TSTP Solution File: GEO223+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEO223+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO223+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 22:39:14 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.55 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.9c6JaWHMiT/cvc5---1.0.5_27085.p...
% 0.20/0.55 ------- get file name : TPTP file name is GEO223+1
% 0.20/0.55 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27085.smt2...
% 0.20/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.55 % SZS status Theorem for GEO223+1
% 0.20/0.55 % SZS output start Proof for GEO223+1
% 0.20/0.55 (
% 0.20/0.55 (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 $$unsorted)) (=> (and (tptp.convergent_lines L M) (tptp.unorthogonal_lines L M)) (or (and (tptp.convergent_lines L N) (tptp.unorthogonal_lines L N)) (and (tptp.convergent_lines M N) (tptp.unorthogonal_lines M N))))))) (let ((_let_7 (forall ((X $$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_8 (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.apart_point_and_line X (tptp.parallel_through_point Y X)))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.convergent_lines (tptp.parallel_through_point Y X) Y))))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z)))))) (let ((_let_11 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z)))))) (let ((_let_12 (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))))) (let ((_let_13 (tptp.orthogonal_through_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (tptp.unorthogonal_lines _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (and (tptp.convergent_lines _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_14))) (let ((_let_16 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13))) (let ((_let_17 (tptp.unorthogonal_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13))) (let ((_let_18 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (and _let_18 (tptp.unorthogonal_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_20 (not _let_17))) (let ((_let_21 (not _let_16))) (let ((_let_22 (or _let_21 _let_20 _let_19 _let_15))) (let ((_let_23 (not _let_15))) (let ((_let_24 (_let_5))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 ((tptp.orthogonal_through_point L A)))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24)) _let_25 :args ((not _let_14) false _let_5)))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_15 1)) :args ((or _let_14 _let_23))) _let_27 :args (_let_23 true _let_14)))) (let ((_let_29 (and _let_16 _let_17))) (let ((_let_30 (tptp.orthogonal_through_point _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (tptp.unorthogonal_lines _let_30 _let_13))) (let ((_let_32 (and (tptp.convergent_lines _let_30 _let_13) _let_31))) (let ((_let_33 (tptp.unorthogonal_lines _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.convergent_lines _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_34 _let_32 _let_29))) (let ((_let_38 (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_39 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 (not (= (tptp.unorthogonal_lines L M) false)))) (let ((_let_42 (_let_41 (tptp.convergent_lines L N)))) (let ((_let_43 (not _let_32))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24)) _let_25 :args ((not _let_31) false _let_5)))) (let ((_let_45 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13))) (let ((_let_46 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_30))) (let ((_let_47 (tptp.distinct_lines _let_30 _let_13))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_46 _let_45 _let_33 _let_14))) (let ((_let_50 (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_51 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (_let_50))) (let ((_let_53 ((not (= (tptp.apart_point_and_line A L) true)) (not (= (tptp.unorthogonal_lines M N) true))))) (let ((_let_54 (tptp.parallel_through_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_55 (tptp.convergent_lines _let_54 _let_13))) (let ((_let_56 (tptp.convergent_lines _let_54 _let_30))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_47 _let_55))) (let ((_let_59 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (tptp.convergent_lines _let_54 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_62 (and _let_61 (tptp.unorthogonal_lines _let_54 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_63 (tptp.unorthogonal_lines _let_54 _let_13))) (let ((_let_64 (not _let_63))) (let ((_let_65 (not _let_55))) (let ((_let_66 (or _let_65 _let_64 _let_62 _let_15))) (let ((_let_67 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_54))) (let ((_let_68 (tptp.distinct_lines _let_54 _let_30))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_67 _let_46 _let_63 _let_31))) (let ((_let_71 (_let_4))) (let ((_let_72 (ASSUME :args _let_71))) (let ((_let_73 ((tptp.orthogonal_through_point L A)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_71)) _let_72 :args ((not _let_46) false _let_4)))) (let ((_let_75 (_let_8))) (let ((_let_76 (ASSUME :args _let_75))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.parallel_through_point Y X)))) :args _let_75)) _let_76 :args ((not _let_67) false _let_8)))) (let ((_let_78 (_let_2))) (let ((_let_79 (ASSUME :args _let_78))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_79) :args _let_78) (REWRITE :args ((=> _let_2 (not _let_69)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_68)) :args (or))) _let_79 :args (_let_68 true _let_1)))) (let ((_let_81 (not _let_62))) (let ((_let_82 (_let_9))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.parallel_through_point Y X)))) :args _let_82)) _let_83 :args ((not _let_61) false _let_9)))) (let ((_let_85 (or _let_69 _let_67 _let_46 _let_56))) (let ((_let_86 (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_87 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_69 _let_67 _let_46 _let_56 (not _let_85)))) _let_80 _let_77 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_54 _let_30 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_lines Y Z) false)) (not (= (tptp.apart_point_and_line X Y) true))))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_56 false _let_68 true _let_67 true _let_46 false _let_85)))) (let ((_let_89 (or _let_57 _let_61 _let_35))) (let ((_let_90 (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_91 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_34 _let_32 _let_29 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_61 _let_57 _let_35 (not _let_89)))) _let_84 _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_54 _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.convergent_lines X Y) false)) (not (= (tptp.convergent_lines X Z) true))))) :args (_let_90))) _let_91 :args (_let_89 false _let_90)) :args (_let_35 true _let_61 false _let_56 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_14 _let_45 _let_46 _let_33 _let_48 (not _let_49)))) _let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_71)) _let_72 :args ((not _let_45) false _let_4)) _let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_55 _let_47 (not _let_58)))) _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_62 _let_64 _let_65 _let_15 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_62 0)) :args ((or _let_61 _let_81))) _let_84 :args (_let_81 true _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_69 _let_67 _let_31 _let_46 _let_63 (not _let_70)))) _let_80 _let_77 _let_44 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_54 _let_30 _let_13 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52)) _let_51 :args (_let_70 false _let_50)) :args (_let_63 false _let_68 true _let_67 true _let_31 true _let_46 false _let_70)) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_54 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.convergent_lines M N) _let_41))) :args _let_40)) _let_39 :args (_let_66 false _let_38)) :args (_let_65 true _let_62 false _let_63 true _let_15 false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_54 _let_30 _let_13 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.convergent_lines X Y) false)) (not (= (tptp.distinct_lines Y Z) true))))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_47 false _let_56 true _let_55 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_30 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52)) _let_51 :args (_let_49 false _let_50)) :args (_let_33 true _let_14 true _let_45 true _let_46 false _let_47 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_32 1)) :args ((or _let_31 _let_43))) _let_44 :args (_let_43 true _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13 QUANTIFIERS_INST_E_MATCHING _let_42)) :args _let_40)) _let_39 :args (_let_37 false _let_38)) :args (_let_29 false _let_35 false _let_33 true _let_32 false _let_37)))) (let ((_let_93 (not _let_29))) (let ((_let_94 (not _let_19))) (let ((_let_95 (_let_12))) (let ((_let_96 (ASSUME :args _let_95))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_15 _let_20 _let_21 _let_19 (not _let_22)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_19 0)) :args ((or _let_18 _let_94))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X X) false))))) :args _let_95)) _let_96 :args ((not _let_18) false _let_12)) :args (_let_94 true _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_42)) :args _let_40)) _let_39 :args (_let_22 false _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 1)) :args ((or _let_17 _let_93))) _let_92 :args (_let_17 false _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 0)) :args ((or _let_16 _let_93))) _let_92 :args (_let_16 false _let_29)) _let_28 :args (false true _let_19 false _let_22 false _let_17 false _let_16 true _let_15)) :args ((forall ((X $$unsorted)) (not (tptp.distinct_points X X))) (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))) _let_12 (forall ((X $$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 $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))) _let_11 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line X (tptp.line_connecting X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line Y (tptp.line_connecting X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.convergent_lines X Y) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) X)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.convergent_lines X Y) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) Y)))) (forall ((X $$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 $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_lines Y Z) (tptp.apart_point_and_line X Z)))) _let_10 _let_9 _let_8 _let_7 (forall ((L $$unsorted) (M $$unsorted)) (or (tptp.convergent_lines L M) (tptp.unorthogonal_lines L M))) _let_6 _let_5 _let_4 _let_3 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.56 )
% 0.20/0.56 % SZS output end Proof for GEO223+1
% 0.20/0.56 % cvc5---1.0.5 exiting
% 0.20/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------