TSTP Solution File: GEO255+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEO255+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 22:50:54 EDT 2023
% Result : Theorem 0.22s 0.67s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO255+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n002.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Tue Aug 29 23:36:50 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.67 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.oSLF56W7LJ/cvc5---1.0.5_13380.p...
% 0.22/0.67 ------- get file name : TPTP file name is GEO255+3
% 0.22/0.67 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_13380.smt2...
% 0.22/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.67 % SZS status Theorem for GEO255+3
% 0.22/0.67 % SZS output start Proof for GEO255+3
% 0.22/0.67 (
% 0.22/0.67 (let ((_let_1 (not (forall ((L $$unsorted) (A $$unsorted) (B $$unsorted)) (not (and (tptp.before_on_line L A B) (tptp.before_on_line L B A))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.distinct_points A B) (tptp.equally_directed_lines (tptp.line_connecting A B) (tptp.reverse_line (tptp.line_connecting B A))))))) (let ((_let_3 (forall ((L $$unsorted) (M $$unsorted)) (or (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L (tptp.reverse_line M)))))) (let ((_let_4 (forall ((L $$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_5 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.unequally_directed_lines L M) (or (tptp.unequally_directed_lines L N) (tptp.unequally_directed_lines M N)))))) (let ((_let_6 (forall ((L $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.before_on_line L A B) (and (tptp.distinct_points A B) (tptp.incident_point_and_line A L) (tptp.incident_point_and_line B L) (tptp.equally_directed_lines L (tptp.line_connecting A B))))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.equally_directed_lines X Y) (not (tptp.unequally_directed_lines X Y)))))) (let ((_let_8 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_9 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (tptp.unequally_directed_lines _let_9 _let_8))) (let ((_let_11 (tptp.unequally_directed_lines _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (tptp.unequally_directed_lines _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (not _let_10))) (let ((_let_14 (or _let_13 _let_12 _let_11))) (let ((_let_15 (tptp.reverse_line _let_8))) (let ((_let_16 (tptp.unequally_directed_lines _let_9 _let_15))) (let ((_let_17 (or _let_10 _let_16))) (let ((_let_18 (_let_3))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 ((not (= (tptp.unequally_directed_lines L (tptp.reverse_line M)) true))))) (let ((_let_21 (not _let_16))) (let ((_let_22 (tptp.equally_directed_lines _let_9 _let_15))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (_let_7))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 ((tptp.equally_directed_lines X Y)))) (let ((_let_27 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_22))) (let ((_let_30 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.distinct_points A B)) (tptp.equally_directed_lines (tptp.line_connecting A B) (tptp.reverse_line (tptp.line_connecting B A))))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (_let_30))) (let ((_let_33 ((not (= (tptp.distinct_points A B) false))))) (let ((_let_34 (tptp.equally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_35 (tptp.incident_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_36 (tptp.incident_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (and _let_27 _let_36 _let_35 _let_34))) (let ((_let_38 (tptp.before_on_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_39 (= _let_38 _let_37))) (let ((_let_40 (_let_6))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 ((tptp.before_on_line L A B)))) (let ((_let_43 (tptp.before_on_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_44 (not _let_43))) (let ((_let_45 (not _let_38))) (let ((_let_46 (or _let_45 _let_44))) (let ((_let_47 (forall ((L $$unsorted) (A $$unsorted) (B $$unsorted)) (or (not (tptp.before_on_line L A B)) (not (tptp.before_on_line L B A)))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (or))) (let ((_let_51 (not _let_47))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_49) :args (_let_51))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_47))) (REFL :args (_let_48)) :args _let_50)) _let_49 :args (_let_48 true _let_47)))) (let ((_let_53 (REFL :args (_let_46)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or _let_45 _let_37 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_38))) :args _let_50)) :args ((or _let_38 _let_46))) _let_52 :args (_let_38 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_42)) :args _let_40)) _let_41 :args (_let_39 false _let_6)) :args (_let_37 false _let_38 false _let_39)))) (let ((_let_55 (not _let_37))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_23)) :args ((or (not _let_22) _let_21 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_22 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 0)) :args ((or _let_27 _let_55))) _let_54 :args (_let_27 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_32)) _let_31 :args (_let_29 false _let_30)) :args (_let_22 false _let_27 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (_let_9 _let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24)) _let_25 :args (_let_23 false _let_7)) :args (_let_21 false _let_22 false _let_23)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_16 _let_10 (not _let_17)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (_let_9 _let_8 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_18)) _let_19 :args (_let_17 false _let_3)) :args (_let_10 true _let_16 false _let_17)))) (let ((_let_58 (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_59 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (_let_58))) (let ((_let_61 (not (= (tptp.unequally_directed_lines L N) true)))) (let ((_let_62 (_let_61 (not (= (tptp.unequally_directed_lines M N) true))))) (let ((_let_63 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_64 (tptp.unequally_directed_lines _let_9 _let_9))) (let ((_let_65 (not _let_12))) (let ((_let_66 (or _let_65 _let_64 _let_63))) (let ((_let_67 (and _let_10 _let_16))) (let ((_let_68 (tptp.reverse_line _let_9))) (let ((_let_69 (tptp.unequally_directed_lines _let_9 _let_68))) (let ((_let_70 (not _let_69))) (let ((_let_71 (not _let_64))) (let ((_let_72 (or _let_71 _let_70 _let_67 _let_67))) (let ((_let_73 (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_74 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (_let_73))) (let ((_let_76 ((tptp.unequally_directed_lines L (tptp.reverse_line N)) (tptp.reverse_line M)))) (let ((_let_77 (not _let_67))) (let ((_let_78 (tptp.unequally_directed_lines _let_8 _let_68))) (let ((_let_79 (tptp.unequally_directed_lines _let_8 _let_9))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_80 _let_78 _let_69))) (let ((_let_82 ((not (= (tptp.unequally_directed_lines L M) false)) _let_61))) (let ((_let_83 (or _let_79 _let_78))) (let ((_let_84 (not _let_78))) (let ((_let_85 (tptp.equally_directed_lines _let_8 _let_68))) (let ((_let_86 (= _let_85 _let_84))) (let ((_let_87 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or _let_88 _let_85))) (let ((_let_90 (tptp.equally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8))) (let ((_let_91 (and _let_87 _let_35 _let_36 _let_90))) (let ((_let_92 (= _let_43 _let_91))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_92)) :args ((or _let_44 _let_91 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_50)) :args ((or _let_43 _let_46))) _let_52 :args (_let_43 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_42)) :args _let_40)) _let_41 :args (_let_92 false _let_6)) :args (_let_91 false _let_43 false _let_92)))) (let ((_let_94 (not _let_91))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_86)) :args ((or (not _let_85) _let_84 (not _let_86)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_88 _let_85 (not _let_89)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_91 0)) :args ((or _let_87 _let_94))) _let_93 :args (_let_87 false _let_91)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_32)) _let_31 :args (_let_89 false _let_30)) :args (_let_85 false _let_87 false _let_89)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (_let_8 _let_68 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24)) _let_25 :args (_let_86 false _let_7)) :args (_let_84 false _let_85 false _let_86)))) (let ((_let_96 (not _let_63))) (let ((_let_97 (= _let_34 _let_96))) (let ((_let_98 (tptp.unequally_directed_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8))) (let ((_let_99 (tptp.unequally_directed_lines _let_8 _let_8))) (let ((_let_100 (not _let_11))) (let ((_let_101 (or _let_100 _let_99 _let_98))) (let ((_let_102 (and _let_79 _let_78))) (let ((_let_103 (tptp.unequally_directed_lines _let_8 _let_15))) (let ((_let_104 (not _let_103))) (let ((_let_105 (not _let_99))) (let ((_let_106 (or _let_105 _let_104 _let_102 _let_102))) (let ((_let_107 (not _let_102))) (let ((_let_108 (or _let_13 _let_16 _let_103))) (let ((_let_109 (not _let_98))) (let ((_let_110 (= _let_90 _let_109))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_13 _let_11 _let_12 (not _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_98 _let_99 _let_100 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_110)) :args ((or (not _let_90) _let_109 (not _let_110)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_91 3)) :args ((or _let_90 _let_94))) _let_93 :args (_let_90 false _let_91)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24)) _let_25 :args (_let_110 false _let_7)) :args (_let_109 false _let_90 false _let_110)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_106))) :args ((or _let_105 _let_104 _let_102 (not _let_106)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_16 _let_103 _let_13 (not _let_108)))) _let_56 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_9 _let_8 _let_15 QUANTIFIERS_INST_E_MATCHING _let_82)) :args _let_60)) _let_59 :args (_let_108 false _let_58)) :args (_let_103 true _let_16 false _let_10 false _let_108)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_102 1)) :args ((or _let_78 _let_107))) _let_95 :args (_let_107 true _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (_let_8 _let_8 _let_9 QUANTIFIERS_INST_E_MATCHING _let_76)) :args _let_75)) _let_74 :args (_let_106 false _let_73)) :args (_let_105 false _let_103 true _let_102 false _let_106)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8 QUANTIFIERS_INST_E_MATCHING _let_62)) :args _let_60)) _let_59 :args (_let_101 false _let_58)) :args (_let_100 true _let_98 true _let_99 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_63 _let_64 _let_65 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_97)) :args ((or (not _let_34) _let_96 (not _let_97)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 3)) :args ((or _let_34 _let_55))) _let_54 :args (_let_34 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24)) _let_25 :args (_let_97 false _let_7)) :args (_let_96 false _let_34 false _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_72))) :args ((or _let_71 _let_70 _let_67 (not _let_72)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_78 _let_69 _let_80 (not _let_81)))) _let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_78 _let_79 (not _let_83)))) _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (_let_8 _let_9 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_18)) _let_19 :args (_let_83 false _let_3)) :args (_let_79 true _let_78 false _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_8 _let_9 _let_68 QUANTIFIERS_INST_E_MATCHING _let_82)) :args _let_60)) _let_59 :args (_let_81 false _let_58)) :args (_let_69 true _let_78 false _let_79 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 1)) :args ((or _let_16 _let_77))) _let_56 :args (_let_77 true _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (_let_9 _let_9 _let_8 QUANTIFIERS_INST_E_MATCHING _let_76)) :args _let_75)) _let_74 :args (_let_72 false _let_73)) :args (_let_71 false _let_69 true _let_67 false _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_E_MATCHING _let_62)) :args _let_60)) _let_59 :args (_let_66 false _let_58)) :args (_let_65 true _let_63 true _let_64 false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_9 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_62)) :args _let_60)) _let_59 :args (_let_14 false _let_58)) _let_57 :args (false true _let_11 true _let_12 false _let_14 false _let_10)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unequally_directed_opposite_lines X Y) (tptp.unequally_directed_lines X (tptp.reverse_line Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.right_apart_point X Y) (tptp.left_apart_point X (tptp.reverse_line Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.right_convergent_lines X Y) (tptp.left_convergent_lines X (tptp.reverse_line Y)))) _let_7 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.equally_directed_opposite_lines X Y) (not (tptp.unequally_directed_opposite_lines X Y)))) (forall ((A $$unsorted) (L $$unsorted)) (= (tptp.apart_point_and_line A L) (or (tptp.left_apart_point A L) (tptp.right_apart_point A L)))) (forall ((L $$unsorted) (M $$unsorted)) (= (tptp.convergent_lines L M) (and (tptp.unequally_directed_lines L M) (tptp.unequally_directed_opposite_lines L M)))) (forall ((A $$unsorted) (B $$unsorted) (L $$unsorted)) (= (tptp.divides_points L A B) (or (and (tptp.left_apart_point A L) (tptp.right_apart_point B L)) (and (tptp.right_apart_point A L) (tptp.left_apart_point B L))))) _let_6 (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)))) (forall ((L $$unsorted)) (tptp.equally_directed_lines L L)) _let_5 _let_4 _let_3 (forall ((L $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.reverse_line M))) (=> (and (tptp.unequally_directed_lines L M) (tptp.unequally_directed_lines L _let_1)) (or (tptp.left_convergent_lines L M) (tptp.left_convergent_lines L _let_1))))) (forall ((A $$unsorted) (L $$unsorted)) (not (or (tptp.left_apart_point A L) (tptp.left_apart_point A (tptp.reverse_line L))))) (forall ((L $$unsorted) (M $$unsorted)) (not (or (tptp.left_convergent_lines L M) (tptp.left_convergent_lines L (tptp.reverse_line M))))) (forall ((A $$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 $$unsorted)) (tptp.equally_directed_lines (tptp.parallel_through_point L A) L)) (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.67 )
% 0.22/0.67 % SZS output end Proof for GEO255+3
% 0.22/0.67 % cvc5---1.0.5 exiting
% 0.22/0.67 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------