TSTP Solution File: GEO260+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEO260+1 : TPTP v8.1.2. Bugfixed v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 22:50:55 EDT 2023
% Result : Theorem 4.32s 4.68s
% Output : Proof 4.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEO260+1 : TPTP v8.1.2. Bugfixed v8.1.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 21:44:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 4.32/4.68 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.J5zQNuctSq/cvc5---1.0.5_30292.p...
% 4.32/4.68 ------- get file name : TPTP file name is GEO260+1
% 4.32/4.68 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30292.smt2...
% 4.32/4.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 4.32/4.68 % SZS status Theorem for GEO260+1
% 4.32/4.68 % SZS output start Proof for GEO260+1
% 4.32/4.68 (
% 4.32/4.68 (let ((_let_1 (not (forall ((L $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.line L) (tptp.distinct_points A C) (tptp.distinct_points B C) (tptp.distinct_points A B)) (not (and (tptp.between_on_line L A B C) (tptp.between_on_line L A C B)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.unequally_directed_lines (tptp.line_connecting A B) (tptp.reverse_line (tptp.line_connecting B A))))))) (let ((_let_3 (forall ((L $$unsorted)) (=> (tptp.line L) (tptp.line (tptp.reverse_line L)))))) (let ((_let_4 (forall ((L $$unsorted) (M $$unsorted)) (not (or (tptp.left_convergent_lines L M) (tptp.left_convergent_lines L (tptp.reverse_line M))))))) (let ((_let_5 (forall ((L $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.reverse_line M))) (=> (and (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L _let_1)) (or (tptp.left_convergent_lines L M) (tptp.left_convergent_lines L _let_1))))))) (let ((_let_6 (forall ((L $$unsorted) (M $$unsorted)) (=> (and (tptp.line L) (tptp.line M)) (or (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L (tptp.reverse_line M))))))) (let ((_let_7 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.unequally_directed_lines L M) (or (tptp.unequally_directed_lines L N) (tptp.unequally_directed_lines M N)))))) (let ((_let_8 (forall ((L $$unsorted)) (not (tptp.unequally_directed_lines L L))))) (let ((_let_9 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (or (not (tptp.unequally_directed_lines L M)) (tptp.unequally_directed_lines L N) (tptp.unequally_directed_lines M N))))) (let ((_let_10 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (tptp.reverse_line _let_10))) (let ((_let_12 (tptp.reverse_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (tptp.unequally_directed_lines _let_12 _let_11))) (let ((_let_14 (tptp.unequally_directed_lines _let_10 _let_11))) (let ((_let_15 (tptp.unequally_directed_lines _let_10 _let_12))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14 _let_13))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (tptp.unequally_directed_lines _let_12 _let_12))) (let ((_let_21 (tptp.unequally_directed_lines _let_12 _let_10))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_15))) (let ((_let_24 (_let_9))) (let ((_let_25 (not (= (tptp.unequally_directed_lines L M) false)))) (let ((_let_26 (_let_25 (not (= (tptp.unequally_directed_lines M N) true))))) (let ((_let_27 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10))) (let ((_let_28 (tptp.unequally_directed_lines _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_21 _let_27))) (let ((_let_31 (_let_25 (not (= (tptp.unequally_directed_lines L N) true))))) (let ((_let_32 (tptp.line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.line _let_12))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_28 _let_20))) (let ((_let_37 (forall ((L $$unsorted) (M $$unsorted)) (or (not (tptp.line L)) (not (tptp.line M)) (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L (tptp.reverse_line M)))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (_let_8))) (let ((_let_40 (ASSUME :args _let_39))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.unequally_directed_lines L L) false))))) :args _let_39)) _let_40 :args ((not _let_20) false _let_8)))) (let ((_let_42 (or _let_33 _let_34))) (let ((_let_43 (forall ((L $$unsorted)) (or (not (tptp.line L)) (tptp.line (tptp.reverse_line L)))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (or _let_33 (not (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.between_on_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.between_on_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_46 (forall ((L $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.line L)) (not (tptp.distinct_points A C)) (not (tptp.distinct_points B C)) (not (tptp.distinct_points A B)) (not (tptp.between_on_line L A B C)) (not (tptp.between_on_line L A C B)))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or))) (let ((_let_50 (not _let_46))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG (REFL :args (_let_45)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_49)) :args ((or _let_32 _let_45))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_48) :args (_let_50))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_46))) (REFL :args (_let_47)) :args _let_49)) _let_48 :args (_let_47 true _let_46)) :args (_let_32 true _let_45)))) (let ((_let_52 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11))) (let ((_let_53 (not _let_27))) (let ((_let_54 (or _let_53 _let_52 _let_14))) (let ((_let_55 (tptp.left_convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11))) (let ((_let_56 (tptp.left_convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10))) (let ((_let_57 (not _let_52))) (let ((_let_58 (or _let_53 _let_57 _let_56 _let_55))) (let ((_let_59 (_let_2))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.line_connecting A B)))) :args _let_59)) _let_60 :args ((not _let_14) false _let_2)))) (let ((_let_62 (forall ((BOUND_VARIABLE_1022 $$unsorted) (BOUND_VARIABLE_1024 $$unsorted)) (not (tptp.left_convergent_lines BOUND_VARIABLE_1022 BOUND_VARIABLE_1024))))) (let ((_let_63 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) :args (0)))) (let ((_let_64 (_let_62))) (let ((_let_65 ((not (= (tptp.left_convergent_lines BOUND_VARIABLE_1022 BOUND_VARIABLE_1024) false))))) (let ((_let_66 (ASSUME :args _let_64))) (let ((_let_67 (forall ((L $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.reverse_line M))) (or (not (tptp.unequally_directed_lines L M)) (not (tptp.unequally_directed_lines L _let_1)) (tptp.left_convergent_lines L M) (tptp.left_convergent_lines L _let_1)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (_let_67))) (let ((_let_70 ((not (= (tptp.unequally_directed_lines L (tptp.reverse_line M)) false))))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_27 _let_29 _let_21 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_53 _let_57 _let_56 _let_55 (not _let_58)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10 QUANTIFIERS_INST_E_MATCHING _let_70)) :args _let_69)) _let_68 :args (_let_58 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_65)) :args _let_64)) _let_63 :args ((not _let_56) false _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_65)) :args _let_64)) _let_63 :args ((not _let_55) false _let_62)) (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_14 _let_52 (not _let_54)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10 _let_11 QUANTIFIERS_INST_E_MATCHING _let_26)) :args _let_24)) _let_18 :args (_let_54 false _let_9)) _let_61 :args (_let_53 false _let_58 true _let_56 true _let_55 false _let_52 false _let_54 true _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_33 _let_35 _let_20 _let_28 (not _let_36)))) _let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_33 _let_34 (not _let_42)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.reverse_line L)))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_34 false _let_32 false _let_42)) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.unequally_directed_lines L (tptp.reverse_line M)) true))))) :args (_let_37))) _let_38 :args (_let_36 false _let_37)) :args (_let_28 false _let_32 false _let_34 true _let_20 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10 QUANTIFIERS_INST_E_MATCHING _let_31)) :args _let_24)) _let_18 :args (_let_30 false _let_9)) :args (_let_21 true _let_27 false _let_28 false _let_30)))) (let ((_let_72 (tptp.left_convergent_lines _let_12 _let_11))) (let ((_let_73 (tptp.left_convergent_lines _let_12 _let_10))) (let ((_let_74 (not _let_13))) (let ((_let_75 (or _let_22 _let_74 _let_73 _let_72))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (_let_10 _let_12 _let_11 QUANTIFIERS_INST_E_MATCHING _let_31)) :args _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_14 _let_13 _let_16 _let_19))) _let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_22 _let_74 _let_73 _let_72 (not _let_75)))) _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_12 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_65)) :args _let_64)) _let_63 :args ((not _let_73) false _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_12 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_65)) :args _let_64)) _let_63 :args ((not _let_72) false _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_12 _let_10 QUANTIFIERS_INST_E_MATCHING _let_70)) :args _let_69)) _let_68 :args (_let_75 false _let_67)) :args (_let_74 false _let_21 true _let_73 true _let_72 false _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_20 _let_22 _let_15 (not _let_23)))) _let_41 _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (_let_12 _let_10 _let_12 QUANTIFIERS_INST_E_MATCHING _let_26)) :args _let_24)) _let_18 :args (_let_23 false _let_9)) :args (_let_15 true _let_20 false _let_21 false _let_23)) :args (_let_19 true _let_14 true _let_13 false _let_15)) _let_18 :args (false true _let_17 false _let_9)) :args ((forall ((A $$unsorted) (L $$unsorted)) (= (tptp.apart_point_and_line A L) (or (tptp.left_apart_point A L) (tptp.left_apart_point A (tptp.reverse_line L))))) (forall ((L $$unsorted) (M $$unsorted)) (= (tptp.convergent_lines L M) (and (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L (tptp.reverse_line M))))) (forall ((A $$unsorted) (B $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.reverse_line L))) (= (tptp.divides_points L A B) (or (and (tptp.left_apart_point A L) (tptp.left_apart_point B _let_1)) (and (tptp.left_apart_point A _let_1) (tptp.left_apart_point B L)))))) (forall ((L $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.reverse_line L))) (= (tptp.before_on_line L A B) (and (tptp.distinct_points A B) (not (or (tptp.left_apart_point A L) (tptp.left_apart_point A _let_1))) (not (or (tptp.left_apart_point B L) (tptp.left_apart_point B _let_1))) (not (tptp.unequally_directed_lines L (tptp.line_connecting A B))))))) (forall ((L $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.between_on_line L A B C) (or (and (tptp.before_on_line L A B) (tptp.before_on_line L B C)) (and (tptp.before_on_line L C B) (tptp.before_on_line L B A))))) (forall ((A $$unsorted)) (not (tptp.distinct_points A A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.distinct_points A B) (or (tptp.distinct_points A C) (tptp.distinct_points B C)))) (forall ((L $$unsorted)) (not (tptp.distinct_lines L L))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.distinct_lines L M) (or (tptp.distinct_lines L N) (tptp.distinct_lines M N)))) _let_8 _let_7 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.reverse_line N))) (=> (and (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L (tptp.reverse_line M))) (or (and (tptp.unequally_directed_lines L N) (tptp.unequally_directed_lines L _let_1)) (and (tptp.unequally_directed_lines M N) (tptp.unequally_directed_lines M _let_1)))))) _let_6 _let_5 (forall ((A $$unsorted) (L $$unsorted)) (not (or (tptp.left_apart_point A L) (tptp.left_apart_point A (tptp.reverse_line L))))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.point A) (tptp.point B) (tptp.distinct_points A B)) (tptp.line (tptp.line_connecting A B)))) (forall ((L $$unsorted) (M $$unsorted)) (=> (and (tptp.line L) (tptp.line M) (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L (tptp.reverse_line M))) (tptp.point (tptp.intersection_point L M)))) (forall ((L $$unsorted) (A $$unsorted)) (=> (and (tptp.point A) (tptp.line L)) (tptp.line (tptp.parallel_through_point L A)))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.line_connecting A B))) (=> (tptp.distinct_points A B) (and (not (tptp.apart_point_and_line A _let_1)) (not (tptp.apart_point_and_line B _let_1)))))) (forall ((L $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.intersection_point L M))) (=> (and (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L (tptp.reverse_line M))) (and (not (tptp.apart_point_and_line _let_1 L)) (not (tptp.apart_point_and_line _let_1 M)))))) (forall ((A $$unsorted) (L $$unsorted)) (not (tptp.apart_point_and_line A (tptp.parallel_through_point L A)))) (forall ((L $$unsorted)) (not (tptp.distinct_lines L (tptp.reverse_line L)))) _let_2 (forall ((A $$unsorted) (L $$unsorted)) (not (tptp.unequally_directed_lines (tptp.parallel_through_point L A) L))) (forall ((A $$unsorted) (B $$unsorted) (L $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.reverse_line M))) (let ((_let_2 (tptp.reverse_line L))) (=> (and (tptp.distinct_points A B) (tptp.distinct_lines L M)) (or (tptp.left_apart_point A L) (tptp.left_apart_point B L) (tptp.left_apart_point A M) (tptp.left_apart_point B M) (tptp.left_apart_point A _let_2) (tptp.left_apart_point B _let_2) (tptp.left_apart_point A _let_1) (tptp.left_apart_point B _let_1)))))) (forall ((A $$unsorted) (B $$unsorted) (L $$unsorted)) (=> (and (tptp.distinct_points A B) (tptp.left_apart_point A L)) (or (tptp.left_apart_point B L) (tptp.left_convergent_lines (tptp.line_connecting A B) L)))) (forall ((A $$unsorted) (B $$unsorted) (L $$unsorted)) (=> (tptp.left_apart_point A L) (or (tptp.distinct_points A B) (tptp.left_apart_point B L)))) (forall ((A $$unsorted) (L $$unsorted) (M $$unsorted)) (=> (and (tptp.left_apart_point A L) (tptp.unequally_directed_lines L M)) (or (tptp.distinct_lines L M) (tptp.left_apart_point A (tptp.reverse_line M))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.left_convergent_lines L M) (or (tptp.unequally_directed_lines M N) (tptp.left_convergent_lines L N)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 4.32/4.69 )
% 4.32/4.69 % SZS output end Proof for GEO260+1
% 4.32/4.69 % cvc5---1.0.5 exiting
% 4.32/4.69 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------