%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP015+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 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 03:15:16 EDT 2023

% Result   : Theorem 0.57s 0.77s
% Output   : Proof 0.57s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15  % Problem    : ITP015+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.14/0.16  % Command    : do_cvc5 %s %d
% 0.17/0.37  % Computer : n005.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit   : 300
% 0.17/0.37  % WCLimit    : 300
% 0.17/0.37  % DateTime   : Sun Aug 27 13:47:53 EDT 2023
% 0.17/0.38  % CPUTime    : 
% 0.23/0.54  %----Proving TF0_NAR, FOF, or CNF
% 0.57/0.77  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.igRjjpOPZh/cvc5---1.0.5_16330.p...
% 0.57/0.77  ------- get file name : TPTP file name is ITP015+1
% 0.57/0.77  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16330.smt2...
% 0.57/0.77  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.57/0.77  % SZS status Theorem for ITP015+1
% 0.57/0.77  % SZS output start Proof for ITP015+1
% 0.57/0.77  (
% 0.57/0.77  (let ((_let_1 (forall ((A_27a $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum tptp.c_2Enum_2E0_2E0))) (let ((_let_2 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (= (tptp.s _let_2 (tptp.c_2Einteger__word_2Ei2w_2E1 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 _let_1)))) (tptp.s _let_2 (tptp.c_2Ewords_2En2w_2E1 _let_1)))))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((A_27a $$unsorted)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (let ((_let_2 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum tptp.c_2Enum_2E0_2E0))))) (= (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 _let_2)) _let_2)))))) (let ((_let_4 (forall ((A_27a $$unsorted) (V0i_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Einteger_2Eint V0i_2E0))) (let ((_let_2 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (= (tptp.s _let_2 (tptp.c_2Einteger__word_2Ei2w_2E1 _let_1)) (tptp.s _let_2 (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Einteger_2Eint__lt_2E2 _let_1 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 (tptp.s tptp.tyop_2Enum_2Enum tptp.c_2Enum_2E0_2E0))))) (tptp.s _let_2 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_2 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Einteger_2ENum_2E1 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__neg_2E1 _let_1)))))))) (tptp.s _let_2 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Einteger_2ENum_2E1 _let_1)))))))))))) (let ((_let_5 (forall ((V0n_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum V0n_2E0))) (= (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Einteger_2ENum_2E1 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 _let_1)))) _let_1))))) (let ((_let_6 (forall ((V0n_2E0 $$unsorted) (V1m_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum V1m_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 _let_1)))) (let ((_let_3 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__neg_2E1 _let_2)))) (let ((_let_4 (tptp.s tptp.tyop_2Enum_2Enum V0n_2E0))) (let ((_let_5 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 _let_4)))) (let ((_let_6 (tptp.s tptp.tyop_2Enum_2Enum tptp.c_2Enum_2E0_2E0))) (let ((_let_7 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__neg_2E1 _let_5)))) (and (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Einteger_2Eint__lt_2E2 _let_5 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eprim__rec_2E_3C_2E2 _let_4 _let_1))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Einteger_2Eint__lt_2E2 _let_7 _let_3)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eprim__rec_2E_3C_2E2 _let_1 _let_4))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Einteger_2Eint__lt_2E2 _let_7 _let_2))) (or (not (= _let_4 _let_6)) (not (= _let_1 _let_6)))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Einteger_2Eint__lt_2E2 _let_5 _let_3)) (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0))))))))))))) (let ((_let_7 (tptp.s tptp.tyop_2Enum_2Enum tptp.c_2Enum_2E0_2E0))) (let ((_let_8 (tptp.c_2Einteger_2Eint__of__num_2E1 _let_7))) (let ((_let_9 (tptp.s tptp.tyop_2Einteger_2Eint _let_8))) (let ((_let_10 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__neg_2E1 _let_9)))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (forall ((A_27a $$unsorted)) (and (forall ((V0t1_2E0 $$unsorted) (V1t2_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V0t1_2E0))) (= (tptp.s A_27a (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0) _let_1 (tptp.s A_27a V1t2_2E0))) _let_1))) (forall ((V2t1_2E0 $$unsorted) (V3t2_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V3t2_2E0))) (= (tptp.s A_27a (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0) (tptp.s A_27a V2t1_2E0) _let_1)) _let_1))))))) (let ((_let_13 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0)))) (let ((_let_14 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0))) (let ((_let_15 (= _let_9 _let_10))) (let ((_let_16 (tptp.c_2Ewords_2En2w_2E1 _let_7))) (let ((_let_17 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (tptp.s _let_17 _let_16))) (let ((_let_19 (tptp.s _let_17 (tptp.c_2Einteger__word_2Ei2w_2E1 _let_9)))) (let ((_let_20 (= _let_19 _let_18))) (let ((_let_21 (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Einteger_2ENum_2E1 _let_9)))) (let ((_let_22 (= _let_7 _let_21))) (let ((_let_23 (= _let_19 (tptp.s _let_17 (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Einteger_2Eint__lt_2E2 _let_9 _let_9)) (tptp.s _let_17 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_17 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Einteger_2ENum_2E1 _let_10)))))) (tptp.s _let_17 (tptp.c_2Ewords_2En2w_2E1 _let_21))))))) (let ((_let_24 (= _let_18 (tptp.s _let_17 (tptp.c_2Ewords_2Eword__2comp_2E1 _let_18))))) (let ((_let_25 (= _let_14 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Einteger_2Eint__lt_2E2 _let_9 _let_10))))) (let ((_let_26 (= _let_18 (tptp.s _let_17 (tptp.c_2Ebool_2ECOND_2E3 _let_14 _let_18 _let_18))))) (let ((_let_27 (SYMM (ASSUME :args (_let_11))))) (let ((_let_28 (not _let_20))) (let ((_let_29 (_let_2))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (or))) (let ((_let_32 (_let_28))) (let ((_let_33 (forall ((V0n_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum V0n_2E0))) (= _let_1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Einteger_2ENum_2E1 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 _let_1))))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_4))) (let ((_let_36 (ASSUME :args _let_35))) (let ((_let_37 (forall ((A_27a $$unsorted)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (let ((_let_2 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum tptp.c_2Enum_2E0_2E0))))) (= _let_2 (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 _let_2)))))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (forall ((BOUND_VARIABLE_1551 $$unsorted) (BOUND_VARIABLE_1553 $$unsorted)) (= (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Einteger_2Eint__lt_2E2 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 (tptp.s tptp.tyop_2Enum_2Enum BOUND_VARIABLE_1551))) (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__neg_2E1 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 (tptp.s tptp.tyop_2Enum_2Enum BOUND_VARIABLE_1553))))))))))) (let ((_let_40 (_let_39))) (let ((_let_41 (forall ((BOUND_VARIABLE_1461 $$unsorted) (V2t1_2E0 $$unsorted) (V3t2_2E0 $$unsorted)) (let ((_let_1 (tptp.s BOUND_VARIABLE_1461 V3t2_2E0))) (= _let_1 (tptp.s BOUND_VARIABLE_1461 (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0) (tptp.s BOUND_VARIABLE_1461 V2t1_2E0) _let_1))))))) (let ((_let_42 (_let_41))) (let ((_let_43 (not _let_26))) (let ((_let_44 (_let_43))) (let ((_let_45 (ASSUME :args (_let_26)))) (let ((_let_46 (ASSUME :args _let_32))) (let ((_let_47 (ASSUME :args (_let_23)))) (let ((_let_48 (APPLY_UF tptp.s))) (let ((_let_49 (APPLY_UF tptp.c_2Ewords_2En2w_2E1))) (let ((_let_50 (ASSUME :args (_let_22)))) (let ((_let_51 (REFL :args (_let_17)))) (let ((_let_52 (CONG _let_51 (CONG (SYMM (SYMM _let_50)) :args _let_49) :args _let_48))) (let ((_let_53 (SYMM _let_27))) (let ((_let_54 (ASSUME :args (_let_24)))) (let ((_let_55 (ASSUME :args (_let_25)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_47 _let_27 _let_50 _let_54 _let_55 _let_46) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (TRANS (CONG _let_51 (CONG (TRANS (SYMM (SYMM _let_55)) (CONG (REFL :args (tptp.tyop_2Emin_2Ebool)) (CONG (REFL :args (_let_9)) _let_53 :args (APPLY_UF tptp.c_2Einteger_2Eint__lt_2E2)) :args _let_48)) (TRANS (SYMM (SYMM _let_54)) (CONG _let_51 (CONG (TRANS _let_52 (CONG _let_51 (CONG (CONG (REFL :args (tptp.tyop_2Enum_2Enum)) (CONG (SYMM _let_53) :args (APPLY_UF tptp.c_2Einteger_2ENum_2E1)) :args _let_48) :args _let_49) :args _let_48)) :args (APPLY_UF tptp.c_2Ewords_2Eword__2comp_2E1)) :args _let_48)) _let_52 :args (APPLY_UF tptp.c_2Ebool_2ECOND_2E3)) :args _let_48) (SYMM _let_47)) (REFL :args (_let_18)) :args (=)) (FALSE_INTRO _let_46)) :args ((= _let_26 false)))) :args (_let_23 _let_15 _let_22 _let_24 _let_25 _let_28))) _let_45) :args (_let_15 _let_28 _let_22 _let_23 _let_24 _let_25 _let_26)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_44))) (TRUE_INTRO _let_45))) :args (_let_43 _let_26)) :args ((not (and _let_15 _let_28 _let_22 _let_23 _let_24 _let_25 _let_26)) SB_LITERAL))) (CONG (REFL :args ((not _let_15))) (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_20))) (REFL :args ((not _let_22))) (REFL :args ((not _let_23))) (REFL :args ((not _let_24))) (REFL :args ((not _let_25))) (REFL :args _let_44) :args _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args (_let_17 _let_16 _let_16 QUANTIFIERS_INST_E_MATCHING ((tptp.c_2Ebool_2ECOND_2E3 _let_14 (tptp.s BOUND_VARIABLE_1461 V2t1_2E0) (tptp.s BOUND_VARIABLE_1461 V3t2_2E0))))) :args _let_42)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_26 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_40) :args (tptp.c_2Enum_2E0_2E0 tptp.c_2Enum_2E0_2E0 QUANTIFIERS_INST_E_MATCHING ((tptp.c_2Einteger_2Eint__lt_2E2 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 (tptp.s tptp.tyop_2Enum_2Enum BOUND_VARIABLE_1551))) (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__neg_2E1 (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 (tptp.s tptp.tyop_2Enum_2Enum BOUND_VARIABLE_1553))))))))) :args _let_40)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args (3)) :args (_let_25 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a)))) :args (_let_37))) _let_38 :args (_let_24 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8 QUANTIFIERS_INST_E_MATCHING ((tptp.s (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a) (tptp.c_2Einteger__word_2Ei2w_2E1 (tptp.s tptp.tyop_2Einteger_2Eint V0i_2E0)))))) :args _let_35)) _let_36 :args (_let_23 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.c_2Enum_2E0_2E0 QUANTIFIERS_INST_E_MATCHING ((tptp.c_2Einteger_2Eint__of__num_2E1 (tptp.s tptp.tyop_2Enum_2Enum V0n_2E0))))) :args (_let_33))) _let_34 :args (_let_22 false _let_33)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_30) :args _let_29)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args _let_32) :args _let_31)) _let_30 :args (_let_28 true _let_1)) _let_27 :args (false false _let_26 false _let_25 false _let_24 false _let_23 false _let_22 true _let_20 false _let_15)) :args ((forall ((A_27a $$unsorted) (A_27b $$unsorted) (V0f_2E0 $$unsorted) (V1g_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a A_27b))) (=> (forall ((V2x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V2x_2E0))) (let ((_let_2 (tptp.tyop_2Emin_2Efun A_27a A_27b))) (= (tptp.s A_27b (tptp.app_2E2 (tptp.s _let_2 V0f_2E0) _let_1)) (tptp.s A_27b (tptp.app_2E2 (tptp.s _let_2 V1g_2E0) _let_1)))))) (= (tptp.s _let_1 V0f_2E0) (tptp.s _let_1 V1g_2E0))))) (forall ((V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (=> (= (tptp.p _let_2) (tptp.p _let_1)) (= _let_2 _let_1))))) _let_13 (not (tptp.p _let_14)) (forall ((V0t_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0))) (or (= _let_1 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0)) (= _let_1 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0))))) (forall ((A_27a $$unsorted) (V0x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V0x_2E0))) (= (tptp.s A_27a (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a A_27a) tptp.combin_i_2E0) _let_1)) _let_1))) (forall ((A_27a $$unsorted) (A_27b $$unsorted) (V0x_2E0 $$unsorted) (V1y_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V0x_2E0))) (let ((_let_2 (tptp.tyop_2Emin_2Efun A_27b A_27a))) (= (tptp.s A_27a (tptp.app_2E2 (tptp.s _let_2 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_2) tptp.combin_k_2E0) _let_1)) (tptp.s A_27b V1y_2E0))) _let_1)))) (forall ((A_27a $$unsorted) (A_27b $$unsorted) (A_27c $$unsorted) (V0f_2E0 $$unsorted) (V1g_2E0 $$unsorted) (V2x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V2x_2E0))) (let ((_let_2 (tptp.tyop_2Emin_2Efun A_27a A_27b))) (let ((_let_3 (tptp.s _let_2 V1g_2E0))) (let ((_let_4 (tptp.tyop_2Emin_2Efun A_27b A_27c))) (let ((_let_5 (tptp.tyop_2Emin_2Efun A_27a _let_4))) (let ((_let_6 (tptp.s _let_5 V0f_2E0))) (let ((_let_7 (tptp.tyop_2Emin_2Efun A_27a A_27c))) (let ((_let_8 (tptp.tyop_2Emin_2Efun _let_2 _let_7))) (= (tptp.s A_27c (tptp.app_2E2 (tptp.s _let_7 (tptp.app_2E2 (tptp.s _let_8 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_5 _let_8) tptp.combin_s_2E0) _let_6)) _let_3)) _let_1)) (tptp.s A_27c (tptp.app_2E2 (tptp.s _let_4 (tptp.app_2E2 _let_6 _let_1)) (tptp.s A_27b (tptp.app_2E2 _let_3 _let_1)))))))))))))) (forall ((V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_2F_5C_2E2 _let_2 _let_1))) (and (tptp.p _let_2) (tptp.p _let_1)))))) (forall ((V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_5C_2F_2E2 _let_2 _let_1))) (or (tptp.p _let_2) (tptp.p _let_1)))))) (forall ((V0_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_7E_2E1 _let_1))) (not (tptp.p _let_1))))) (forall ((V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_3D_3E_2E2 _let_2 _let_1))) (=> (tptp.p _let_2) (tptp.p _let_1)))))) (forall ((A_27a $$unsorted) (V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V1_2E0))) (let ((_let_2 (tptp.s A_27a V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_2E2 _let_2 _let_1))) (= _let_2 _let_1))))) (forall ((A_27a $$unsorted) (V0f_2E0 $$unsorted)) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 (tptp.s (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool) V0f_2E0)))) (forall ((V1x_2E0 $$unsorted)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool) V0f_2E0) (tptp.s A_27a V1x_2E0))))))) (forall ((A_27a $$unsorted) (V0f_2E0 $$unsorted)) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 (tptp.s (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool) V0f_2E0)))) (exists ((V1x_2E0 $$unsorted)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool) V0f_2E0) (tptp.s A_27a V1x_2E0))))))) (forall ((X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool X1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool))) (= (and (tptp.p _let_2) (tptp.p _let_1)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool _let_3) tptp.c_2Ebool_2E_2F_5C_2E0) _let_2)) _let_1)))))))) (forall ((X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool X1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool))) (= (or (tptp.p _let_2) (tptp.p _let_1)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool _let_3) tptp.c_2Ebool_2E_5C_2F_2E0) _let_2)) _let_1)))))))) (forall ((X0_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (= (not (tptp.p _let_1)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool) tptp.c_2Ebool_2E_7E_2E0) _let_1)))))) (forall ((X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool X1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool))) (= (=> (tptp.p _let_2) (tptp.p _let_1)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool _let_3) tptp.c_2Emin_2E_3D_3D_3E_2E0) _let_2)) _let_1)))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a X1_2E0))) (let ((_let_2 (tptp.s A_27a X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (= (= _let_2 _let_1) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_3) tptp.c_2Emin_2E_3D_2E0) _let_2)) _let_1)))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 tptp.tyop_2Emin_2Ebool) tptp.c_2Ebool_2E_21_2E0) _let_2)))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 tptp.tyop_2Emin_2Ebool) tptp.c_2Ebool_2E_3F_2E0) _let_2)))))) (forall ((X0_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Einteger_2Eint X0_2E0))) (= (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Einteger_2ENum_2E1 _let_1)) (tptp.s tptp.tyop_2Enum_2Enum (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Enum_2Enum) tptp.c_2Einteger_2ENum_2E0) _let_1))))) (forall ((X0_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum X0_2E0))) (= (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__of__num_2E1 _let_1)) (tptp.s tptp.tyop_2Einteger_2Eint (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Einteger_2Eint) tptp.c_2Einteger_2Eint__of__num_2E0) _let_1))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Einteger_2Eint X0_2E0))) (let ((_let_2 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (= (tptp.s _let_2 (tptp.c_2Einteger__word_2Ei2w_2E1 _let_1)) (tptp.s _let_2 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint _let_2) tptp.c_2Einteger__word_2Ei2w_2E0) _let_1)))))) (forall ((X0_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Einteger_2Eint X0_2E0))) (= (tptp.s tptp.tyop_2Einteger_2Eint (tptp.c_2Einteger_2Eint__neg_2E1 _let_1)) (tptp.s tptp.tyop_2Einteger_2Eint (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Einteger_2Eint) tptp.c_2Einteger_2Eint__neg_2E0) _let_1))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum X0_2E0))) (let ((_let_2 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (= (tptp.s _let_2 (tptp.c_2Ewords_2En2w_2E1 _let_1)) (tptp.s _let_2 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum _let_2) tptp.c_2Ewords_2En2w_2E0) _let_1)))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 _let_2)) (tptp.s _let_1 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 _let_1) tptp.c_2Ewords_2Eword__2comp_2E0) _let_2)))))) (forall ((X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum X1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Enum_2Enum X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Emin_2Ebool))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eprim__rec_2E_3C_2E2 _let_2 _let_1)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum _let_3) tptp.c_2Eprim__rec_2E_3C_2E0) _let_2)) _let_1))))))) (forall ((X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum X1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Enum_2Enum X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Enum_2Enum))) (= (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Earithmetic_2EMOD_2E2 _let_2 _let_1)) (tptp.s tptp.tyop_2Enum_2Enum (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum _let_3) tptp.c_2Earithmetic_2EMOD_2E0) _let_2)) _let_1))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Ebool_2Eitself A_27a))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Ewords_2Edimword_2E1 _let_2)) (tptp.s tptp.tyop_2Enum_2Enum (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 tptp.tyop_2Enum_2Enum) tptp.c_2Ewords_2Edimword_2E0) _let_2)))))) (forall ((X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Einteger_2Eint X1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Einteger_2Eint X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Emin_2Ebool))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Einteger_2Eint__lt_2E2 _let_2 _let_1)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint _let_3) tptp.c_2Einteger_2Eint__lt_2E0) _let_2)) _let_1))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted) (X1_2E0 $$unsorted) (X2_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a X2_2E0))) (let ((_let_2 (tptp.s A_27a X1_2E0))) (let ((_let_3 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (let ((_let_4 (tptp.tyop_2Emin_2Efun A_27a A_27a))) (let ((_let_5 (tptp.tyop_2Emin_2Efun A_27a _let_4))) (= (tptp.s A_27a (tptp.c_2Ebool_2ECOND_2E3 _let_3 _let_2 _let_1)) (tptp.s A_27a (tptp.app_2E2 (tptp.s _let_4 (tptp.app_2E2 (tptp.s _let_5 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool _let_5) tptp.c_2Ebool_2ECOND_2E0) _let_3)) _let_2)) _let_1))))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted) (X1_2E0 $$unsorted) (X2_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (let ((_let_2 (tptp.s _let_1 X2_2E0))) (let ((_let_3 (tptp.s _let_1 X1_2E0))) (let ((_let_4 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (let ((_let_5 (tptp.tyop_2Emin_2Efun _let_1 _let_1))) (let ((_let_6 (tptp.tyop_2Emin_2Efun _let_1 _let_5))) (= (tptp.s _let_1 (tptp.c_2Ebool_2ECOND_2E3 _let_4 _let_3 _let_2)) (tptp.s _let_1 (tptp.app_2E2 (tptp.s _let_5 (tptp.app_2E2 (tptp.s _let_6 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool _let_6) tptp.c_2Ebool_2ECOND_2E0) _let_4)) _let_3)) _let_2)))))))))) _let_13 (forall ((V0t1_2E0 $$unsorted) (V1t2_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1t2_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0t1_2E0))) (let ((_let_3 (tptp.p _let_2))) (let ((_let_4 (tptp.p _let_1))) (=> (=> _let_3 _let_4) (=> (=> _let_4 _let_3) (= _let_2 _let_1)))))))) (forall ((V0t_2E0 $$unsorted)) (=> (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0)))) (forall ((A_27a $$unsorted) (V0x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V0x_2E0))) (= (= _let_1 _let_1) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0))))) (forall ((A_27a $$unsorted) (V0x_2E0 $$unsorted) (V1y_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V0x_2E0))) (let ((_let_2 (tptp.s A_27a V1y_2E0))) (= (= _let_1 _let_2) (= _let_2 _let_1))))) (forall ((V0t1_2E0 $$unsorted) (V1t2_2E0 $$unsorted) (V2t3_2E0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V2t3_2E0)))) (let ((_let_2 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V1t2_2E0)))) (let ((_let_3 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V0t1_2E0)))) (= (=> _let_3 (=> _let_2 _let_1)) (=> (and _let_3 _let_2) _let_1)))))) (forall ((A_27a $$unsorted) (V0P_2E0 $$unsorted) (V1Q_2E0 $$unsorted) (V2x_2E0 $$unsorted) (V3x_27_2E0 $$unsorted) (V4y_2E0 $$unsorted) (V5y_27_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V5y_27_2E0))) (let ((_let_2 (tptp.s A_27a V3x_27_2E0))) (let ((_let_3 (tptp.s tptp.tyop_2Emin_2Ebool V1Q_2E0))) (let ((_let_4 (tptp.s A_27a V4y_2E0))) (let ((_let_5 (tptp.s A_27a V2x_2E0))) (let ((_let_6 (tptp.s tptp.tyop_2Emin_2Ebool V0P_2E0))) (let ((_let_7 (tptp.p _let_3))) (=> (and (= _let_6 _let_3) (=> _let_7 (= _let_5 _let_2)) (=> (not _let_7) (= _let_4 _let_1))) (= (tptp.s A_27a (tptp.c_2Ebool_2ECOND_2E3 _let_6 _let_5 _let_4)) (tptp.s A_27a (tptp.c_2Ebool_2ECOND_2E3 _let_3 _let_2 _let_1)))))))))))) _let_12 _let_11 _let_6 _let_5 _let_4 (forall ((V0n_2E0 $$unsorted)) (not (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eprim__rec_2E_3C_2E2 (tptp.s tptp.tyop_2Enum_2Enum V0n_2E0) (tptp.s tptp.tyop_2Enum_2Enum tptp.c_2Enum_2E0_2E0)))))) (forall ((A_27a $$unsorted) (V0m_2E0 $$unsorted) (V1n_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Ewords_2Edimword_2E1 (tptp.s (tptp.tyop_2Ebool_2Eitself A_27a) tptp.c_2Ebool_2Ethe__value_2E0))))) (let ((_let_2 (tptp.s tptp.tyop_2Enum_2Enum V1n_2E0))) (let ((_let_3 (tptp.s tptp.tyop_2Enum_2Enum V0m_2E0))) (let ((_let_4 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (= (= (tptp.s _let_4 (tptp.c_2Ewords_2En2w_2E1 _let_3)) (tptp.s _let_4 (tptp.c_2Ewords_2En2w_2E1 _let_2))) (= (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Earithmetic_2EMOD_2E2 _let_3 _let_1)) (tptp.s tptp.tyop_2Enum_2Enum (tptp.c_2Earithmetic_2EMOD_2E2 _let_2 _let_1))))))))) _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.57/0.78  )
% 0.57/0.78  % SZS output end Proof for ITP015+1
% 0.57/0.78  % cvc5---1.0.5 exiting
% 0.57/0.78  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------