TSTP Solution File: GEO222+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEO222+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 22:50:38 EDT 2023
% Result : Theorem 0.36s 0.57s
% Output : Proof 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO222+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 21:54:05 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.36/0.57 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.0rbx0mb2qx/cvc5---1.0.5_18783.p...
% 0.36/0.57 ------- get file name : TPTP file name is GEO222+2
% 0.36/0.57 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18783.smt2...
% 0.36/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.36/0.57 % SZS status Theorem for GEO222+2
% 0.36/0.57 % SZS output start Proof for GEO222+2
% 0.36/0.57 (
% 0.36/0.57 (let ((_let_1 (forall ((A $$unsorted) (L $$unsorted)) (not (tptp.convergent_lines L (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 $$unsorted)) (=> (tptp.convergent_lines X Y) (tptp.distinct_lines X Y))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z)))))) (let ((_let_10 (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))))) (let ((_let_11 (tptp.orthogonal_through_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (tptp.orthogonal_through_point _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12))) (let ((_let_14 (tptp.unorthogonal_lines _let_12 _let_11))) (let ((_let_15 (tptp.convergent_lines _let_12 _let_11))) (let ((_let_16 (and _let_15 _let_14))) (let ((_let_17 (tptp.unorthogonal_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12))) (let ((_let_18 (tptp.unorthogonal_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11))) (let ((_let_19 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11))) (let ((_let_20 (and _let_19 _let_18))) (let ((_let_21 (not _let_17))) (let ((_let_22 (not _let_13))) (let ((_let_23 (or _let_22 _let_21 _let_20 _let_16))) (let ((_let_24 (_let_2))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_25) :args _let_24) (REWRITE :args ((=> _let_2 (not _let_22)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_13)) :args (or))) _let_25 :args (_let_13 true _let_1)))) (let ((_let_27 (not _let_16))) (let ((_let_28 (_let_5))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 ((tptp.orthogonal_through_point L A)))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_28)) _let_29 :args ((not _let_14) false _let_5)))) (let ((_let_32 (and _let_13 _let_17))) (let ((_let_33 (tptp.convergent_lines _let_12 _let_12))) (let ((_let_34 (and _let_33 (tptp.unorthogonal_lines _let_12 _let_12)))) (let ((_let_35 (tptp.unorthogonal_lines _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.convergent_lines _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36 _let_34 _let_32))) (let ((_let_40 (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_41 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_40))) (let ((_let_43 (tptp.convergent_lines M N))) (let ((_let_44 (_let_43 (tptp.convergent_lines L N)))) (let ((_let_45 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_46 (or _let_22 _let_45 _let_37))) (let ((_let_47 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (_let_47))) (let ((_let_50 (not (= (tptp.convergent_lines Y Z) true)))) (let ((_let_51 (_let_10))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 ((not (= (tptp.convergent_lines X X) false))))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_53)) :args _let_51)) _let_52 :args ((not _let_45) false _let_10)))) (let ((_let_55 (tptp.unorthogonal_lines _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_56 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11))) (let ((_let_57 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12))) (let ((_let_58 (tptp.distinct_lines _let_12 _let_11))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 _let_57 _let_56 _let_35 _let_55))) (let ((_let_61 (forall ((A $$unsorted) (L $$unsorted) (M $$unsorted) (N $$unsorted)) (or (not (tptp.distinct_lines L M)) (tptp.apart_point_and_line A L) (tptp.apart_point_and_line A M) (tptp.unorthogonal_lines L N) (tptp.unorthogonal_lines M N))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 ((not (= (tptp.unorthogonal_lines M N) true)) (not (= (tptp.apart_point_and_line A L) true))))) (let ((_let_65 (not _let_15))) (let ((_let_66 (or _let_65 _let_58))) (let ((_let_67 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.distinct_lines X Y))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (or _let_15 _let_14))) (let ((_let_70 (_let_7))) (let ((_let_71 (ASSUME :args _let_70))) (let ((_let_72 ((not (= (tptp.unorthogonal_lines L M) true))))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_58 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_14 _let_15 (not _let_69)))) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_12 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_72)) :args _let_70)) _let_71 :args (_let_69 false _let_7)) :args (_let_15 true _let_14 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_12 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X Y) false))))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_58 false _let_15 false _let_66)))) (let ((_let_74 (_let_4))) (let ((_let_75 (ASSUME :args _let_74))) (let ((_let_76 ((tptp.orthogonal_through_point L A)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_76)) :args _let_74)) _let_75 :args ((not _let_57) false _let_4)))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_76)) :args _let_74)) _let_75 :args ((not _let_56) false _let_4)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_28)) _let_29 :args ((not _let_55) false _let_5)))) (let ((_let_80 (not _let_34))) (let ((_let_81 (not _let_20))) (let ((_let_82 (tptp.convergent_lines _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_83 (and _let_82 _let_55))) (let ((_let_84 (and _let_45 (tptp.unorthogonal_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_85 (not _let_18))) (let ((_let_86 (not _let_19))) (let ((_let_87 (or _let_86 _let_85 _let_84 _let_83))) (let ((_let_88 (not _let_84))) (let ((_let_89 (tptp.convergent_lines _let_11 _let_11))) (let ((_let_90 (not _let_82))) (let ((_let_91 (or _let_90 _let_89 _let_19))) (let ((_let_92 (tptp.unorthogonal_lines _let_11 _let_11))) (let ((_let_93 (not _let_92))) (let ((_let_94 (not _let_89))) (let ((_let_95 (or _let_94 _let_93 _let_83 _let_83))) (let ((_let_96 (not _let_83))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_83 1)) :args ((or _let_55 _let_96))) _let_79 :args (_let_96 true _let_55)))) (let ((_let_98 (or _let_59 _let_57 _let_56 _let_14 _let_92))) (let ((_let_99 (or _let_82 _let_55))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_21 _let_16 _let_20 (not _let_23)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12 _let_11 QUANTIFIERS_INST_E_MATCHING (_let_43 (not (= (tptp.unorthogonal_lines L M) false))))) :args _let_42)) _let_41 :args (_let_23 false _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 1)) :args ((or _let_18 _let_81))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_83 _let_86 _let_85 _let_84 (not _let_87)))) _let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_90 _let_89 _let_19 (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_55 _let_82 (not _let_99)))) _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_72)) :args _let_70)) _let_71 :args (_let_99 false _let_7)) :args (_let_82 true _let_55 false _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_95))) :args ((or _let_94 _let_93 _let_83 (not _let_95)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_14 _let_56 _let_57 _let_59 _let_92 (not _let_98)))) _let_31 _let_78 _let_77 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12 _let_11 _let_11 QUANTIFIERS_INST_E_MATCHING _let_64)) :args _let_63)) _let_62 :args (_let_98 false _let_61)) :args (_let_92 true _let_14 true _let_56 true _let_57 false _let_58 false _let_98)) _let_97 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_11 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_44)) :args _let_42)) _let_41 :args (_let_95 false _let_40)) :args (_let_94 false _let_92 true _let_83 false _let_95)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.convergent_lines X Z) true)) _let_50))) :args _let_49)) _let_48 :args (_let_91 false _let_47)) :args (_let_19 false _let_82 true _let_89 false _let_91)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_84 0)) :args ((or _let_45 _let_88))) _let_54 :args (_let_88 true _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_44)) :args _let_42)) _let_41 :args (_let_87 false _let_40)) :args (_let_85 true _let_83 false _let_19 true _let_84 false _let_87)) :args (_let_81 true _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_32 1)) :args ((or _let_17 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_32 _let_34 _let_36 _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_33 _let_80))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_53)) :args _let_51)) _let_52 :args ((not _let_33) false _let_10)) :args (_let_80 true _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_55 _let_56 _let_57 _let_59 _let_35 (not _let_60)))) _let_79 _let_78 _let_77 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_64)) :args _let_63)) _let_62 :args (_let_60 false _let_61)) :args (_let_35 true _let_55 true _let_56 true _let_57 false _let_58 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_22 _let_45 _let_37 (not _let_46)))) _let_26 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING (_let_50 (not (= (tptp.convergent_lines X Y) false))))) :args _let_49)) _let_48 :args (_let_46 false _let_47)) :args (_let_37 false _let_13 true _let_45 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12 QUANTIFIERS_INST_E_MATCHING _let_44)) :args _let_42)) _let_41 :args (_let_39 false _let_40)) :args (_let_32 true _let_34 false _let_35 false _let_37 false _let_39)) :args (_let_17 false _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 1)) :args ((or _let_14 _let_27))) _let_31 :args (_let_27 true _let_14)) _let_26 :args (false false _let_23 true _let_20 false _let_17 true _let_16 false _let_13)) :args ((forall ((X $$unsorted)) (not (tptp.distinct_points X X))) (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))) _let_10 (forall ((X $$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 $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))) _let_9 (forall ((X $$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 $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_lines Y Z) (tptp.apart_point_and_line X Z)))) _let_8 (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.convergent_lines (tptp.parallel_through_point Y X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.apart_point_and_line X (tptp.parallel_through_point Y X)))) (forall ((X $$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_7 _let_6 _let_5 _let_4 _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.36/0.57 )
% 0.36/0.57 % SZS output end Proof for GEO222+2
% 0.36/0.58 % cvc5---1.0.5 exiting
% 0.36/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------