TSTP Solution File: GEO223+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEO223+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 : Wed Aug 30 22:50:39 EDT 2023
% Result : Theorem 0.16s 0.50s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : GEO223+2 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.11 % Command : do_cvc5 %s %d
% 0.11/0.31 % Computer : n006.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Aug 29 21:46:36 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.43 %----Proving TF0_NAR, FOF, or CNF
% 0.16/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.9ysNFmznli/cvc5---1.0.5_4032.p...
% 0.16/0.50 ------- get file name : TPTP file name is GEO223+2
% 0.16/0.50 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4032.smt2...
% 0.16/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.16/0.50 % SZS status Theorem for GEO223+2
% 0.16/0.50 % SZS output start Proof for GEO223+2
% 0.16/0.50 (
% 0.16/0.50 (let ((_let_1 (forall ((A $$unsorted) (L $$unsorted)) (not (tptp.distinct_lines (tptp.parallel_through_point L A) (tptp.orthogonal_through_point (tptp.orthogonal_through_point L A) A)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((A $$unsorted) (L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.distinct_lines L M) (or (tptp.apart_point_and_line A L) (tptp.apart_point_and_line A M) (tptp.unorthogonal_lines L N) (tptp.unorthogonal_lines M N)))))) (let ((_let_4 (forall ((A $$unsorted) (L $$unsorted)) (not (tptp.apart_point_and_line A (tptp.orthogonal_through_point L A)))))) (let ((_let_5 (forall ((A $$unsorted) (L $$unsorted)) (not (tptp.unorthogonal_lines (tptp.orthogonal_through_point L A) L))))) (let ((_let_6 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (and (tptp.convergent_lines L M) (tptp.unorthogonal_lines L M)) (or (and (tptp.convergent_lines L N) (tptp.unorthogonal_lines L N)) (and (tptp.convergent_lines M N) (tptp.unorthogonal_lines M N))))))) (let ((_let_7 (forall ((L $$unsorted) (M $$unsorted)) (or (tptp.convergent_lines L M) (tptp.unorthogonal_lines L M))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_lines Y Z) (or (tptp.apart_point_and_line X Y) (tptp.apart_point_and_line X Z) (tptp.convergent_lines Y Z)))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.apart_point_and_line X (tptp.parallel_through_point Y X)))))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.convergent_lines (tptp.parallel_through_point Y X) Y))))) (let ((_let_11 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.convergent_lines X Y) (tptp.distinct_lines X Y))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z)))))) (let ((_let_13 (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))))) (let ((_let_14 (tptp.orthogonal_through_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.unorthogonal_lines _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (tptp.convergent_lines _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (and _let_16 _let_15))) (let ((_let_18 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14))) (let ((_let_19 (tptp.unorthogonal_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14))) (let ((_let_20 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (and _let_20 (tptp.unorthogonal_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_22 (not _let_19))) (let ((_let_23 (not _let_18))) (let ((_let_24 (or _let_23 _let_22 _let_21 _let_17))) (let ((_let_25 (not _let_17))) (let ((_let_26 (_let_5))) (let ((_let_27 (ASSUME :args _let_26))) (let ((_let_28 ((tptp.orthogonal_through_point L A)))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_28)) :args _let_26)) _let_27 :args ((not _let_15) false _let_5)))) (let ((_let_30 (tptp.convergent_lines _let_14 _let_14))) (let ((_let_31 (not _let_16))) (let ((_let_32 (or _let_31 _let_30 _let_18))) (let ((_let_33 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 (not (= (tptp.convergent_lines X Y) false)))) (let ((_let_37 (_let_13))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 ((not (= (tptp.convergent_lines X X) false))))) (let ((_let_40 (or _let_16 _let_15))) (let ((_let_41 (_let_7))) (let ((_let_42 (ASSUME :args _let_41))) (let ((_let_43 ((not (= (tptp.unorthogonal_lines L M) true))))) (let ((_let_44 (and _let_18 _let_19))) (let ((_let_45 (tptp.orthogonal_through_point _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_46 (tptp.unorthogonal_lines _let_45 _let_14))) (let ((_let_47 (tptp.convergent_lines _let_45 _let_14))) (let ((_let_48 (and _let_47 _let_46))) (let ((_let_49 (tptp.unorthogonal_lines _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.convergent_lines _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_50 _let_48 _let_44))) (let ((_let_54 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (or (not (tptp.convergent_lines L M)) (not (tptp.unorthogonal_lines L M)) (and (tptp.convergent_lines L N) (tptp.unorthogonal_lines L N)) (and (tptp.convergent_lines M N) (tptp.unorthogonal_lines M N)))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (_let_54))) (let ((_let_57 ((tptp.convergent_lines M N) (not (= (tptp.unorthogonal_lines L M) false))))) (let ((_let_58 (not _let_48))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_28)) :args _let_26)) _let_27 :args ((not _let_46) false _let_5)))) (let ((_let_60 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_61 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_45))) (let ((_let_62 (tptp.distinct_lines _let_45 _let_14))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_63 _let_61 _let_60 _let_49 _let_15))) (let ((_let_65 (forall ((A $$unsorted) (L $$unsorted) (M $$unsorted) (N $$unsorted)) (or (not (tptp.distinct_lines L M)) (tptp.apart_point_and_line A L) (tptp.apart_point_and_line A M) (tptp.unorthogonal_lines L N) (tptp.unorthogonal_lines M N))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (not _let_47))) (let ((_let_68 (or _let_67 _let_62))) (let ((_let_69 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.distinct_lines X Y))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (or _let_47 _let_46))) (let ((_let_72 (_let_4))) (let ((_let_73 (ASSUME :args _let_72))) (let ((_let_74 ((tptp.orthogonal_through_point L A)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_74)) :args _let_72)) _let_73 :args ((not _let_61) false _let_4)))) (let ((_let_76 (tptp.parallel_through_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_77 (tptp.convergent_lines _let_76 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_78 (tptp.convergent_lines _let_76 _let_45))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_77 _let_51))) (let ((_let_81 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_76))) (let ((_let_82 (tptp.distinct_lines _let_76 _let_45))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_83 _let_81 _let_61 _let_78))) (let ((_let_85 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_lines Y Z)) (tptp.apart_point_and_line X Y) (tptp.apart_point_and_line X Z) (tptp.convergent_lines Y Z))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (_let_9))) (let ((_let_88 (ASSUME :args _let_87))) (let ((_let_89 (_let_2))) (let ((_let_90 (ASSUME :args _let_89))) (let ((_let_91 (_let_10))) (let ((_let_92 (ASSUME :args _let_91))) (let ((_let_93 (not _let_21))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_17 _let_23 _let_22 _let_21 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 0)) :args ((or _let_20 _let_93))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_37)) _let_38 :args ((not _let_20) false _let_13)) :args (_let_93 true _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_57)) :args _let_56)) _let_55 :args (_let_24 false _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 1)) :args ((or _let_19 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_52 _let_50 _let_48 _let_44 (not _let_53)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_77 _let_79 _let_51 (not _let_80)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.parallel_through_point Y X)))) :args _let_91)) _let_92 :args ((not _let_77) false _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_83 _let_81 _let_61 _let_78 (not _let_84)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_90) :args _let_89) (REWRITE :args ((=> _let_2 (not _let_83)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_82)) :args (or))) _let_90 :args (_let_82 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.parallel_through_point Y X)))) :args _let_87)) _let_88 :args ((not _let_81) false _let_9)) _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_76 _let_45 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_lines Y Z) false)) (not (= (tptp.apart_point_and_line X Y) true))))) :args (_let_85))) _let_86 :args (_let_84 false _let_85)) :args (_let_78 false _let_82 true _let_81 true _let_61 false _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_76 _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING (_let_36 (not (= (tptp.convergent_lines X Z) true))))) :args _let_35)) _let_34 :args (_let_80 false _let_33)) :args (_let_51 true _let_77 false _let_78 false _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_15 _let_60 _let_61 _let_49 _let_63 (not _let_64)))) _let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_74)) :args _let_72)) _let_73 :args ((not _let_60) false _let_4)) _let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_62 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_46 _let_47 (not _let_71)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_45 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_43)) :args _let_41)) _let_42 :args (_let_71 false _let_7)) :args (_let_47 true _let_46 false _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_45 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X Y) false))))) :args (_let_69))) _let_70 :args (_let_68 false _let_69)) :args (_let_62 false _let_47 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_45 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.unorthogonal_lines M N) true)) (not (= (tptp.apart_point_and_line A L) true))))) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_49 true _let_15 true _let_60 true _let_61 false _let_62 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_48 1)) :args ((or _let_46 _let_58))) _let_59 :args (_let_58 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14 QUANTIFIERS_INST_E_MATCHING _let_57)) :args _let_56)) _let_55 :args (_let_53 false _let_54)) :args (_let_44 false _let_51 false _let_49 true _let_48 false _let_53)) :args (_let_19 false _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_30 _let_18 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_15 _let_16 (not _let_40)))) _let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_43)) :args _let_41)) _let_42 :args (_let_40 false _let_7)) :args (_let_16 true _let_15 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_37)) _let_38 :args ((not _let_30) false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.convergent_lines Y Z) true)) _let_36))) :args _let_35)) _let_34 :args (_let_32 false _let_33)) :args (_let_18 false _let_16 true _let_30 false _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_17 1)) :args ((or _let_15 _let_25))) _let_29 :args (_let_25 true _let_15)) :args (false true _let_21 false _let_24 false _let_19 false _let_18 true _let_17)) :args ((forall ((X $$unsorted)) (not (tptp.distinct_points X X))) (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))) _let_13 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (or (tptp.distinct_points X Z) (tptp.distinct_points Y Z)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))) _let_12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (=> (tptp.apart_point_and_line Z (tptp.line_connecting X Y)) (and (tptp.distinct_points Z X) (tptp.distinct_points Z Y))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (=> (or (tptp.apart_point_and_line Z X) (tptp.apart_point_and_line Z Y)) (tptp.distinct_points Z (tptp.intersection_point X Y))))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (=> (and (tptp.distinct_points X Y) (tptp.distinct_lines U V)) (or (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V) (tptp.apart_point_and_line Y U) (tptp.apart_point_and_line Y V)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_points X Z) (tptp.apart_point_and_line Z Y)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_lines Y Z) (tptp.apart_point_and_line X Z)))) _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.16/0.50 )
% 0.16/0.50 % SZS output end Proof for GEO223+2
% 0.16/0.51 % cvc5---1.0.5 exiting
% 0.16/0.51 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------