TSTP Solution File: SWW191+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW191+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 : Fri Sep 1 00:19:54 EDT 2023
% Result : Theorem 111.48s 111.75s
% Output : Proof 111.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.23 % Problem : SWW191+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.24 % Command : do_cvc5 %s %d
% 0.24/0.45 % Computer : n014.cluster.edu
% 0.24/0.45 % Model : x86_64 x86_64
% 0.24/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.45 % Memory : 8042.1875MB
% 0.24/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.24/0.45 % CPULimit : 300
% 0.24/0.45 % WCLimit : 300
% 0.24/0.45 % DateTime : Sun Aug 27 18:03:01 EDT 2023
% 0.24/0.45 % CPUTime :
% 0.31/0.68 %----Proving TF0_NAR, FOF, or CNF
% 111.48/111.75 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.p0blcBnD7m/cvc5---1.0.5_20780.p...
% 111.48/111.75 ------- get file name : TPTP file name is SWW191+1
% 111.48/111.75 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20780.smt2...
% 111.48/111.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 111.48/111.75 --- Run --no-e-matching --full-saturate-quant at 5...
% 111.48/111.75 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 111.48/111.75 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 111.48/111.75 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 111.48/111.75 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 111.48/111.75 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 111.48/111.75 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 111.48/111.75 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 111.48/111.75 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 111.48/111.75 --- Run --relevant-triggers --full-saturate-quant at 5...
% 111.48/111.75 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 111.48/111.75 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 111.48/111.75 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 111.48/111.75 --- Run --no-cbqi --full-saturate-quant at 10...
% 111.48/111.75 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 111.48/111.75 % SZS status Theorem for SWW191+1
% 111.48/111.75 % SZS output start Proof for SWW191+1
% 111.48/111.75 (
% 111.48/111.75 (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal))) (let ((_let_4 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))) (let ((_let_5 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (let ((_let_6 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_7 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_8 (tptp.c_Nat_OSuc _let_7))) (let ((_let_9 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_10 (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))) (let ((_let_11 (tptp.c_Orderings_Obot__class_Obot _let_10))) (let ((_let_12 (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 B_m) (tptp.hAPP V_f_2 B_n)))))))) (let ((_let_13 (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))))) (let ((_let_14 (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) (let ((_let_15 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))))) (let ((_let_16 (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))))) (let ((_let_17 (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_xa_2 V_A_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)))))) (let ((_let_18 (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2)))) (let ((_let_19 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)))) (let ((_let_20 (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal _let_19 (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) tptp.v_L____))) (let ((_let_21 (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_z)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____))))) (let ((_let_22 (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal _let_19 tptp.v_P))) (let ((_let_23 (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal _let_19 tptp.v_P))) (let ((_let_24 (= _let_23 _let_22))) (let ((_let_25 (tptp.hBOOL (tptp.hAPP _let_22 tptp.v_y____)))) (let ((_let_26 (tptp.hBOOL (tptp.hAPP _let_23 tptp.v_y____)))) (let ((_let_27 (not _let_3))) (let ((_let_28 (or _let_27 _let_24))) (let ((_let_29 (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))))) (let ((_let_30 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468)))))) (let ((_let_31 (TRUST_SUBS_EQ (ASSUME :args (_let_17)) :args ((= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475)))))))) (let ((_let_32 (AND_INTRO _let_31 _let_30))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_32 :args ((forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_34 (ASSUME :args (_let_3)))) (let ((_let_35 (not _let_25))) (let ((_let_36 (or _let_35 _let_1))) (let ((_let_37 (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))) (let ((_let_38 (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ _let_22))) (let ((_let_39 (= _let_38 _let_37))) (let ((_let_40 (or _let_27 _let_39))) (let ((_let_41 (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_32 :args ((forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_43 (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal _let_19 tptp.v_P tptp.v_L____))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_27 _let_44 _let_38))) (let ((_let_46 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (_let_37))) (let ((_let_49 (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____))))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_27 _let_50 _let_26))) (let ((_let_52 (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_32 :args ((forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_54 (forall ((B_z $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_z))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____))))) (let ((_let_55 (ASSUME :args (_let_26)))) (let ((_let_56 (ASSUME :args (_let_24)))) (let ((_let_57 (ASSUME :args (_let_35)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_55 _let_56 _let_57) :args (_let_24 _let_35 _let_26)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_57)) (CONG (CONG (SYMM _let_56) (REFL :args (tptp.v_y____)) :args (APPLY_UF tptp.hAPP)) :args (APPLY_UF tptp.hBOOL)) (TRUE_INTRO _let_55))) :args (_let_26 _let_24 _let_35)) :args ((not (and _let_24 _let_35 _let_26)) SB_LITERAL))) (CONG (REFL :args ((not _let_24))) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_25))) (REFL :args ((not _let_26))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_27 _let_26 _let_50 (not _let_51)))) _let_34 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_54 (= B_z B_y)))) (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))) :args (_let_49 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.v_y____ tptp.v_P tptp.tc_RealDef_Oreal QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_26 false _let_3 false _let_49 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_1 _let_35 (not _let_36)))) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_48) :args (tptp.v_y____ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x) true))))) :args _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or (not _let_38) _let_37 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_27 _let_38 (not _let_45)))) (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO (AND_INTRO (TRUST_SUBS_EQ (ASSUME :args (_let_4)) :args ((= tptp.c_Nat_OSuc (lambda ((BOUND_VARIABLE_19872 $$unsorted)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat BOUND_VARIABLE_19872 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))) (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.c_SEQ_Osubseq (lambda ((BOUND_VARIABLE_19269 $$unsorted)) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP BOUND_VARIABLE_19269 B_m) (tptp.hAPP BOUND_VARIABLE_19269 B_n)))))))) _let_31 _let_30) :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.v_L____ tptp.v_P _let_19 tptp.tc_RealDef_Oreal QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) false))))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_38 false _let_43 false _let_3 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_27 _let_39 (not _let_40)))) _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_22 tptp.v_L____ tptp.tc_RealDef_Oreal QUANTIFIERS_INST_CBQI_PROP)) :args (_let_41))) _let_42 :args (_let_40 false _let_41)) :args (_let_39 false _let_3 false _let_40)) :args (_let_37 false _let_38 false _let_39)) :args (_let_36 false _let_37)) :args (_let_35 true _let_1 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_24 (not _let_28)))) _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_33 :args (tptp.v_P _let_19 tptp.tc_RealDef_Oreal QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) :args (_let_29)))) _let_33 :args (_let_28 false _let_29)) :args (_let_24 false _let_3 false _let_28)) :args (false false _let_26 true _let_25 false _let_24)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) _let_21 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_y____ tptp.v_L____) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_Y____) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_x)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_x tptp.v_L____))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))) (forall ((V_z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P V_z_2)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_y____ V_z_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_y____ tptp.v_L____)))) (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_w)) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or 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V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= V_x V_y))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_xa_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= V_xa_2 V_ya_2))))) (forall ((V_xa_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_g_2 V_xa_2))))) _let_20 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (not (=> (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.v_P B_x1))) (forall ((B_Y $$unsorted)) (not (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_x B_Y))))))) (forall ((T_a $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Odense__linorder T_a) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_x V_z))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Odense__linorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (forall ((B_w $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x B_w) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_w V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_w V_z)))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z))))) (forall ((V_f_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b V_c_2 (tptp.hAPP V_f_2 V_b_2)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_y B_x) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_f_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless T_b V_c_2 (tptp.hAPP V_f_2 V_a_2))))))) (forall ((V_f_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_c_2 (tptp.hAPP V_f_2 V_b_2)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y B_x) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_f_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless T_b V_c_2 (tptp.hAPP V_f_2 V_a_2))))))) (forall ((V_c_2 $$unsorted) (V_f_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_a) (tptp.class_Orderings_Oorder T_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_b_2) V_c_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_x B_y) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_a_2) V_c_2)))))) (forall ((V_c_2 $$unsorted) (V_f_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_a) (tptp.class_Orderings_Oorder T_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_b_2) V_c_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a B_x B_y) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_a_2) V_c_2)))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_f_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_a) (tptp.class_Orderings_Oorder T_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.hAPP V_f_2 V_b_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b V_b_2 V_c_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b B_x B_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.hAPP V_f_2 V_c_2))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_f_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_a) (tptp.class_Orderings_Oorder T_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.hAPP V_f_2 V_b_2)) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 V_c_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_b B_x B_y) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.hAPP V_f_2 V_c_2))))))) (forall ((V_xa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b T_a)) V_xa_2) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless _let_1 V_f_2 V_g_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_f_2 V_g_2) (not (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_g_2 V_f_2))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)))) (not (forall ((B_L $$unsorted)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) B_L)))) (exists ((B_x1 $$unsorted)) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) B_x1)) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_xa_2))) (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P)) B_x1))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted)) (=> (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal V_R_2 V_S_2 V_xa_2) (=> (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal V_R_2 V_S_2 V_ya_2) (= V_xa_2 V_ya_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Orderings_Otop__class_Otop _let_1)))) _let_18 (exists ((B_x $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal B_x (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P))) (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oord T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_f_2 V_b_2) V_a_2) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_c_2 V_b_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_b B_y B_x) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_f_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 V_c_2) V_a_2)))))) (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 V_b_2) V_a_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b V_c_2 V_b_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b B_y B_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_f_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 V_c_2) V_a_2)))))) (forall ((V_c_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.c_member T_a V_c_2 V_B_2))) (let ((_let_2 (tptp.c_member T_a V_c_2 V_A_2))) (=> (= V_A_2 V_B_2) (=> (=> _let_2 (not _let_1)) (not (=> (not _let_2) _let_1))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2) (= V_A_2 V_B_2))))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_xa_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_c_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (not (= V_A_2 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (or (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (= V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2)))) (forall ((V_c_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_C_2))))) _let_17 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_xa_2 (tptp.c_fequal V_ya_2)) (= V_xa_2 V_ya_2))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (= (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_member T_a V_xa_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (=> (= V_xa_2 V_ya_2) (= (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_member T_a V_ya_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (= V_a_2 V_b_2) (=> (tptp.c_member T_a V_b_2 V_A_2) (tptp.c_member T_a V_a_2 V_A_2)))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (= V_A_2 V_B_2) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (not (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2))))) (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_member T_a V_xa_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_xa_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_member T_a V_xa_2 V_B_2)))) (forall ((V_xa_2 $$unsorted) (V_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_Pa_2 V_Q_2) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_xa_2)) (tptp.hBOOL (tptp.hAPP V_Q_2 V_xa_2))))) (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_member T_a V_xa_2 V_B_2)))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))) (forall ((V_Q_2 $$unsorted) (T_a $$unsorted) (V_xa_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_xa_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_Pa_2 V_Q_2) (tptp.hBOOL (tptp.hAPP V_Q_2 V_xa_2))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2)) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)) (=> (tptp.c_member T_a V_ya_2 V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (=> (tptp.c_member T_a V_ya_2 V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2))))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2))))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)) (tptp.c_member T_a V_xa_2 V_R_2)))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_member T_a V_xa_2 V_R_2)))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_xa_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_S_2 $$unsorted)) (=> (exists ((B_X $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal B_X V_S_2)) (=> (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) V_S_2) B_x1))) (exists ((B_x1 $$unsorted)) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) V_S_2 B_x1))))) (forall ((V_S_2 $$unsorted)) (=> (and (exists ((B_x $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal B_x V_S_2)) (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) V_S_2) B_x1)))) (exists ((B_x1 $$unsorted)) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) V_S_2 B_x1)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_C_2))))) _let_16 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_xa_2)) (=> (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Set_OCollect T_a _let_1)) (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OleastP T_a V_Pa_2 V_xa_2) (=> (tptp.c_member T_a V_ya_2 (tptp.c_Set_OCollect T_a V_Pa_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2))))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_OleastP T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OleastP T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2) (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_OleastP T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)))) (forall ((V_R_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2) (=> (tptp.c_member T_a V_xa_2 V_R_2) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)))))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)) (and (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2) (tptp.c_member T_a V_xa_2 V_R_2))))) (forall ((V_ya_2 $$unsorted) (V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (=> (tptp.c_member T_a V_ya_2 V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2))))) (forall ((V_xa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OleastP T_a V_Pa_2 V_xa_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 V_xa_2))))) (forall ((V_xa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_OleastP T_a V_Pa_2 V_xa_2) (and (tptp.hBOOL (tptp.hAPP V_Pa_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Set_OCollect T_a V_Pa_2)))))) (forall ((V_xa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OleastP T_a V_Pa_2 V_xa_2) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Set_OCollect T_a V_Pa_2))))) _let_15 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_x V_xa_2)))))) _let_14 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2)))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)) (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2) (=> (tptp.c_member T_a V_ya_2 V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2))))) _let_13 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) (tptp.c_Predicate_OPowp T_a V_A_2) (tptp.c_Predicate_OPowp T_a V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (tptp.c_member T_a B_x V_B_2))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_x V_xa_2))) (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2)))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))) (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2)))) (forall ((T_a $$unsorted) (V_Q_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)) (tptp.hBOOL (tptp.hAPP V_Q_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_OCollect T_a V_Pa_2) (tptp.c_Set_OCollect T_a V_Q_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (tptp.c_member T_a B_x V_A_2)) (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))) (forall ((T_a $$unsorted)) (exists ((B_x $$unsorted)) (tptp.c_member T_a B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Odecseq T_a V_X_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 B_m))))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Oincseq T_a V_X_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m) (tptp.hAPP V_X_2 B_n))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) (tptp.c_Set_OPow T_a V_A_2) (tptp.c_Set_OPow T_a V_B_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Olinorder T_a)) (=> (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_c_2 V_d_2)) (and (or (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_d_2) (or (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_d_2)))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_d_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Olinorder T_a)) (=> (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) V_B_2) (and (tptp.c_member T_a V_xa_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2))))) (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_A_2)) (=> (not (= V_a_2 V_b_2)) (tptp.c_member T_a V_a_2 V_A_2)))) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_a_2 V_B_2)) (= V_a_2 V_b_2)) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_member _let_1 V_A_2 (tptp.c_Set_OPow T_a V_B_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_OPow T_a V_A_2))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Olinorder T_a)) (=> (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2) (= (= (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)) (= V_xa_2 V_ya_2))))) (forall ((V_xa_2 $$unsorted) (V_A_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert T_a V_ya_2 V_A_2) V_xa_2)) (or (= V_ya_2 V_xa_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2))))) (forall ((V_A_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Set_Oinsert T_a V_ya_2 V_A_2)) (tptp.c_Set_Oinsert T_a V_ya_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2))) (= (tptp.c_Set_Oinsert T_a V_xa_2 _let_1) _let_1))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2))) (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_A_2)) (or (= V_a_2 V_b_2) (tptp.c_member T_a V_a_2 V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (=> (not (tptp.c_member T_a V_xa_2 V_B_2)) (= (= (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (= V_A_2 V_B_2))))) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_B_2) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) V_A_2))) (forall ((V_a_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 V_D_2))))) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2))))) (forall ((V_a_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Set_OPow T_a (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member _let_1 V_A_2 (tptp.c_Set_OPow T_a V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_member _let_1 V_A_2 (tptp.c_Set_OPow T_a V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2)))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_c_2 V_d_2)) (or (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_d_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2))))) (forall ((V_k_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OatMost T_a V_less__eq_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_i_2) V_k_2)))) (forall ((V_k_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OatLeast T_a V_less__eq_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_k_2) V_i_2)))) (forall ((V_k_2 $$unsorted) (V_less_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OlessThan T_a V_less_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_i_2) V_k_2)))) (forall ((V_k_2 $$unsorted) (V_less_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OgreaterThan T_a V_less_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_k_2) V_i_2)))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OatLeastAtMost T_a V_less__eq_2 V_l_2 V_u_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_l_2) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_i_2) V_u_2))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (V_less_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OgreaterThanLessThan T_a V_less_2 V_l_2 V_u_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_l_2) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_i_2) V_u_2))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (V_less_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OatLeastLessThan T_a V_less__eq_2 V_less_2 V_l_2 V_u_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_l_2) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_i_2) V_u_2))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (V_less_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OgreaterThanAtMost T_a V_less__eq_2 V_less_2 V_l_2 V_u_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_l_2) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_i_2) V_u_2))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Omonoseq T_a V_X_2) (or (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m) (tptp.hAPP V_X_2 B_n)))) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 B_m)))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (not (= V_m_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (not (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m) (not (= V_m V_n)))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_s V_t) (not (= V_s V_t)))) (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_n_2) V_m_2)))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (=> (=> (= V_m_2 V_n_2) _let_1) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) _let_1) _let_1))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_SEQ_Oincseq T_a V_X_2) (tptp.c_SEQ_Omonoseq T_a V_X_2)))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_SEQ_Odecseq T_a V_X_2) (tptp.c_SEQ_Omonoseq T_a V_X_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_n)) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 B_m)))) (tptp.c_SEQ_Omonoseq T_a V_X_2)))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m) (tptp.hAPP V_X_2 B_n)))) (tptp.c_SEQ_Omonoseq T_a V_X_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_m_2) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_n_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_m_2 V_n_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2)))) (forall ((V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_x B_y) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2)))) (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_k_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_k_2 V_i_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OlessThan T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_ya_2)) (= V_xa_2 V_ya_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_ya_2)) (= V_xa_2 V_ya_2)))) (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord__class_OlessThan T_a V_k_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_i_2 V_k_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatMost T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OatMost T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2)))) (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord__class_OatMost T_a V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_i_2 V_k_2)))) (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord__class_OatLeast T_a V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_k_2 V_i_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) (tptp.c_RComplete_Onatceiling V_y)))) (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i B_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 B_i) (tptp.hAPP V_f_2 B_j)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_i_2) (tptp.hAPP V_f_2 V_j_2))))) (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_xa_2 V_A_2) (not (forall ((B_B $$unsorted)) (=> (= V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 B_B)) (tptp.c_member T_a V_xa_2 B_B)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatLeast T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_ya_2)) (= V_xa_2 V_ya_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatMost T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OatMost T_a V_ya_2)) (= V_xa_2 V_ya_2)))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_l_2))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_l_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatMost T_a V_u_2))))) (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (exists ((B_B $$unsorted)) (and (= V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 B_B)) (not (tptp.c_member T_a V_a_2 B_B)))))) (forall ((V_n_2 $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.c_SEQ_Osubseq V_f_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 (tptp.hAPP V_f_2 V_n_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) (tptp.c_RComplete_Onatfloor V_y)))) (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2))) (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2))))) (forall ((T_a $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (V_B_2 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2))) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (=> (not (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)) (= (tptp.c_SetInterval_Oord__class_OatLeast tptp.tc_Nat_Onat _let_7) (tptp.c_Orderings_Otop__class_Otop _let_10)) (forall ((V_n_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat V_n_2))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x))) (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) V_A_2)) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 _let_2) _let_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2))))) (forall ((V_Pa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (or (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x))))))) (forall ((V_Pa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (and (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x))))))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_xa_2 $$unsorted) (V_B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (= V_n_2 V_m_2))) (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x) V_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_RComplete_Onatfloor V_a)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (or (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 _let_2) _let_2)))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 _let_2 V_B_2) _let_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_B_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_A_2)))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_C_2))))) (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_C_2 V_D_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_2 (tptp.c_Set_OPow T_a V_A_2) (tptp.c_Set_OPow T_a V_B_2)) (tptp.c_Set_OPow T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2)))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_n _let_1)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (not (= V_n_2 _let_1)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 _let_1) (= V_n_2 _let_1)))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)) (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)))) _let_12 (forall ((V_xa_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_b T_a) V_f_2 V_g_2) V_xa_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_g_2 V_xa_2))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x _let_1) _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a _let_1 V_x) _let_1)))) (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted)) (= (forall ((B_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m V_n_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_m)))) (forall ((B_x $$unsorted)) (=> (tptp.c_member tptp.tc_Nat_Onat B_x (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))) (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted)) (= (exists ((B_m $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m V_n_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_m)))) (exists ((B_x $$unsorted)) (and (tptp.c_member tptp.tc_Nat_Onat B_x (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_x) V_x))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_a)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a _let_1) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x _let_1) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x _let_1) _let_1)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_c)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_c))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_c) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_c))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_x) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x))))))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_c V_d)))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z) V_x))))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_y)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))) (forall ((V_z_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_xa_2 V_ya_2) V_z_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_z_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_z_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_xa_2 V_ya_2) V_ya_2)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_l_2))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatMost T_a V_l_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_u_2))))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_n)))) (forall ((V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_l_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_l_2)) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_l_2))))) (forall ((V_a_2 $$unsorted) (V_xa_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_xa_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_xa_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2))))) (forall ((V_a_2 $$unsorted) (V_xa_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_xa_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_a_2 (tptp.c_RComplete_Onatfloor V_xa_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2) V_xa_2)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (not (tptp.c_member T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Orderings_Obot__class_Obot _let_1) V_A_2))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (forall ((V_k_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_k_2) (= (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_k_2 V_l_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Set_OPow T_a _let_2) (tptp.c_Set_Oinsert _let_1 _let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))))))) (forall ((V_xa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b T_a)) V_xa_2) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_member T_a V_a_2 V_A_2)))) (forall ((V_c_2 $$unsorted) (T_a $$unsorted)) (not (tptp.c_member T_a V_c_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (exists ((B_x $$unsorted)) (tptp.c_member T_a B_x V_A_2)) (not (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (not (tptp.c_member T_a B_x V_A_2))) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (= (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat _let_7) _let_11) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 _let_1)) (tptp.c_Set_Oinsert T_a V_c_2 (tptp.c_Set_Oinsert T_a V_d_2 _let_1))) (or (and (= V_a_2 V_c_2) (= V_b_2 V_d_2)) (and (= V_a_2 V_d_2) (= V_b_2 V_c_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (= (tptp.c_Set_Oinsert T_a V_a_2 _let_1) (tptp.c_Set_Oinsert T_a V_b_2 _let_1)) (= V_a_2 V_b_2)))) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Set_OCollect T_a V_Pa_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect T_a V_Pa_2)) (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 _let_2) (= V_A_2 _let_2))))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Orderings_Obot__class_Obot _let_1) V_B_2) V_B_2))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) _let_2) (and (= V_A_2 _let_2) (= V_B_2 _let_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_OPow T_a V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_xa_2 V_ya_2) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_b_2 V_a_2))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_b_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_b_2 V_a_2))) (forall ((V_xa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert T_a V_xa_2 _let_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 _let_3) (or (= V_A_2 _let_2) (= V_A_2 _let_3))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a_2 V_b_2) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_Set_Oinsert T_a V_c_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (and (= V_a_2 V_b_2) (= V_b_2 V_c_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_a_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_7) _let_9) (forall ((V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_member _let_1 (tptp.c_Orderings_Obot__class_Obot _let_1) (tptp.c_Set_OPow T_a V_B_2)))) (= (tptp.c_RComplete_Onatfloor _let_9) _let_7) (= (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat _let_7) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat _let_7 _let_11)) (= (tptp.c_RComplete_Onatceiling _let_9) _let_7) (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) V_x))) (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2))) (forall ((V_u_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_SetInterval_Oord__class_OlessThan T_a V_u_2) (tptp.c_Set_Oinsert T_a V_u_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_SetInterval_Oord__class_OatMost T_a V_u_2))))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Othe__elem T_a (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_xa_2)) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2) (tptp.c_Set_Oinsert T_a V_u_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_l_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2)))))) (forall ((V_n_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat V_n_2))) (forall ((V_m_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_c_2 V_d_2)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_d_2) (= V_b_2 V_d_2)))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_c_2 V_d_2)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_d_2) (= V_a_2 V_c_2)))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_d_2) (= (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_c_2 V_d_2)) (and (= V_a_2 V_c_2) (= V_b_2 V_d_2))))))) (= (tptp.c_Orderings_Obot__class_Obot tptp.tc_Nat_Onat) _let_7) (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted)) (= (forall ((B_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m V_n_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_m)))) (forall ((B_x $$unsorted)) (=> (tptp.c_member tptp.tc_Nat_Onat B_x (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))) (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted)) (= (exists ((B_m $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m V_n_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_m)))) (exists ((B_x $$unsorted)) (and (tptp.c_member tptp.tc_Nat_Onat B_x (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_c_2 V_d_2)) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_d_2)))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2)))))) (forall ((V_k_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_k_2) (= (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_k_2 V_l_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_k_2 V_l_2)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_k_2 V_l_2))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_k_2 V_l_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_Orderings_Oord__class_Oless T_a V_k_2 V_l_2))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_l_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_u_2))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_l_2))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatMost T_a V_l_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatMost T_a V_u_2))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_l_2))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2) (tptp.c_Set_Oinsert T_a V_u_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_l_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2)))))) (forall ((V_B_2 $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_member T_a V_xa_2 V_A_2))) (let ((_let_3 (tptp.c_member T_a V_xa_2 V_B_2))) (= (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2)) (=> (not _let_3) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B_2)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2)))))))))) (forall ((V_n_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OatMost T_a V_n_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_n_2)) (tptp.c_Set_Oinsert T_a V_n_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_n_2 $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Nat_Osemiring__1__class_ONats tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted)) (=> (tptp.class_GCD_Ogcd T_a) (= (tptp.c_GCD_Ogcd__class_OGcd T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_B_2 $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B_2) (=> (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2))))) (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)) (not (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)) (not (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_c_2 V_A_2) (not (tptp.c_member T_a V_c_2 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Obot__class_Obot _let_1)) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) V_A_2)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x _let_1) _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a _let_1 V_x) _let_1)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z) V_x) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_z V_x))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z) V_x) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_z V_x))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)) V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Orderings_Otop__class_Otop T_a) V_x) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_xa_2 V_ya_2) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (and (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_B_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (and (tptp.c_member T_a V_c_2 V_A_2) (not (tptp.c_member T_a V_c_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Obot__class_Obot _let_1)) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_B_2) (not (= B_x B_xa))))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 _let_2) _let_2)))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 _let_2 V_B_2) _let_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A_2))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 V_A_2) _let_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Orderings_Otop__class_Otop _let_1) V_B_2) V_B_2))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Orderings_Otop__class_Otop _let_1)) V_A_2))) (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_D_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2)))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_B_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_A_2))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_C_2 V_A_2)) V_A_2))))) (forall ((V_B_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_D_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_C_2 V_D_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) V_A_2))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_A_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_C_2 V_A_2))))) (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_C_2 V_A_2))))) (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_A_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_C_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_C_2))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_C_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2)) V_A_2))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_x) V_x))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_a)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a _let_1) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x _let_1) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x _let_1) _let_1)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_c)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_c))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_c) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_c))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))) (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a) V_A_2 V_B_2) V_xa_2) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP V_A_2 V_xa_2) (tptp.hAPP V_B_2 V_xa_2))))) (forall ((V_xa_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b T_a) V_f_2 V_g_2) V_xa_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_g_2 V_xa_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Set_OPow T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) (tptp.c_Set_OPow T_a V_A_2) (tptp.c_Set_OPow T_a V_B_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) V_A_2)) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 _let_2) _let_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_C_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 V_B_2) _let_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_C_2))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 V_B_2))))) (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)))) (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)) (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_x) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))) (forall ((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b))))))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_c V_d)))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x)))) (forall ((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))) (forall ((V_z_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_ya_2 V_z_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_z_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_xa_2 V_ya_2) V_xa_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_a_2 V_C_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_a_2 V_C_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_a_2 V_A_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2))) (let ((_let_4 (tptp.c_member T_a V_a_2 V_C_2))) (and (=> _let_4 (= _let_3 (tptp.c_Set_Oinsert T_a V_a_2 _let_2))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)))) (let ((_let_4 (tptp.c_member T_a V_a_2 V_A_2))) (and (=> _let_4 (= _let_3 (tptp.c_Set_Oinsert T_a V_a_2 _let_2))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_xa_2 V_B_2) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2))) (let ((_let_3 (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) V_B_2))) (let ((_let_4 (tptp.c_member T_a V_xa_2 V_B_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.c_Set_Oinsert T_a V_xa_2 _let_2))))))))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2)))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B_2)))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_i_2 V_n_2) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_i_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_i_2 V_n_2)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_n_2 V_m_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_A_2)))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) V_B_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_A_2)))) (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A_2)))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_k_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Set_Oinsert T_a V_k_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 (tptp.c_SetInterval_Oord__class_OlessThan T_a V_k_2)) _let_2))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OlessThan T_a V_l_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OlessThan T_a V_l_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OatMost T_a V_l_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OatMost T_a V_l_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_u_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (tptp.c_member T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_ONats T_a)))) (forall ((V_B_2 $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_member T_a V_xa_2 V_A_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B_2)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_d_2))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_d_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 V_b_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) _let_1) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_m) _let_1) (= V_m V_n))))) (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat _let_1 V_n) _let_1))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_n) V_k))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_m)) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m)))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_l)))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_i)) V_i))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_m) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x _let_1)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_a))))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x _let_1)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_m))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_c V_a) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a V_c) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_b V_c))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ozero T_a) (= (= _let_1 V_xa_2) (= V_xa_2 _let_1))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (= V_a_2 V_b_2) (= V_c_2 V_d_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)) (tptp.hBOOL (tptp.hAPP V_Q_2 B_x))))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Set_OCollect T_a V_Pa_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 (tptp.c_Set_OCollect T_a V_Q_2))))))) (forall ((V_ya_2 $$unsorted) (V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_xa_2 V_A_2) (=> (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_ya_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 V_A_2 (tptp.hAPP (tptp.hAPP V_f_2 V_xa_2) V_ya_2)))))) (forall ((V_p_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_a V_p_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_p_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_k) V_j))) (forall ((V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_z_2)) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a1_2 V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_a2_2)) (forall ((V_a5_2 $$unsorted) (V_a1_2 $$unsorted) (V_a2_2 $$unsorted) (V_a4_2 $$unsorted) (V_a3_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2))) (= (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 V_a2_2 _let_1) (or (and (= V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= _let_1 V_a4_2)) (exists ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (and (= (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2) (tptp.hAPP (tptp.hAPP V_a3_2 B_x) B_y)) (tptp.c_member T_a B_x V_a2_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_a2_2 (tptp.c_Set_Oinsert T_a B_x (tptp.c_Orderings_Obot__class_Obot _let_1))) B_y)))))))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))) (and (=> _let_2 (= _let_1 (tptp.c_Set_Oinsert tptp.tc_Nat_Onat V_n_2 (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_m_2 V_n_2)))) (=> (not _let_2) (= _let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_n))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_k))) (not (= _let_9 _let_6)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_8) _let_6) (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_nat_H)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_nat_H_1 $$unsorted)) (not (= (tptp.c_Nat_OSuc V_nat_H_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeast tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_SetInterval_Oord__class_OgreaterThan tptp.tc_Nat_Onat V_k_2))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_l_2) V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan tptp.tc_Nat_Onat V_l_2 V_u_2))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Nat_OSuc V_x) (tptp.c_Nat_OSuc V_y)) (= V_x V_y))) (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= (tptp.c_Nat_OSuc V_nat_2) (tptp.c_Nat_OSuc V_nat_H_2)) (= V_nat_2 V_nat_H_2))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Nat_OSuc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_n))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m _let_1) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n)) (= V_m _let_1))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) (tptp.c_Nat_OSuc V_m_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_n_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 _let_1) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 _let_1))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_i) V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_m))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (not (= _let_1 V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_m)) (= V_m V_n)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_l_2) V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost tptp.tc_Nat_Onat V_l_2 V_u_2))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Groups_Oone T_a) (= (= _let_1 V_xa_2) (= V_xa_2 _let_1))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_j $$unsorted)) (and (= V_m_2 (tptp.c_Nat_OSuc B_j)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_n_2)))))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc _let_1)) (= V_n_2 _let_1)))) (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (exists ((B_m $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc B_m))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc V_m))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Omonoseq T_a V_X_2) (or (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 (tptp.c_Nat_OSuc B_n)))) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 (tptp.c_Nat_OSuc B_n)) (tptp.hAPP V_X_2 B_n))))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_l_2 (tptp.c_Nat_OSuc V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_l_2 V_u_2))) (forall ((V_k_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Nat_OSuc V_k_2))) (= (tptp.c_SetInterval_Oord__class_OgreaterThan tptp.tc_Nat_Onat _let_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_SetInterval_Oord__class_OgreaterThan tptp.tc_Nat_Onat V_k_2) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (tptp.c_member T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Nat_Osemiring__1__class_ONats T_a)))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat V_k_2 (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat V_k_2)))) (forall ((V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_k_2))) (= (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat _let_1) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat _let_1 (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat V_k_2))))) (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_2) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 B_n) (tptp.hAPP V_f_2 (tptp.c_Nat_OSuc B_n)))))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat V_k_2))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc _let_1))) V_n)))) (forall ((V_i $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_i)) V_n))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_n_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 _let_1) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_m_2 _let_1) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat _let_1 (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_m_2 V_n_2)))))) (forall ((V_m_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_m_2)) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat V_m_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))))) (forall ((V_k_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))) (= (tptp.c_SetInterval_Oord__class_OatLeast tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_SetInterval_Oord__class_OatLeast tptp.tc_Nat_Onat V_k_2) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat V_k_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Nat_OSuc V_j_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 _let_2) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_i_2 _let_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_i_2 V_j_2) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Nat_OSuc _let_2)) (or (= V_x _let_1) (= V_x _let_2)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= _let_5 _let_8) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_5) _let_6) (= (tptp.c_RComplete_Onatfloor _let_6) _let_5) (= (tptp.c_RComplete_Onatceiling _let_6) _let_5) (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= V_n (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))) (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n))) (forall ((V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_xa_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_xa_2))) (forall ((V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_xa_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (=> (tptp.class_GCD_Ogcd T_a) (= (tptp.c_GCD_Ogcd__class_OLcm T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_r $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat B_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)))))) (forall ((V_r $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n) V_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_n))))))) (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 _let_2) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_i_2 _let_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_i_2 V_j_2) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))))) (forall ((V_n $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_z (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatfloor V_x) V_n))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) _let_2) (or (and (= V_m_2 _let_2) (= V_n_2 _let_1)) (and (= V_m_2 _let_1) (= V_n_2 _let_2))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (= (= _let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (and (= V_m_2 _let_2) (= V_n_2 _let_1)) (and (= V_m_2 _let_1) (= V_n_2 _let_2))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k)))))) (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_i)))) (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_m)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2)) (= V_b_2 V_c_2)))) (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2)) (= V_b_2 V_c_2)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))) (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_y)))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_i))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_i))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_k))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x V_z)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (= V_m_2 V_n_2))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) V_n)) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (= V_a_2 _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a)))) (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_a)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_xa_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_ya_2) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_xa_2 V_ya_2) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n) V_m)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_n) V_m)) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Ominus__class_Ominus T_a V_c V_d))))) (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))) _let_4 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) V_j)))) (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted) (V_j_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2) V_i_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_k)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k)))) (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_j_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n) V_m))) (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2) V_k_2) (= V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_i_2))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osemiring__1__class_ONats T_a))) (=> (tptp.class_Rings_Osemiring__1 T_a) (=> (tptp.c_member T_a V_a_2 _let_1) (=> (tptp.c_member T_a V_b_2 _let_1) (tptp.c_member T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) _let_1)))))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1))))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_Pa_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((B_d $$unsorted)) (=> (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_d))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_Pa_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (not (or (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (exists ((B_d $$unsorted)) (and (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 B_d))))))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_j) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Nat_OSuc V_j))))) (forall ((V_n $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j_2 V_k_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_i_2 _let_1) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_i_2 V_j_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_j_2 _let_1)))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))) (let ((_let_2 (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (and (=> _let_2 (= _let_1 V_n)) (=> (not _let_2) (= _let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_l_2) (exists ((B_n $$unsorted)) (= V_l_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 B_n))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a_2) V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (tptp.c_member T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Oring__1__class_OInts T_a)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Oring__1__class_OInts T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (=> (tptp.c_member T_a V_a_2 _let_1) (=> (tptp.c_member T_a V_b_2 _let_1) (tptp.c_member T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) _let_1)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Oring__1__class_OInts T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (=> (tptp.c_member T_a V_a_2 _let_1) (=> (tptp.c_member T_a V_b_2 _let_1) (tptp.c_member T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) _let_1)))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (tptp.c_member T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Oring__1__class_OInts T_a)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (forall ((V_n_2 $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Int_Oring__1__class_OInts tptp.tc_RealDef_Oreal))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Int_Oring__char__0 T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (= V_a_2 _let_1)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Oring__char__0 T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_n_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_n_2)) (exists ((B_k $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_k V_n_2) (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i B_k) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 B_i))))) (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_k (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) _let_1) (= _let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))) (forall ((V_w_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (tptp.c_member T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2) (tptp.c_Int_Oring__1__class_OInts T_a)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_xa_2 V_ya_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_xa_2 V_ya_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (= V_xa_2 V_ya_2)))) (forall ((V_xa_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (=> (tptp.class_Int_Onumber T_a) (= (= _let_1 V_xa_2) (= V_xa_2 _let_1))))) (forall ((V_w_2 $$unsorted) (V_v_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_v_2))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (=> (and (tptp.class_Int_Onumber T_a) (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 _let_2) (not (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_c $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_c)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_c)))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_z)))) (forall ((V_M_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))) (=> (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_M_2) (= (tptp.c_GCD_Ogcd__class_OGcd tptp.tc_Nat_Onat V_M_2) (tptp.c_GCD_Ogcd__class_OGcd tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus _let_1 V_M_2 (tptp.c_Set_Oinsert tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Orderings_Obot__class_Obot _let_1)))))))) (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__1__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_u V_x) (tptp.c_Groups_Otimes__class_Otimes T_a V_v V_y)) V_a))))))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_l_2 V_u_2))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_l_2 V_u_2))) (forall ((V_k_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat V_k_2))) (forall ((V_k_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat V_k_2))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost tptp.tc_Nat_Onat V_l_2 V_u_2))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan tptp.tc_Nat_Onat V_l_2 V_u_2))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Oring__1__class_OInts T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (=> (tptp.c_member T_a V_a_2 _let_1) (=> (tptp.c_member T_a V_b_2 _let_1) (tptp.c_member T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_b_2) _let_1)))))) (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_n))) (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_n))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_z)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w)) V_z)))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Oring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Groups_Ominus__class_Ominus T_b V_a V_b) _let_1) (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.c_Groups_Otimes__class_Otimes T_b V_a _let_1) (tptp.c_Groups_Otimes__class_Otimes T_b V_b _let_1)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Oring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 (tptp.c_Groups_Ominus__class_Ominus T_b V_b V_c)) (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 V_b) (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 V_c)))))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 (tptp.c_Groups_Oplus__class_Oplus T_b V_b V_c)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 V_b) (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 V_c)))))) (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Groups_Oplus__class_Oplus T_b V_a V_b) _let_1) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.c_Groups_Otimes__class_Otimes T_b V_a _let_1) (tptp.c_Groups_Otimes__class_Otimes T_b V_b _let_1)))))) (forall ((V_z $$unsorted)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z))))) (forall ((V_z_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z_2) V_z_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z_2 _let_1)))) (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Int_Oint tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i_2 _let_2) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Int_Oint V_i_2 _let_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Int_Oint V_i_2 V_j_2) (tptp.c_Set_Oinsert tptp.tc_Int_Oint _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_l_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan tptp.tc_Int_Oint V_l_2 V_u_2))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Int_Oint V_l_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_u_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Int_Oint V_l_2 V_u_2))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_z_2))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2 V_z_2))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_z_2) (= V_w_2 V_z_2)))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_l_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost tptp.tc_Int_Oint V_l_2 V_u_2))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_n)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n V_k)))) (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_H V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_H V_z_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_i) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_j)))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z1 V_z2) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z1 V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z2 V_w)))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1 V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z2 V_w)))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_z3) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z2 V_z3)))) (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z1) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z2)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_z)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_e) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_e) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_e) V_c)))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) V_z)) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a) V_b))))) (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_d_2)) (= V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_a_2) V_e_2) V_d_2))))) (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_d_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) V_e_2) V_c_2) V_d_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_xa_2 V_xa_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_ya_2 V_ya_2)) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1)))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z1) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z2)))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1 V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z2 V_w)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k V_i) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k V_j))))) (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_w)) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_k)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z) (= V_z V_w)))) (forall ((V_w_2 $$unsorted) (V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z_2 V_w_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_2 V_w_2) (not (= V_z_2 V_w_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_m_2) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_m_2 V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1)))))) (forall ((V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z_2))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_z_2))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_xa_2 V_xa_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_ya_2 V_ya_2)) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1))))) (forall ((V_M_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_M_2) (=> (not (= V_M_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))) (= (= (tptp.c_GCD_Ogcd__class_OLcm tptp.tc_Nat_Onat V_M_2) _let_1) (tptp.c_member tptp.tc_Nat_Onat _let_1 V_M_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osemiring__1__class_ONats T_a))) (=> (tptp.class_Rings_Osemiring__1 T_a) (=> (tptp.c_member T_a V_a_2 _let_1) (=> (tptp.c_member T_a V_b_2 _let_1) (tptp.c_member T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_b_2) _let_1)))))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_z) V_z)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2)) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n) V_n)) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) V_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_m) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_n) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_m V_n))))))) (forall ((V_M_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_M_2) (=> (tptp.c_member tptp.tc_Nat_Onat _let_1 V_M_2) (= (tptp.c_GCD_Ogcd__class_OLcm tptp.tc_Nat_Onat V_M_2) _let_1))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_i) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_j))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j V_k))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n_2 V_k_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_z_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_xa_2 V_z_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_ya_2 V_z_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 V_ya_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z V_x) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z V_y))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_k_2))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_k_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_k_2))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_n_2)) (= V_m_2 V_n_2)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c))))) (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_m))) (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_m)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_i) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_j)))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j V_l))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_x) V_x))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b))) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a _let_1) _let_1)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))) (forall ((V_N_2 $$unsorted)) (= (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_N_2) (exists ((B_m $$unsorted)) (forall ((B_x $$unsorted)) (=> (tptp.c_member tptp.tc_Nat_Onat B_x V_N_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_x B_m)))))) (forall ((V_N_2 $$unsorted)) (= (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_N_2) (exists ((B_m $$unsorted)) (forall ((B_x $$unsorted)) (=> (tptp.c_member tptp.tc_Nat_Onat B_x V_N_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_x B_m)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1) (or (= V_a _let_1) (= V_b _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a _let_1)) (=> (not (= V_b _let_1)) (not (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__no__zero__divisors T_a) (= (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_b_2) _let_1) (or (= V_a_2 _let_1) (= V_b_2 _let_1)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 V_a) _let_1)))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n_2 V_k_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_n_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (or (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m _let_1) _let_1))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_n) _let_1))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_a_2 V_c_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_b_2 V_c_2)) (= V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_c_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_c_2 V_b_2)) (= V_a_2 V_b_2)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_a) (tptp.c_RComplete_Onatfloor V_b)) (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_a V_b))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__comm__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_a) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) 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(tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Olinordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semidom (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Groups_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__idom (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Opreorder (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Osemiring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Ogroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Omult__zero (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oorder (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Int_Oring__char__0 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Int_Onumber__ring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oord (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Oring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Ominus (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ozero T_1) (tptp.class_Groups_Ozero (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Oring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Int_Onumber (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Oone (tptp.tc_Polynomial_Opoly T_1)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_x_2) V_y_2))) (= V_x_2 V_y_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_x_2) V_y_2)))) _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 111.57/111.78 )
% 111.57/111.78 % SZS output end Proof for SWW191+1
% 111.57/111.78 % cvc5---1.0.5 exiting
% 111.57/111.78 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------