TSTP Solution File: GEO231+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEO231+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 22:50:42 EDT 2023
% Result : Theorem 0.19s 0.77s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO231+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Aug 29 20:56:47 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.77 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.lf8rH7siex/cvc5---1.0.5_30775.p...
% 0.19/0.77 ------- get file name : TPTP file name is GEO231+1
% 0.19/0.77 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_30775.smt2...
% 0.19/0.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.77 % SZS status Theorem for GEO231+1
% 0.19/0.77 % SZS output start Proof for GEO231+1
% 0.19/0.77 (
% 0.19/0.77 (let ((_let_1 (not (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (and (not (tptp.unequally_directed_lines L (tptp.reverse_line M))) (not (tptp.unequally_directed_lines L N))) (not (tptp.unequally_directed_lines M (tptp.reverse_line N)))))))) (let ((_let_2 (forall ((A $$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) (M $$unsorted)) (not (or (tptp.left_convergent_lines L M) (tptp.left_convergent_lines L (tptp.reverse_line M))))))) (let ((_let_4 (forall ((L $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.reverse_line M))) (=> (and (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L _let_1)) (or (tptp.left_convergent_lines L M) (tptp.left_convergent_lines L _let_1))))))) (let ((_let_5 (forall ((L $$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 ((_let_6 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.unequally_directed_lines L M) (or (tptp.unequally_directed_lines L N) (tptp.unequally_directed_lines M N)))))) (let ((_let_7 (forall ((L $$unsorted)) (not (tptp.unequally_directed_lines L L))))) (let ((_let_8 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (tptp.line_connecting _let_8 _let_8))) (let ((_let_10 (tptp.reverse_line _let_9))) (let ((_let_11 (tptp.unequally_directed_lines _let_9 _let_10))) (let ((_let_12 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_10))) (let ((_let_13 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_11))) (let ((_let_16 (_let_2))) (let ((_let_17 (ASSUME :args _let_16))) (let ((_let_18 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (_let_8 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.line_connecting A B)))) :args _let_16)) _let_17 :args ((not _let_11) false _let_2)))) (let ((_let_19 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (or (not (tptp.unequally_directed_lines L M)) (tptp.unequally_directed_lines L N) (tptp.unequally_directed_lines M N))))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (_let_19))) (let ((_let_22 (not (= (tptp.unequally_directed_lines L M) false)))) (let ((_let_23 (_let_22 (not (= (tptp.unequally_directed_lines M N) true))))) (let ((_let_24 (tptp.reverse_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_25 (tptp.unequally_directed_lines _let_24 _let_9))) (let ((_let_26 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_24))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_13 _let_25))) (let ((_let_29 (tptp.unequally_directed_lines _let_24 _let_10))) (let ((_let_30 (not _let_25))) (let ((_let_31 (or _let_30 _let_29 _let_11))) (let ((_let_32 (tptp.left_convergent_lines _let_24 _let_10))) (let ((_let_33 (tptp.left_convergent_lines _let_24 _let_9))) (let ((_let_34 (not _let_29))) (let ((_let_35 (or _let_30 _let_34 _let_33 _let_32))) (let ((_let_36 (forall ((BOUND_VARIABLE_1021 $$unsorted) (BOUND_VARIABLE_1023 $$unsorted)) (not (tptp.left_convergent_lines BOUND_VARIABLE_1021 BOUND_VARIABLE_1023))))) (let ((_let_37 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) :args (0)))) (let ((_let_38 (_let_36))) (let ((_let_39 ((not (= (tptp.left_convergent_lines BOUND_VARIABLE_1021 BOUND_VARIABLE_1023) false))))) (let ((_let_40 (ASSUME :args _let_38))) (let ((_let_41 (forall ((L $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.reverse_line M))) (or (not (tptp.unequally_directed_lines L M)) (not (tptp.unequally_directed_lines L _let_1)) (tptp.left_convergent_lines L M) (tptp.left_convergent_lines L _let_1)))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 ((not (= (tptp.unequally_directed_lines L (tptp.reverse_line M)) false))))) (let ((_let_45 (tptp.reverse_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_46 (tptp.unequally_directed_lines _let_45 _let_24))) (let ((_let_47 (tptp.unequally_directed_lines _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_46 _let_26))) (let ((_let_50 (_let_22 (not (= (tptp.unequally_directed_lines L N) true))))) (let ((_let_51 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_45))) (let ((_let_52 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_53 (and _let_52 _let_51))) (let ((_let_54 (tptp.unequally_directed_lines _let_45 _let_45))) (let ((_let_55 (and _let_47 _let_54))) (let ((_let_56 (not _let_46))) (let ((_let_57 (tptp.unequally_directed_lines _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56 _let_55 _let_53))) (let ((_let_60 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.reverse_line N))) (or (not (tptp.unequally_directed_lines L M)) (not (tptp.unequally_directed_lines L (tptp.reverse_line M))) (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 ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (not _let_55))) (let ((_let_63 (_let_7))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 ((not (= (tptp.unequally_directed_lines L L) false))))) (let ((_let_66 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_67 (not _let_51))) (let ((_let_68 (or _let_67 _let_66 _let_57))) (let ((_let_69 (or (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_24) (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) _let_67))) (let ((_let_70 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (or (tptp.unequally_directed_lines L (tptp.reverse_line M)) (tptp.unequally_directed_lines L N) (not (tptp.unequally_directed_lines M (tptp.reverse_line N))))))) (let ((_let_71 (not _let_69))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (or))) (let ((_let_74 (not _let_70))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 2)) (CONG (REFL :args (_let_69)) (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_51))) :args _let_73)) :args ((or _let_51 _let_69))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_72) :args (_let_74))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_70))) (REFL :args (_let_71)) :args _let_73)) _let_72 :args (_let_71 true _let_70)) :args (_let_51 true _let_69)))) (let ((_let_76 (not _let_53))) (let ((_let_77 (tptp.left_convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_45))) (let ((_let_78 (tptp.left_convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_79 (not _let_52))) (let ((_let_80 (or _let_79 _let_67 _let_78 _let_77))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_67 _let_79 _let_78 _let_77 (not _let_80)))) _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args ((not _let_78) false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_45 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args ((not _let_77) false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_44)) :args _let_43)) _let_42 :args (_let_80 false _let_41)) :args (_let_79 false _let_51 true _let_78 true _let_77 false _let_80)))) (let ((_let_82 (or _let_67 _let_52 _let_47))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_13 _let_25 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_26 _let_48 _let_46 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_67 _let_52 _let_47 (not _let_82)))) _let_75 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_50)) :args _let_21)) _let_20 :args (_let_82 false _let_19)) :args (_let_47 false _let_51 true _let_52 false _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_53 _let_58 _let_56 _let_55 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_53 0)) :args ((or _let_52 _let_76))) _let_81 :args (_let_76 true _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_66 _let_57 (not _let_68)))) _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_65)) :args _let_63)) _let_64 :args ((not _let_66) false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_50)) :args _let_21)) _let_20 :args (_let_68 false _let_19)) :args (_let_57 false _let_51 true _let_66 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_55 1)) :args ((or _let_54 _let_62))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_45 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_65)) :args _let_63)) _let_64 :args ((not _let_54) false _let_7)) :args (_let_62 true _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (_let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.unequally_directed_lines M (tptp.reverse_line N)) (not (= (tptp.unequally_directed_lines L (tptp.reverse_line M)) false))))) :args (_let_60))) _let_61 :args (_let_59 false _let_60)) :args (_let_56 true _let_53 false _let_57 true _let_55 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (_let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_24 QUANTIFIERS_INST_E_MATCHING _let_50)) :args _let_21)) _let_20 :args (_let_49 false _let_19)) :args (_let_26 false _let_47 true _let_46 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_30 _let_34 _let_33 _let_32 (not _let_35)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_24 _let_9 QUANTIFIERS_INST_E_MATCHING _let_44)) :args _let_43)) _let_42 :args (_let_35 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_24 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args ((not _let_33) false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_24 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args ((not _let_32) false _let_36)) (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_11 _let_30 _let_29 (not _let_31)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (_let_24 _let_9 _let_10 QUANTIFIERS_INST_E_MATCHING _let_23)) :args _let_21)) _let_20 :args (_let_31 false _let_19)) _let_18 :args (_let_30 false _let_35 true _let_33 true _let_32 false _let_29 false _let_31 true _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_24 _let_9 QUANTIFIERS_INST_E_MATCHING _let_23)) :args _let_21)) _let_20 :args (_let_28 false _let_19)) :args (_let_13 false _let_26 true _let_25 false _let_28)))) (let ((_let_84 (tptp.left_convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_10))) (let ((_let_85 (tptp.left_convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9))) (let ((_let_86 (not _let_12))) (let ((_let_87 (or _let_14 _let_86 _let_85 _let_84))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_11 _let_12 (not _let_15)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_14 _let_86 _let_85 _let_84 (not _let_87)))) _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args ((not _let_85) false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args ((not _let_84) false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9 QUANTIFIERS_INST_E_MATCHING _let_44)) :args _let_43)) _let_42 :args (_let_87 false _let_41)) :args (_let_86 false _let_13 true _let_85 true _let_84 false _let_87)) _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9 _let_10 QUANTIFIERS_INST_E_MATCHING _let_23)) :args _let_21)) _let_20 :args (_let_15 false _let_19)) _let_18 :args (false true _let_12 false _let_13 false _let_15 true _let_11)) :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 $$unsorted)) (=> (tptp.distinct_lines L M) (or (tptp.distinct_lines L N) (tptp.distinct_lines M N)))) _let_7 _let_6 _let_5 (forall ((L $$unsorted) (M $$unsorted)) (=> (and (tptp.line L) (tptp.line M)) (or (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L (tptp.reverse_line M))))) _let_4 (forall ((A $$unsorted) (L $$unsorted)) (not (or (tptp.left_apart_point A L) (tptp.left_apart_point A (tptp.reverse_line L))))) _let_3 (forall ((A $$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 $$unsorted)) (=> (and (tptp.point A) (tptp.line L)) (tptp.line (tptp.parallel_through_point L A)))) (forall ((L $$unsorted)) (=> (tptp.line L) (tptp.line (tptp.reverse_line L)))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.78 )
% 0.19/0.78 % SZS output end Proof for GEO231+1
% 0.19/0.78 % cvc5---1.0.5 exiting
% 0.19/0.78 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------