%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP012_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n021.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 03:14:48 EDT 2023

% Result   : Theorem 0.21s 0.63s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15  % Problem    : ITP012_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.11/0.16  % Command    : do_cvc5 %s %d
% 0.15/0.37  % Computer : n021.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Sun Aug 27 13:47:27 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.21/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.63  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.P1dr3u6I4l/cvc5---1.0.5_3810.p...
% 0.21/0.63  ------- get file name : TPTP file name is ITP012_1
% 0.21/0.63  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3810.smt2...
% 0.21/0.63  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.63  % SZS status Theorem for ITP012_1
% 0.21/0.63  % SZS output start Proof for ITP012_1
% 0.21/0.63  (
% 0.21/0.63  (let ((_let_1 (not (forall ((V0p_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V1q_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V2r_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (=> (tptp.p (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 V1q_2E0)) (= (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 (tptp.mono_2Ec_2Einteger_2Eint__sub_2E2 V2r_2E0 V1q_2E0)) (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 V2r_2E0))))))) (let ((_let_2 (forall ((V0p_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V1q_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (let ((_let_1 (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 V1q_2E0))) (and (= (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 (tptp.mono_2Ec_2Einteger_2Eint__neg_2E1 V1q_2E0)) _let_1) (= (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 (tptp.mono_2Ec_2Einteger_2Eint__neg_2E1 V0p_2E0) V1q_2E0) _let_1)))))) (let ((_let_3 (forall ((V0p_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V1q_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V2r_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (=> (tptp.p (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 V1q_2E0)) (= (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 (tptp.mono_2Ec_2Einteger_2Eint__add_2E2 V2r_2E0 V1q_2E0)) (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 V2r_2E0)))))) (let ((_let_4 (forall ((V0x_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V1y_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (= (tptp.mono_2Ec_2Einteger_2Eint__sub_2E2 V0x_2E0 V1y_2E0) (tptp.mono_2Ec_2Einteger_2Eint__add_2E2 V0x_2E0 (tptp.mono_2Ec_2Einteger_2Eint__neg_2E1 V1y_2E0)))))) (let ((_let_5 (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))))))) (let ((_let_6 (tptp.p tptp.mono_2Ec_2Ebool_2ET_2E0))) (let ((_let_7 (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0))) (let ((_let_8 (not _let_7))) (let ((_let_9 (not _let_6))) (let ((_let_10 (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_11 (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_12 (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (= tptp.mono_2Ec_2Ebool_2ET_2E0 _let_12))) (let ((_let_14 (tptp.mono_2Ec_2Einteger_2Eint__neg_2E1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_16 (= _let_12 _let_15))) (let ((_let_17 (= tptp.mono_2Ec_2Ebool_2ET_2E0 _let_15))) (let ((_let_18 (tptp.p _let_12))) (let ((_let_19 (not _let_18))) (let ((_let_20 (= _let_6 _let_19))) (let ((_let_21 (or _let_20 _let_13))) (let ((_let_22 (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_23 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (not _let_20))) (let ((_let_25 (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_26 (tptp.mono_2Ec_2Einteger_2Eint__sub_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_27 (= (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_26) _let_25))) (let ((_let_28 (or _let_19 _let_27))) (let ((_let_29 (forall ((V0p_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V1q_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V2r_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (or (not (tptp.p (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 V1q_2E0))) (= (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 (tptp.mono_2Ec_2Einteger_2Eint__sub_2E2 V2r_2E0 V1q_2E0)) (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 V2r_2E0)))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (or))) (let ((_let_33 (not _let_29))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_31) :args (_let_33))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_32)) _let_31 :args (_let_30 true _let_29)))) (let ((_let_35 (forall ((BOUND_VARIABLE_1798 tptp.mono_2Etyop_2Einteger_2Eint) (BOUND_VARIABLE_1800 tptp.mono_2Etyop_2Einteger_2Eint)) (= (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 BOUND_VARIABLE_1798 BOUND_VARIABLE_1800) (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 BOUND_VARIABLE_1798 (tptp.mono_2Ec_2Einteger_2Eint__neg_2E1 BOUND_VARIABLE_1800)))))) (let ((_let_36 (0))) (let ((_let_37 (_let_35))) (let ((_let_38 (tptp.p _let_15))) (let ((_let_39 (= _let_38 _let_17))) (let ((_let_40 (not _let_17))) (let ((_let_41 (forall ((BOUND_VARIABLE_1736 tptp.mono_2Etyop_2Emin_2Ebool)) (= (tptp.p BOUND_VARIABLE_1736) (= tptp.mono_2Ec_2Ebool_2ET_2E0 BOUND_VARIABLE_1736))))) (let ((_let_42 (_let_41))) (let ((_let_43 (tptp.mono_2Ec_2Einteger_2Eint__add_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14))) (let ((_let_44 (= _let_25 (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_43)))) (let ((_let_45 (not _let_38))) (let ((_let_46 (or _let_45 _let_44))) (let ((_let_47 (forall ((V0p_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V1q_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (V2r_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (or (not (tptp.p (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 V1q_2E0))) (= (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 (tptp.mono_2Ec_2Einteger_2Eint__add_2E2 V2r_2E0 V1q_2E0)) (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 V2r_2E0)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (= _let_26 _let_43))) (let ((_let_50 (not _let_44))) (let ((_let_51 (_let_4))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 (not _let_27))) (let ((_let_54 (and _let_53 _let_49))) (let ((_let_55 (ASSUME :args (_let_53)))) (let ((_let_56 (ASSUME :args (_let_49)))) (let ((_let_57 (and _let_13 _let_16))) (let ((_let_58 (ASSUME :args (_let_16)))) (let ((_let_59 (ASSUME :args (_let_13)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_57)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_58 _let_59) (SCOPE (TRANS (SYMM (SYMM _let_59)) (SYMM (SYMM _let_58))) :args (_let_16 _let_13))) :args (_let_13 _let_16))) :args (true _let_57)) :args ((or (not _let_13) _let_17 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_39)) :args ((or _let_38 _let_40 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_44 (not _let_46)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_54)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_56 _let_55) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (SYMM _let_56) :args (APPLY_UF tptp.mono_2Ec_2Einteger_2Eint__divides_2E2)) (REFL :args (_let_25)) :args (=)) (FALSE_INTRO _let_55)) :args ((= _let_44 false)))) :args (_let_49 _let_53))) :args (_let_53 _let_49))) :args (true _let_54)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_27))) (REFL :args ((not _let_49))) (REFL :args (_let_50)) :args _let_32)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 1)) _let_34 :args (_let_53 true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.mono_2Ec_2Einteger_2Eint__sub_2E2 V0x_2E0 V1y_2E0)))) :args _let_51)) _let_52 :args (_let_49 false _let_4)) :args (_let_50 true _let_27 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 V0p_2E0 (tptp.mono_2Ec_2Einteger_2Eint__add_2E2 V2r_2E0 V1q_2E0))))) :args (_let_47)))) _let_48 :args (_let_46 false _let_47)) :args (_let_45 true _let_44 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args (_let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.p BOUND_VARIABLE_1736)))) :args _let_42)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args _let_36) :args (_let_39 false _let_41)) :args (_let_40 true _let_38 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_37) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 BOUND_VARIABLE_1798 (tptp.mono_2Ec_2Einteger_2Eint__neg_2E1 BOUND_VARIABLE_1800))))) :args _let_37)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args _let_36) :args (_let_16 false _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_13 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_20)) :args ((or _let_9 _let_19 _let_24))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) :args (3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_32)) :args ((or _let_18 _let_28))) _let_34 :args (_let_18 true _let_28)) :args (_let_24 false _let_6 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_12 tptp.mono_2Ec_2Ebool_2ET_2E0 QUANTIFIERS_INST_E_MATCHING ((tptp.p V1_2E0) (tptp.p V0_2E0)))) :args (_let_22)))) _let_23 :args (_let_21 false _let_22)) :args (_let_13 true _let_20 false _let_21)) :args (false true _let_17 false _let_16 false _let_13)) :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_11 _let_6 _let_8 (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_2Einteger_2Eint tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Einteger_2Eint)))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Einteger_2Eint))) (let ((_let_2 (tptp.s _let_1 V0_2E0))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (tptp.s tptp.tyop_2Einteger_2Eint V0_2E0))) (= (tptp.s tptp.tyop_2Einteger_2Eint (tptp.i_mono_2Etyop_2Einteger_2Eint (tptp.j_mono_2Etyop_2Einteger_2Eint _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_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Emin_2Ebool) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Emin_2Ebool)) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Einteger_2Eint)) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29)) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Einteger_2Eint) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 V0_2E0))) V0_2E0)) (forall ((V0_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (= (tptp.j_mono_2Etyop_2Einteger_2Eint (tptp.s tptp.tyop_2Einteger_2Eint (tptp.i_mono_2Etyop_2Einteger_2Eint 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_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 ((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 ((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 ((X0_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (X1_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (= (tptp.mono_2Ec_2Einteger_2Eint__add_2E2 X0_2E0 X1_2E0) (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 tptp.mono_2Ec_2Einteger_2Eint__add_2E0 X0_2E0) X1_2E0))) (forall ((X0_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (X1_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (= (tptp.mono_2Ec_2Einteger_2Eint__divides_2E2 X0_2E0 X1_2E0) (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 tptp.mono_2Ec_2Einteger_2Eint__divides_2E0 X0_2E0) X1_2E0))) (forall ((X0_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (= (tptp.mono_2Ec_2Einteger_2Eint__neg_2E1 X0_2E0) (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint tptp.mono_2Ec_2Einteger_2Eint__neg_2E0 X0_2E0))) (forall ((X0_2E0 tptp.mono_2Etyop_2Einteger_2Eint) (X1_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (= (tptp.mono_2Ec_2Einteger_2Eint__sub_2E2 X0_2E0 X1_2E0) (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 tptp.mono_2Ec_2Einteger_2Eint__sub_2E0 X0_2E0) X1_2E0))) (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_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29) (V1_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_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_2Einteger_2Eint tptp.tyop_2Emin_2Ebool) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 V0_2E0)) (tptp.s tptp.tyop_2Einteger_2Eint (tptp.i_mono_2Etyop_2Einteger_2Eint V1_2E0)))))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29) (V1_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Emin_2Ebool))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 V0_2E0 V1_2E0))) (tptp.s _let_1 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint _let_1) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 V0_2E0)) (tptp.s tptp.tyop_2Einteger_2Eint (tptp.i_mono_2Etyop_2Einteger_2Eint V1_2E0))))))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29) (V1_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (let ((_let_1 (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Einteger_2Eint))) (= (tptp.s _let_1 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 V0_2E0 V1_2E0))) (tptp.s _let_1 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint _let_1) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 V0_2E0)) (tptp.s tptp.tyop_2Einteger_2Eint (tptp.i_mono_2Etyop_2Einteger_2Eint V1_2E0))))))) (forall ((V0_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29) (V1_2E0 tptp.mono_2Etyop_2Einteger_2Eint)) (= (tptp.s tptp.tyop_2Einteger_2Eint (tptp.i_mono_2Etyop_2Einteger_2Eint (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint V0_2E0 V1_2E0))) (tptp.s tptp.tyop_2Einteger_2Eint (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Einteger_2Eint tptp.tyop_2Einteger_2Eint) (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 V0_2E0)) (tptp.s tptp.tyop_2Einteger_2Eint (tptp.i_mono_2Etyop_2Einteger_2Eint V1_2E0)))))) _let_6 (forall ((V0t1_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1t2_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V0t1_2E0))) (let ((_let_2 (tptp.p V1t2_2E0))) (=> (=> _let_1 _let_2) (=> (=> _let_2 _let_1) (= V0t1_2E0 V1t2_2E0)))))) (forall ((V0t_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V0t_2E0))) (=> (=> _let_1 (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0)) (not _let_1)))) (forall ((V0t_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V0t_2E0))) (=> (not _let_1) (=> _let_1 (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0))))) _let_10 (and (forall ((V0t_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V0t_2E0))) (= (not (not _let_1)) _let_1))) (= _let_9 _let_7) (= _let_8 _let_6)) _let_5 (forall ((A_27a tptp.d) (V0P_2E0 tptp.u)) (= (not (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) V0P_2E0) (tptp.s A_27a V1x_2E0))))))) (exists ((V2x_2E0 tptp.u)) (not (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) V0P_2E0) (tptp.s A_27a V2x_2E0))))))))) (forall ((A_27a tptp.d) (V0P_2E0 tptp.u) (V1Q_2E0 tptp.u)) (= (forall ((V2x_2E0 tptp.u)) (let ((_let_1 (tptp.s A_27a V2x_2E0))) (let ((_let_2 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (and (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_2 V0P_2E0) _let_1)))) (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_2 V1Q_2E0) _let_1)))))))) (and (forall ((V3x_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) V0P_2E0) (tptp.s A_27a V3x_2E0)))))) (forall ((V4x_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) V1Q_2E0) (tptp.s A_27a V4x_2E0))))))))) (forall ((V0A_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1B_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V2C_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (or (tptp.p V0A_2E0) (tptp.p V1B_2E0) (tptp.p V2C_2E0)))) (= _let_1 _let_1))) (forall ((V0A_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1B_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V0A_2E0))) (let ((_let_2 (tptp.p V1B_2E0))) (= (or _let_1 _let_2) (or _let_2 _let_1))))) (forall ((V0A_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1B_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V1B_2E0))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p V0A_2E0))) (let ((_let_4 (not _let_3))) (and (= (not (and _let_3 _let_1)) (or _let_4 _let_2)) (= (not (or _let_3 _let_1)) (and _let_4 _let_2)))))))) _let_4 _let_3 _let_2 (forall ((V0t_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V0t_2E0))) (= (not (not _let_1)) _let_1))) (forall ((V0A_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V0A_2E0))) (=> _let_1 (=> (not _let_1) (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0))))) (forall ((V0B_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1A_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0))) (let ((_let_2 (tptp.p V0B_2E0))) (let ((_let_3 (tptp.p V1A_2E0))) (= (=> (not (or _let_3 _let_2)) _let_1) (=> (=> _let_3 _let_1) (=> (not _let_2) _let_1))))))) (forall ((V0B_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1A_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0))) (let ((_let_2 (tptp.p V0B_2E0))) (let ((_let_3 (tptp.p V1A_2E0))) (= (=> (not (or (not _let_3) _let_2)) _let_1) (=> _let_3 (=> (not _let_2) _let_1))))))) (forall ((V0A_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0))) (let ((_let_2 (tptp.p V0A_2E0))) (=> (=> (not _let_2) _let_1) (=> (=> _let_2 _let_1) _let_1))))) (forall ((V0r_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1q_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V2p_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V2p_2E0))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p V1q_2E0))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.p V0r_2E0))) (let ((_let_6 (not _let_5))) (= (= _let_1 (= V1q_2E0 V0r_2E0)) (and (or _let_1 _let_3 _let_5) (or _let_1 _let_6 _let_4) (or _let_3 _let_6 _let_2) (or _let_5 _let_4 _let_2)))))))))) (forall ((V0r_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1q_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V2p_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V2p_2E0))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p V0r_2E0))) (let ((_let_4 (tptp.p V1q_2E0))) (= (= _let_1 (and _let_4 _let_3)) (and (or _let_1 (not _let_4) (not _let_3)) (or _let_4 _let_2) (or _let_3 _let_2)))))))) (forall ((V0r_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1q_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V2p_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V2p_2E0))) (let ((_let_2 (tptp.p V0r_2E0))) (let ((_let_3 (tptp.p V1q_2E0))) (= (= _let_1 (or _let_3 _let_2)) (and (or _let_1 (not _let_3)) (or _let_1 (not _let_2)) (or _let_3 _let_2 (not _let_1)))))))) (forall ((V0r_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1q_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V2p_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V2p_2E0))) (let ((_let_2 (tptp.p V0r_2E0))) (let ((_let_3 (tptp.p V1q_2E0))) (= (= _let_1 (=> _let_3 _let_2)) (and (or _let_1 _let_3) (or _let_1 (not _let_2)) (or (not _let_3) _let_2 (not _let_1)))))))) (forall ((V0q_2E0 tptp.mono_2Etyop_2Emin_2Ebool) (V1p_2E0 tptp.mono_2Etyop_2Emin_2Ebool)) (let ((_let_1 (tptp.p V1p_2E0))) (let ((_let_2 (tptp.p V0q_2E0))) (let ((_let_3 (not _let_2))) (= (= _let_1 _let_3) (and (or _let_1 _let_2) (or _let_3 (not _let_1)))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.63  )
% 0.21/0.63  % SZS output end Proof for ITP012_1
% 0.21/0.63  % cvc5---1.0.5 exiting
% 0.21/0.64  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------