (and (= tptp.n0 E) _let_1) (and (= tptp.n1 E) _let_1) (and (= tptp.n2 E) _let_1) (= tptp.use (tptp.a_select3 tptp.z_defuse E F))))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (or))) (let ((_let_43 (not _let_40))) (let ((_let_44 (_let_43))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_44)) :args _let_44)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_40))) (REFL :args (_let_41)) :args _let_42)) (NOT_IMPLIES_ELIM2 _let_32) :args (_let_41 true _let_40)))) (let ((_let_46 (REFL :args (_let_39)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 2)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_42)) :args ((or _let_24 _let_39))) _let_45 :args (_let_24 true _let_39)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_42)) :args ((or _let_28 _let_39))) _let_45 :args (_let_28 true _let_39)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_13 _let_9 _let_11 (not _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 3)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_42)) :args ((or _let_12 _let_39))) _let_45 :args (_let_12 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_18)) :args ((or _let_17 _let_19 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_27 _let_25 _let_22 _let_23 (not _let_30)))) _let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 1)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_42)) :args ((or _let_26 _let_39))) _let_45 :args (_let_26 true _let_39)) _let_47 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 7)) _let_45 :args ((not _let_22) true _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.a_select3 tptp.z_defuse C D) tptp.use))))) :args _let_33)) (AND_ELIM (NOT_IMPLIES_ELIM1 _let_32) :args (31)) :args (_let_30 false _let_31)) :args (_let_23 false _let_28 false _let_26 false _let_24 true _let_22 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.pv5 QUANTIFIERS_INST_E_MATCHING ((tptp.leq X (tptp.pred Y))))) :args _let_20))) _let_21 :args (_let_18 false _let_7)) :args (_let_19 true _let_17 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_16 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.pv5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq X Y) false))))) :args (_let_15)))) _let_16 :args (_let_14 false _let_15)) :args (_let_9 false _let_12 true _let_11 false _let_14)))) (let ((_let_50 (or _let_29 _let_25 _let_10 _let_36 _let_34))) (let ((_let_51 (not _let_9))) (let ((_let_52 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n2)) (= tptp.n0 X) (= tptp.n1 X) (= tptp.n2 X))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_29 _let_25 _let_10 _let_36 _let_34 (not _let_50)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_52))) _let_53 :args (_let_50 false _let_52)) _let_47 _let_48 (REORDERING (CNF_AND_NEG :args (_let_35)) :args ((or _let_35 _let_51 (not _let_34)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 6)) _let_45 :args ((not _let_35) true _let_39)) (REORDERING (CNF_AND_NEG :args (_let_37)) :args ((or _let_37 _let_51 (not _let_36)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 5)) _let_45 :args ((not _let_37) true _let_39)) :args ((or _let_10 _let_51) false _let_50 false _let_24 false _let_28 true _let_34 true _let_35 true _let_36 true _let_37)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_38)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 4)) _let_45 :args ((not _let_38) true _let_39)) _let_49 :args ((not _let_10) true _let_38 false _let_9)) _let_49 :args (false true _let_10 false _let_9)) :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))) _let_8 _let_7 (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_6 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n998 tptp.n4) (tptp.gt tptp.n998 tptp.n5) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n998 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.n998 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.n998 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.n998 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n998 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)))) _let_5 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.67 )
% 0.21/0.67 % SZS output end Proof for SWV203+1
% 0.21/0.67 % cvc5---1.0.5 exiting
% 0.21/0.67 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------