TSTP Solution File: GEO177+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEO177+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 22:50:08 EDT 2023
% Result : Theorem 0.89s 1.06s
% Output : Proof 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEO177+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 21:13:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.89/1.06 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2FuXGh3FcW/cvc5---1.0.5_16120.p...
% 0.89/1.06 ------- get file name : TPTP file name is GEO177+3
% 0.89/1.06 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16120.smt2...
% 0.89/1.06 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.89/1.06 % SZS status Theorem for GEO177+3
% 0.89/1.06 % SZS output start Proof for GEO177+3
% 0.89/1.06 (
% 0.89/1.06 (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.line_connecting X Y))) (let ((_let_2 (tptp.line_connecting U V))) (=> (and (tptp.distinct_points X Y) (tptp.distinct_points U V)) (=> (or (tptp.apart_point_and_line X _let_2) (tptp.apart_point_and_line Y _let_2)) (or (tptp.apart_point_and_line U _let_1) (tptp.apart_point_and_line V _let_1)))))))))) (let ((_let_2 (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.apart_point_and_line X (tptp.parallel_through_point Y X)))))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.convergent_lines (tptp.parallel_through_point Y X) Y))))) (let ((_let_4 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_lines X Y) (tptp.convergent_lines X Y))))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_lines Y Z) (tptp.apart_point_and_line X Z)))))) (let ((_let_6 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (=> (and (tptp.distinct_points X Y) (tptp.distinct_lines U V)) (or (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V) (tptp.apart_point_and_line Y U) (tptp.apart_point_and_line Y V)))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line Y (tptp.line_connecting X Y))))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line X (tptp.line_connecting X Y))))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (or (tptp.distinct_points X Z) (tptp.distinct_points Y Z)))))) (let ((_let_11 (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))))) (let ((_let_12 (forall ((X $$unsorted)) (not (tptp.distinct_points X X))))) (let ((_let_13 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_14 (_let_12))) (let ((_let_15 (ASSUME :args _let_14))) (let ((_let_16 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_13 _let_16))) (let ((_let_20 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_points X Y)) (tptp.distinct_points X Z) (tptp.distinct_points Y Z))))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_23 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22))) (let ((_let_24 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_25 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_24))) (let ((_let_26 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_22))) (let ((_let_27 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_24))) (let ((_let_28 (tptp.distinct_lines _let_24 _let_22))) (let ((_let_29 (not _let_28))) (let ((_let_30 (not _let_16))) (let ((_let_31 (or _let_30 _let_29 _let_27 _let_26 _let_25 _let_23))) (let ((_let_32 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.distinct_lines U V)) (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))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_22))) (let ((_let_35 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_24))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_28 _let_34))) (let ((_let_38 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.apart_point_and_line X Y)) (tptp.distinct_lines Y Z) (tptp.apart_point_and_line X Z))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 ((not (= (tptp.apart_point_and_line X Y) false)) (not (= (tptp.distinct_lines Y Z) true))))) (let ((_let_42 (not _let_34))) (let ((_let_43 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42))) (let ((_let_46 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.apart_point_and_line Y (tptp.line_connecting X Y))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (_let_46))) (let ((_let_49 ((not (= (tptp.distinct_points X Y) false))))) (let ((_let_50 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_24))) (let ((_let_51 (not _let_50))) (let ((_let_52 (and _let_51 _let_36))) (let ((_let_53 (or _let_44 _let_18 _let_52 _let_23 _let_26))) (let ((_let_54 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.line_connecting X Y))) (let ((_let_2 (tptp.line_connecting U V))) (or (not (tptp.distinct_points X Y)) (not (tptp.distinct_points U V)) (and (not (tptp.apart_point_and_line X _let_2)) (not (tptp.apart_point_and_line Y _let_2))) (tptp.apart_point_and_line U _let_1) (tptp.apart_point_and_line V _let_1))))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or))) (let ((_let_58 (not _let_54))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_56) :args (_let_58))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_54))) (REFL :args (_let_55)) :args _let_57)) _let_56 :args (_let_55 true _let_54)))) (let ((_let_60 (REFL :args (_let_53)))) (let ((_let_61 (tptp.parallel_through_point _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_62 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_61))) (let ((_let_63 (tptp.distinct_lines _let_24 _let_61))) (let ((_let_64 (or _let_51 _let_63 _let_62))) (let ((_let_65 (tptp.distinct_lines _let_61 _let_24))) (let ((_let_66 (tptp.distinct_lines _let_24 _let_24))) (let ((_let_67 (not _let_63))) (let ((_let_68 (or _let_67 _let_66 _let_65))) (let ((_let_69 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_lines X Y)) (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (tptp.convergent_lines _let_61 _let_24))) (let ((_let_72 (not _let_65))) (let ((_let_73 (or _let_72 _let_71))) (let ((_let_74 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.distinct_lines X Y)) (tptp.convergent_lines X Y))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (_let_3))) (let ((_let_77 (ASSUME :args _let_76))) (let ((_let_78 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_24 QUANTIFIERS_INST_ENUM))) (let ((_let_79 (_let_11))) (let ((_let_80 (ASSUME :args _let_79))) (let ((_let_81 (_let_2))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (_let_52))) (let ((_let_84 (not _let_27))) (let ((_let_85 (or _let_18 _let_84))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_57)) :args ((or _let_17 _let_53))) _let_59 :args (_let_17 true _let_53)))) (let ((_let_87 (not _let_25))) (let ((_let_88 (or _let_18 _let_87))) (let ((_let_89 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.apart_point_and_line X (tptp.line_connecting X Y))))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_15 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.distinct_points X X) false))))) :args _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_13 _let_16 (not _let_19)))) _let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_23 _let_26 _let_25 _let_27 _let_29 _let_30 (not _let_31)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_53 3)) _let_59 :args ((not _let_23) true _let_53)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_53 4)) _let_59 :args ((not _let_26) true _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_18 _let_87 (not _let_88)))) _let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.distinct_points X Y) false))))) :args (_let_89))) _let_90 :args (_let_88 false _let_89)) :args (_let_87 false _let_17 false _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_18 _let_84 (not _let_85)))) _let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_85 false _let_46)) :args (_let_84 false _let_17 false _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_34 _let_28 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_83) (CONG (REFL :args _let_83) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_57)) :args ((or _let_50 _let_35 _let_52))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_51 _let_62 _let_63 (not _let_64)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args _let_78) :args _let_81)) _let_82 :args ((not _let_62) false _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_66 _let_65 _let_67 (not _let_68)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (_let_24 QUANTIFIERS_INST_ENUM)) :args _let_79)) _let_80 :args ((not _let_66) false _let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_71 _let_72 (not _let_73)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args _let_78) :args _let_76)) _let_77 :args ((not _let_71) false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (_let_61 _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X Y) true))))) :args (_let_74))) _let_75 :args (_let_73 false _let_74)) :args (_let_72 true _let_71 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_24 _let_61 _let_24 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_lines Y Z) true)) (not (= (tptp.distinct_lines X Z) true))))) :args (_let_69))) _let_70 :args (_let_68 false _let_69)) :args (_let_67 true _let_66 true _let_65 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_24 _let_61 QUANTIFIERS_INST_E_MATCHING _let_41)) :args _let_40)) _let_39 :args (_let_64 false _let_38)) :args (_let_51 true _let_62 true _let_63 false _let_64)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_53 2)) _let_59 :args ((not _let_52) true _let_53)) :args (_let_35 true _let_50 true _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_42 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 0)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_57)) :args ((or _let_43 _let_53))) _let_59 :args (_let_43 true _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_45 false _let_46)) :args (_let_42 false _let_43 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_24 _let_22 QUANTIFIERS_INST_E_MATCHING _let_41)) :args _let_40)) _let_39 :args (_let_37 false _let_38)) :args (_let_28 false _let_35 true _let_34 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_24 _let_22 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apart_point_and_line Y V) true)) (not (= (tptp.apart_point_and_line X U) true))))) :args (_let_32))) _let_33 :args (_let_31 false _let_32)) :args (_let_30 true _let_23 true _let_26 true _let_25 true _let_27 false _let_28 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_points X Y) false)) (not (= (tptp.distinct_points X Z) true))))) :args (_let_20))) _let_21 :args (_let_19 false _let_20)) :args (_let_13 false _let_17 true _let_16 false _let_19)) _let_15 :args (false false _let_13 false _let_12)) :args (_let_12 _let_11 (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))) _let_10 _let_9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z)))) _let_8 _let_7 (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)))) _let_6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_points X Z) (tptp.apart_point_and_line Z Y)))) _let_5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z)))) _let_4 _let_3 _let_2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_lines Y Z) (or (tptp.apart_point_and_line X Y) (tptp.apart_point_and_line X Z) (tptp.convergent_lines Y Z)))) (forall ((L $$unsorted) (M $$unsorted)) (or (tptp.convergent_lines L M) (tptp.unorthogonal_lines L M))) (forall ((L $$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))))) (forall ((A $$unsorted) (L $$unsorted)) (not (tptp.unorthogonal_lines (tptp.orthogonal_through_point L A) L))) (forall ((A $$unsorted) (L $$unsorted)) (not (tptp.apart_point_and_line A (tptp.orthogonal_through_point L A)))) (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)))) (forall ((L $$unsorted) (M $$unsorted)) (not (and (not (tptp.convergent_lines L M)) (not (tptp.unorthogonal_lines L M))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (and (or (not (tptp.convergent_lines L M)) (not (tptp.unorthogonal_lines L M))) (or (not (tptp.convergent_lines L N)) (not (tptp.unorthogonal_lines L N)))) (or (not (tptp.convergent_lines M N)) (not (tptp.unorthogonal_lines M N))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (and (not (tptp.unorthogonal_lines L M)) (not (tptp.unorthogonal_lines L N))) (not (tptp.convergent_lines M N)))) (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.convergent_lines L M)) (tptp.point (tptp.intersection_point L M)))) (forall ((L $$unsorted) (A $$unsorted)) (=> (and (tptp.line L) (tptp.point A)) (tptp.line (tptp.parallel_through_point L A)))) (forall ((L $$unsorted) (A $$unsorted)) (=> (and (tptp.line L) (tptp.point A)) (tptp.line (tptp.orthogonal_through_point L A)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.equal_points X Y) (not (tptp.distinct_points X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.equal_lines X Y) (not (tptp.distinct_lines X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.parallel_lines X Y) (not (tptp.convergent_lines X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.incident_point_and_line X Y) (not (tptp.apart_point_and_line X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.orthogonal_lines X Y) (not (tptp.unorthogonal_lines X Y)))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.89/1.07 )
% 0.89/1.07 % SZS output end Proof for GEO177+3
% 0.89/1.07 % cvc5---1.0.5 exiting
% 0.89/1.07 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------