TSTP Solution File: SWV204+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV204+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 0.20s 0.61s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV204+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n019.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 10:27:43 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.61 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.A6o0iZUKMW/cvc5---1.0.5_24852.p...
% 0.20/0.61 ------- get file name : TPTP file name is SWV204+1
% 0.20/0.61 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24852.smt2...
% 0.20/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.61 % SZS status Theorem for SWV204+1
% 0.20/0.61 % SZS output start Proof for SWV204+1
% 0.20/0.61 (
% 0.20/0.61 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))))) (let ((_let_6 (tptp.a_select2 tptp.rho_defuse tptp.n2))) (let ((_let_7 (tptp.a_select2 tptp.rho_defuse tptp.n1))) (let ((_let_8 (tptp.a_select2 tptp.rho_defuse tptp.n0))) (let ((_let_9 (not (=> (and (= _let_8 tptp.use) (= _let_7 tptp.use) (= _let_6 tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n5) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n5) tptp.use) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq tptp.n0 B) (tptp.leq A tptp.n2) (tptp.leq B tptp.n998)) (= (tptp.a_select3 tptp.u_defuse A B) tptp.use))) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq tptp.n0 D) (tptp.leq C tptp.n2) (tptp.leq D tptp.n998)) (= (tptp.a_select3 tptp.z_defuse C D) tptp.use)))) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n2)) (= (tptp.a_select2 tptp.rho_defuse E) tptp.use))))))) (let ((_let_10 (= tptp.use _let_8))) (let ((_let_11 (= tptp.use (tptp.a_select2 tptp.rho_defuse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_12 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_14 (NOT_IMPLIES_ELIM1 _let_13))) (let ((_let_15 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n2))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16 _let_11))) (let ((_let_20 (forall ((E $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n2)) (= tptp.use (tptp.a_select2 tptp.rho_defuse E)))))) (let ((_let_21 (not _let_19))) (let ((_let_22 (or))) (let ((_let_23 (not _let_20))) (let ((_let_24 (_let_23))) (let ((_let_25 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_24)) :args _let_24)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_20))) (REFL :args (_let_21)) :args _let_22)) (NOT_IMPLIES_ELIM2 _let_13) :args (_let_21 true _let_20)))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_19 2)) _let_25 :args ((not _let_11) true _let_19)))) (let ((_let_27 (= tptp.n2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (= tptp.n1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (or _let_18 _let_16 _let_12 _let_28 _let_27))) (let ((_let_30 (forall ((X $$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_31 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (= tptp.use _let_7))) (let ((_let_33 (not _let_28))) (let ((_let_34 (and _let_32 _let_28))) (let ((_let_35 (APPLY_UF tptp.a_select2))) (let ((_let_36 (ASSUME :args (_let_28)))) (let ((_let_37 (REFL :args (tptp.rho_defuse)))) (let ((_let_38 (ASSUME :args (_let_32)))) (let ((_let_39 (= tptp.use _let_6))) (let ((_let_40 (not _let_27))) (let ((_let_41 (and _let_39 _let_27))) (let ((_let_42 (ASSUME :args (_let_27)))) (let ((_let_43 (ASSUME :args (_let_39)))) (let ((_let_44 (REFL :args (_let_19)))) (let ((_let_45 (and _let_10 _let_12))) (let ((_let_46 (ASSUME :args (_let_12)))) (let ((_let_47 (ASSUME :args (_let_10)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_45)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_46 _let_47) (SCOPE (TRANS (SYMM (SYMM _let_47)) (CONG _let_37 (SYMM (SYMM _let_46)) :args _let_35)) :args (_let_12 _let_10))) :args (_let_10 _let_12))) :args (true _let_45)) :args ((or (not _let_10) _let_11 (not _let_12)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_18 _let_16 _let_12 _let_27 _let_28 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 0)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_22)) :args ((or _let_17 _let_19))) _let_25 :args (_let_17 true _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 1)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_22)) :args ((or _let_15 _let_19))) _let_25 :args (_let_15 true _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_41)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_42 _let_43) (SCOPE (TRANS (SYMM (SYMM _let_43)) (CONG _let_37 (SYMM (SYMM _let_42)) :args _let_35)) :args (_let_27 _let_39))) :args (_let_39 _let_27))) :args (true _let_41)) :args ((or (not _let_39) _let_11 _let_40))) (AND_ELIM _let_14 :args (2)) _let_26 :args (_let_40 false _let_39 true _let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_34)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_36 _let_38) (SCOPE (TRANS (SYMM (SYMM _let_38)) (CONG _let_37 (SYMM (SYMM _let_36)) :args _let_35)) :args (_let_28 _let_32))) :args (_let_32 _let_28))) :args (true _let_34)) :args ((or (not _let_32) _let_11 _let_33))) (AND_ELIM _let_14 :args (1)) _let_26 :args (_let_33 false _let_32 true _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_30))) _let_31 :args (_let_29 false _let_30)) :args (_let_12 false _let_17 false _let_15 true _let_27 true _let_28 false _let_29)) _let_26 (AND_ELIM _let_14 :args (0)) :args (false false _let_12 true _let_11 false _let_10)) :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_9 (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))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.61 )
% 0.20/0.61 % SZS output end Proof for SWV204+1
% 0.20/0.61 % cvc5---1.0.5 exiting
% 0.20/0.61 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------