%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP013_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 03:14:57 EDT 2023

% Result   : Theorem 0.23s 0.67s
% Output   : Proof 0.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16  % Problem    : ITP013_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.16/0.17  % Command    : do_cvc5 %s %d
% 0.17/0.38  % Computer : n013.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit   : 300
% 0.17/0.38  % WCLimit    : 300
% 0.17/0.38  % DateTime   : Sun Aug 27 15:51:47 EDT 2023
% 0.17/0.39  % CPUTime    : 
% 0.23/0.55  %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.67  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.sd5yipsW0S/cvc5---1.0.5_4377.p...
% 0.23/0.67  ------- get file name : TPTP file name is ITP013_1
% 0.23/0.67  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4377.smt2...
% 0.23/0.67  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.67  % SZS status Theorem for ITP013_1
% 0.23/0.67  % SZS output start Proof for ITP013_1
% 0.23/0.67  (
% 0.23/0.67  (let ((_let_1 (not (forall ((A_27a tptp.d) (V0a_2E0 tptp.mono_2Etyop_2Enum_2Enum) (V1b_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (=> (tptp.p (tptp.mono_2Ec_2Earithmetic_2E_3C_3D_2E2 V1b_2E0 V0a_2E0)) (= (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 V0a_2E0 V1b_2E0))))) (tptp.s _let_1 (tptp.c_2Ewords_2Eword__sub_2E2 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V0a_2E0)))) (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V1b_2E0))))))))))))) (let ((_let_2 (forall ((A_27a tptp.d) (A_27b tptp.d)) (and (forall ((V0m_2E0 tptp.mono_2Etyop_2Enum_2Enum) (V1n_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (= (tptp.s _let_1 (tptp.c_2Ewords_2Eword__add_2E2 (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V0m_2E0)))))) (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V1n_2E0)))))))) (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2B_2E2 V0m_2E0 V1n_2E0)))))))))) (forall ((V2m_2E0 tptp.mono_2Etyop_2Enum_2Enum) (V3n_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27b))) (= (tptp.s _let_1 (tptp.c_2Ewords_2Eword__add_2E2 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V2m_2E0)))) (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V3n_2E0)))))))) (tptp.s _let_1 (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool (tptp.mono_2Ec_2Earithmetic_2E_3C_3D_2E2 V3n_2E0 V2m_2E0))) (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 V2m_2E0 V3n_2E0))))) (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 V3n_2E0 V2m_2E0)))))))))))))))) (let ((_let_3 (forall ((A_27a tptp.d) (V0v_2E0 tptp.u) (V1w_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (let ((_let_2 (tptp.s _let_1 V1w_2E0))) (let ((_let_3 (tptp.s _let_1 V0v_2E0))) (= (tptp.s _let_1 (tptp.c_2Ewords_2Eword__sub_2E2 _let_3 _let_2)) (tptp.s _let_1 (tptp.c_2Ewords_2Eword__add_2E2 _let_3 (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 _let_2))))))))))) (let ((_let_4 (forall ((A_27a tptp.d)) (and (forall ((V0t1_2E0 tptp.u) (V1t2_2E0 tptp.u)) (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.i_mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2ET_2E0)) _let_1 (tptp.s A_27a V1t2_2E0))) _let_1))) (forall ((V2t1_2E0 tptp.u) (V3t2_2E0 tptp.u)) (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.i_mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2EF_2E0)) (tptp.s A_27a V2t1_2E0) _let_1)) _let_1))))))) (let ((_let_5 (forall ((V0t_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V0t_2E0))) (let ((_let_2 (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0))) (let ((_let_3 (tptp.p tptp.mono_2Ec_2Ebool_2ET_2E0))) (and (= (=> _let_3 _let_1) _let_1) (= (=> _let_1 _let_3) _let_3) (= (=> _let_2 _let_1) _let_3) (= (=> _let_1 _let_1) _let_3) (= (=> _let_1 _let_2) (not _let_1))))))))) (let ((_let_6 (tptp.p tptp.mono_2Ec_2Ebool_2ET_2E0))) (let ((_let_7 (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (=> (= (tptp.p V0_2E0) (tptp.p V1_2E0)) (= V0_2E0 V1_2E0))))) (let ((_let_8 (forall ((BOUND_VARIABLE_1907 tptp.d) (V0t1_2E0 tptp.u) (V1t2_2E0 tptp.u)) (let ((_let_1 (tptp.s BOUND_VARIABLE_1907 V0t1_2E0))) (= _let_1 (tptp.s BOUND_VARIABLE_1907 (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2ET_2E0)) _let_1 (tptp.s BOUND_VARIABLE_1907 V1t2_2E0)))))))) (let ((_let_9 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_9 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))))) (let ((_let_11 (tptp.s _let_9 _let_10))) (let ((_let_12 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_13 (tptp.s _let_9 _let_12))) (let ((_let_14 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2ET_2E0)))) (let ((_let_15 (= _let_13 (tptp.s _let_9 (tptp.c_2Ebool_2ECOND_2E3 _let_14 _let_13 _let_11))))) (let ((_let_16 (tptp.mono_2Ec_2Earithmetic_2E_3C_3D_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_18 (tptp.s _let_9 _let_17))) (let ((_let_19 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_20 (tptp.s _let_9 _let_19))) (let ((_let_21 (tptp.s _let_9 (tptp.c_2Ewords_2Eword__add_2E2 _let_20 (tptp.s _let_9 (tptp.c_2Ewords_2Eword__2comp_2E1 _let_18)))))) (let ((_let_22 (= _let_21 (tptp.s _let_9 (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool _let_16)) _let_13 _let_11))))) (let ((_let_23 (tptp.s _let_9 (tptp.c_2Ewords_2Eword__sub_2E2 _let_20 _let_18)))) (let ((_let_24 (= _let_23 _let_21))) (let ((_let_25 (= tptp.mono_2Ec_2Ebool_2ET_2E0 _let_16))) (let ((_let_26 (= _let_13 _let_23))) (let ((_let_27 (not _let_15))) (let ((_let_28 (forall ((BOUND_VARIABLE_1956 tptp.d) (V2m_2E0 tptp.mono_2Etyop_2Enum_2Enum) (V3n_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool BOUND_VARIABLE_1956))) (= (tptp.s _let_1 (tptp.c_2Ewords_2Eword__add_2E2 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V2m_2E0)))) (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V3n_2E0)))))))) (tptp.s _let_1 (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool (tptp.mono_2Ec_2Earithmetic_2E_3C_3D_2E2 V3n_2E0 V2m_2E0))) (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 V2m_2E0 V3n_2E0))))) (tptp.s _let_1 (tptp.c_2Ewords_2Eword__2comp_2E1 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 V3n_2E0 V2m_2E0)))))))))))))) (let ((_let_29 (_let_28))) (let ((_let_30 (_let_3))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (let ((_let_33 (tptp.p _let_16))) (let ((_let_34 (not _let_33))) (let ((_let_35 (= _let_6 _let_34))) (let ((_let_36 (or _let_35 _let_25))) (let ((_let_37 (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (or (= (tptp.p V1_2E0) (not (tptp.p V0_2E0))) (= V0_2E0 V1_2E0))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (not _let_35))) (let ((_let_40 (or _let_34 _let_26))) (let ((_let_41 (forall ((A_27a tptp.d) (V0a_2E0 tptp.mono_2Etyop_2Enum_2Enum) (V1b_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (or (not (tptp.p (tptp.mono_2Ec_2Earithmetic_2E_3C_3D_2E2 V1b_2E0 V0a_2E0))) (= (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 V0a_2E0 V1b_2E0))))) (tptp.s _let_1 (tptp.c_2Ewords_2Eword__sub_2E2 (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V0a_2E0)))) (tptp.s _let_1 (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V1b_2E0)))))))))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or))) (let ((_let_45 (not _let_41))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_43) :args (_let_45))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_44)) _let_43 :args (_let_42 true _let_41)))) (let ((_let_47 (not _let_26))) (let ((_let_48 (and _let_47 _let_25 _let_24 _let_22))) (let ((_let_49 (ASSUME :args (_let_47)))) (let ((_let_50 (ASSUME :args (_let_24)))) (let ((_let_51 (ASSUME :args (_let_22)))) (let ((_let_52 (APPLY_UF tptp.s))) (let ((_let_53 (REFL :args (_let_13)))) (let ((_let_54 (ASSUME :args (_let_25)))) (let ((_let_55 (_let_8))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_55) :args (_let_9 _let_12 _let_10 QUANTIFIERS_INST_E_MATCHING ((tptp.c_2Ebool_2ECOND_2E3 _let_14 (tptp.s BOUND_VARIABLE_1907 V0t1_2E0) (tptp.s BOUND_VARIABLE_1907 V1t2_2E0))))) :args _let_55)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_48)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_49 _let_50 _let_51 _let_54) (SCOPE (FALSE_ELIM (TRANS (CONG _let_53 (TRANS (CONG (REFL :args (_let_9)) (CONG (CONG (REFL :args (tptp.tyop_2Emin_2Ebool)) (CONG (SYMM (SYMM _let_54)) :args (APPLY_UF tptp.i_mono_2Etyop_2Emin_2Ebool)) :args _let_52) _let_53 (REFL :args (_let_11)) :args (APPLY_UF tptp.c_2Ebool_2ECOND_2E3)) :args _let_52) (SYMM _let_51) (SYMM _let_50)) :args (=)) (FALSE_INTRO _let_49))) :args (_let_47 _let_24 _let_22 _let_25))) :args (_let_47 _let_25 _let_24 _let_22))) :args (true _let_48)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_26))) (REFL :args ((not _let_25))) (REFL :args ((not _let_24))) (REFL :args ((not _let_22))) (REFL :args (_let_27)) :args _let_44)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 1)) _let_46 :args (_let_47 true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_25 (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_35)) :args ((or (not _let_6) _let_34 _let_39))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args (3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_44)) :args ((or _let_33 _let_40))) _let_46 :args (_let_33 true _let_40)) :args (_let_39 false _let_6 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_16 tptp.mono_2Ec_2Ebool_2ET_2E0 QUANTIFIERS_INST_E_MATCHING ((tptp.p V1_2E0) (tptp.p V0_2E0)))) :args (_let_37)))) _let_38 :args (_let_36 false _let_37)) :args (_let_25 true _let_35 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_19 _let_17 QUANTIFIERS_INST_E_MATCHING ((tptp.c_2Ewords_2Eword__sub_2E2 (tptp.s _let_32 V0v_2E0) (tptp.s _let_32 V1w_2E0))))) :args _let_30)) _let_31 :args (_let_24 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_29) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.s (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool BOUND_VARIABLE_1956) (tptp.c_2Ewords_2En2w_2E1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 V2m_2E0 V3n_2E0)))))))) :args _let_29)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_22 false _let_28)) :args (_let_27 true _let_26 false _let_25 false _let_24 false _let_22)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args (false true _let_15 false _let_8)) :args ((forall ((A_27a tptp.d) (A_27b tptp.d) (V0f_2E0 tptp.u) (V1g_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a A_27b))) (=> (forall ((V2x_2E0 tptp.u)) (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))))) _let_7 _let_6 (not (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0)) (forall ((V0t_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (or (= V0t_2E0 tptp.mono_2Ec_2Ebool_2ET_2E0) (= V0t_2E0 tptp.mono_2Ec_2Ebool_2EF_2E0))) (forall ((A_27a tptp.d) (V0x_2E0 tptp.u)) (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 tptp.d) (A_27b tptp.d) (V0x_2E0 tptp.u) (V1y_2E0 tptp.u)) (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 tptp.d) (A_27b tptp.d) (A_27c tptp.d) (V0f_2E0 tptp.u) (V1g_2E0 tptp.u) (V2x_2E0 tptp.u)) (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 tptp.mono_2Etyop_2Emin_2Ebool) (V1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (tptp.p (tptp.mono_2Ec_2Ebool_2E_2F_5C_2E2 V0_2E0 V1_2E0)) (and (tptp.p V0_2E0) (tptp.p V1_2E0)))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (tptp.p (tptp.mono_2Ec_2Ebool_2E_5C_2F_2E2 V0_2E0 V1_2E0)) (or (tptp.p V0_2E0) (tptp.p V1_2E0)))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (tptp.p (tptp.mono_2Ec_2Ebool_2E_7E_2E1 V0_2E0)) (not (tptp.p V0_2E0)))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (tptp.p (tptp.mono_2Ec_2Emin_2E_3D_3D_3E_2E2 V0_2E0 V1_2E0)) (=> (tptp.p V0_2E0) (tptp.p V1_2E0)))) (forall ((A_27a tptp.d) (V0_2E0 tptp.u) (V1_2E0 tptp.u)) (let ((_let_1 (tptp.s A_27a V1_2E0))) (let ((_let_2 (tptp.s A_27a V0_2E0))) (= (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_2E2 _let_2 _let_1)))) (= _let_2 _let_1))))) (forall ((A_27a tptp.d) (V0f_2E0 tptp.u)) (= (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (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 tptp.u)) (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (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 tptp.d) (V0f_2E0 tptp.u)) (= (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (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 tptp.u)) (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (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 ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool (tptp.j_mono_2Etyop_2Emin_2Ebool _let_1))) _let_1))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Enum_2Enum)))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Enum_2Enum))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum V0_2E0))) (= (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.j_mono_2Etyop_2Enum_2Enum _let_1))) _let_1))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool)) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Emin_2Ebool) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Emin_2Ebool)) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Enum_2Enum)) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Enum_2Enum) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (= (tptp.j_mono_2Etyop_2Enum_2Enum (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V0_2E0))) V0_2E0)) (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 _let_2))) (tptp.j_mono_2Etyop_2Emin_2Ebool (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 ((X0_2E0 tptp.mono_2Etyop_2Enum_2Enum) (X1_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (= (tptp.mono_2Ec_2Earithmetic_2E_2B_2E2 X0_2E0 X1_2E0) (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 tptp.mono_2Ec_2Earithmetic_2E_2B_2E0 X0_2E0) X1_2E0))) (forall ((X0_2E0 tptp.mono_2Etyop_2Enum_2Enum) (X1_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (= (tptp.mono_2Ec_2Earithmetic_2E_2D_2E2 X0_2E0 X1_2E0) (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 tptp.mono_2Ec_2Earithmetic_2E_2D_2E0 X0_2E0) X1_2E0))) (forall ((X0_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (X1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (and (tptp.p X0_2E0) (tptp.p X1_2E0)) (tptp.p (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 tptp.mono_2Ec_2Ebool_2E_2F_5C_2E0 X0_2E0) X1_2E0)))) (forall ((X0_2E0 tptp.mono_2Etyop_2Enum_2Enum) (X1_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (= (tptp.mono_2Ec_2Earithmetic_2E_3C_3D_2E2 X0_2E0 X1_2E0) (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 tptp.mono_2Ec_2Earithmetic_2E_3C_3D_2E0 X0_2E0) X1_2E0))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (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.j_mono_2Etyop_2Emin_2Ebool (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 ((X0_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (X1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (=> (tptp.p X0_2E0) (tptp.p X1_2E0)) (tptp.p (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 tptp.mono_2Ec_2Emin_2E_3D_3D_3E_2E0 X0_2E0) X1_2E0)))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 _let_2))) (tptp.j_mono_2Etyop_2Emin_2Ebool (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 ((A_27a tptp.d) (X0_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (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 (tptp.i_mono_2Etyop_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_27b tptp.d) (X0_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27b))) (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 (tptp.i_mono_2Etyop_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)))))))))) (forall ((X0_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (X1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (or (tptp.p X0_2E0) (tptp.p X1_2E0)) (tptp.p (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 tptp.mono_2Ec_2Ebool_2E_5C_2F_2E0 X0_2E0) X1_2E0)))) (forall ((A_27a tptp.d) (X0_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_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_27b tptp.d) (X0_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum X0_2E0)))) (let ((_let_2 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27b))) (= (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 tptp.d) (X0_2E0 tptp.u)) (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 ((A_27b tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27b))) (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 ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (let ((_let_2 (tptp.s _let_1 X1_2E0))) (let ((_let_3 (tptp.s _let_1 X0_2E0))) (let ((_let_4 (tptp.tyop_2Emin_2Efun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.c_2Ewords_2Eword__add_2E2 _let_3 _let_2)) (tptp.s _let_1 (tptp.app_2E2 (tptp.s _let_4 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 _let_4) tptp.c_2Ewords_2Eword__add_2E0) _let_3)) _let_2)))))))) (forall ((A_27b tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27b))) (let ((_let_2 (tptp.s _let_1 X1_2E0))) (let ((_let_3 (tptp.s _let_1 X0_2E0))) (let ((_let_4 (tptp.tyop_2Emin_2Efun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.c_2Ewords_2Eword__add_2E2 _let_3 _let_2)) (tptp.s _let_1 (tptp.app_2E2 (tptp.s _let_4 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 _let_4) tptp.c_2Ewords_2Eword__add_2E0) _let_3)) _let_2)))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Efcp_2Ecart tptp.tyop_2Emin_2Ebool A_27a))) (let ((_let_2 (tptp.s _let_1 X1_2E0))) (let ((_let_3 (tptp.s _let_1 X0_2E0))) (let ((_let_4 (tptp.tyop_2Emin_2Efun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.c_2Ewords_2Eword__sub_2E2 _let_3 _let_2)) (tptp.s _let_1 (tptp.app_2E2 (tptp.s _let_4 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 _let_4) tptp.c_2Ewords_2Eword__sub_2E0) _let_3)) _let_2)))))))) (forall ((X0_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (not (tptp.p X0_2E0)) (tptp.p (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2E_7E_2E0 X0_2E0)))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) (V1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool V0_2E0 V1_2E0))) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0_2E0)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool V1_2E0)))))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) (V1_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0_2E0 V1_2E0))) (tptp.s _let_1 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool _let_1) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0_2E0)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool V1_2E0))))))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) (V1_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool V0_2E0 V1_2E0))) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Emin_2Ebool) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 V0_2E0)) (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V1_2E0)))))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29) (V1_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Emin_2Ebool))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 V0_2E0 V1_2E0))) (tptp.s _let_1 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum _let_1) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 V0_2E0)) (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V1_2E0))))))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29) (V1_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Enum_2Enum))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 V0_2E0 V1_2E0))) (tptp.s _let_1 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum _let_1) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 V0_2E0)) (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V1_2E0))))))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) (V1_2E0 tptp.mono_2Etyop_2Enum_2Enum)) (= (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum V0_2E0 V1_2E0))) (tptp.s tptp.tyop_2Enum_2Enum (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum tptp.tyop_2Enum_2Enum) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 V0_2E0)) (tptp.s tptp.tyop_2Enum_2Enum (tptp.i_mono_2Etyop_2Enum_2Enum V1_2E0)))))) _let_6 _let_5 (forall ((A_27a tptp.d) (V0x_2E0 tptp.u)) (let ((_let_1 (tptp.s A_27a V0x_2E0))) (= (= _let_1 _let_1) (tptp.p tptp.mono_2Ec_2Ebool_2ET_2E0)))) (forall ((A_27a tptp.d) (V0x_2E0 tptp.u) (V1y_2E0 tptp.u)) (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 ((V0t_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V0t_2E0))) (let ((_let_2 (not _let_1))) (and (= (= tptp.mono_2Ec_2Ebool_2ET_2E0 V0t_2E0) _let_1) (= (= V0t_2E0 tptp.mono_2Ec_2Ebool_2ET_2E0) _let_1) (= (= tptp.mono_2Ec_2Ebool_2EF_2E0 V0t_2E0) _let_2) (= (= V0t_2E0 tptp.mono_2Ec_2Ebool_2EF_2E0) _let_2))))) (forall ((V0t1_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1t2_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V2t3_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V2t3_2E0))) (let ((_let_2 (tptp.p V1t2_2E0))) (let ((_let_3 (tptp.p V0t1_2E0))) (= (=> _let_3 (=> _let_2 _let_1)) (=> (and _let_3 _let_2) _let_1)))))) (forall ((V0x_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1x_27_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V2y_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V3y_27_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V1x_27_2E0))) (=> (and (= V0x_2E0 V1x_27_2E0) (=> _let_1 (= V2y_2E0 V3y_27_2E0))) (= (=> (tptp.p V0x_2E0) (tptp.p V2y_2E0)) (=> _let_1 (tptp.p V3y_27_2E0)))))) (forall ((A_27a tptp.d) (V0P_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1Q_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V2x_2E0 tptp.u) (V3x_27_2E0 tptp.u) (V4y_2E0 tptp.u) (V5y_27_2E0 tptp.u)) (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 A_27a V4y_2E0))) (let ((_let_4 (tptp.s A_27a V2x_2E0))) (let ((_let_5 (tptp.p V1Q_2E0))) (=> (and (= V0P_2E0 V1Q_2E0) (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_3 _let_1))) (= (tptp.s A_27a (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool V0P_2E0)) _let_4 _let_3)) (tptp.s A_27a (tptp.c_2Ebool_2ECOND_2E3 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool V1Q_2E0)) _let_2 _let_1)))))))))) _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.68  )
% 0.23/0.68  % SZS output end Proof for ITP013_1
% 0.23/0.68  % cvc5---1.0.5 exiting
% 0.23/0.68  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------