%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEO182+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n001.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 22:50:12 EDT 2023

% Result   : Theorem 0.86s 1.05s
% Output   : Proof 0.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GEO182+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n001.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 21:50:38 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.86/1.05  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.AuQLKNencT/cvc5---1.0.5_3838.p...
% 0.86/1.05  ------- get file name : TPTP file name is GEO182+3
% 0.86/1.05  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3838.smt2...
% 0.86/1.05  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.86/1.05  % SZS status Theorem for GEO182+3
% 0.86/1.05  % SZS output start Proof for GEO182+3
% 0.86/1.05  (
% 0.86/1.05  (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (=> (tptp.apart_point_and_line Z (tptp.line_connecting X Y)) (tptp.apart_point_and_line Z (tptp.line_connecting Y X)))))))) (let ((_let_2 (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.convergent_lines (tptp.parallel_through_point Y X) Y))))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_lines X Y) (tptp.convergent_lines X Y))))) (let ((_let_4 (forall ((X $$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_5 (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_6 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line Y (tptp.line_connecting X Y))))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line X (tptp.line_connecting X Y))))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (or (tptp.distinct_points X Z) (tptp.distinct_points Y Z)))))) (let ((_let_10 (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))))) (let ((_let_11 (forall ((X $$unsorted)) (not (tptp.distinct_points X X))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_points X Y)) (tptp.distinct_points X Z) (tptp.distinct_points Y Z))))) (let ((_let_13 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14 _let_13))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (_let_11))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_22))) (let ((_let_24 (not _let_23))) (let ((_let_25 (not _let_13))) (let ((_let_26 (or _let_25 _let_24))) (let ((_let_27 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_22))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_25 _let_28))) (let ((_let_30 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_31 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_30))) (let ((_let_32 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_30))) (let ((_let_33 (tptp.distinct_lines _let_22 _let_30))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_25 _let_34 _let_23 _let_32 _let_27 _let_31))) (let ((_let_36 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.apart_point_and_line X (tptp.line_connecting X Y))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (_let_36))) (let ((_let_39 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.apart_point_and_line Y (tptp.line_connecting X Y))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (_let_39))) (let ((_let_42 ((tptp.line_connecting X Y)))) (let ((_let_43 (not _let_31))) (let ((_let_44 (or _let_16 _let_43))) (let ((_let_45 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22))) (let ((_let_46 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_30))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_16 _let_47 _let_45))) (let ((_let_49 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.apart_point_and_line Z (tptp.line_connecting X Y))) (tptp.apart_point_and_line Z (tptp.line_connecting Y X)))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (REFL :args (_let_48)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_52)) :args ((or _let_15 _let_48))) _let_54 :args (_let_15 true _let_48)))) (let ((_let_57 (not _let_32))) (let ((_let_58 (or _let_16 _let_57))) (let ((_let_59 (tptp.parallel_through_point _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_60 (tptp.distinct_lines _let_59 _let_30))) (let ((_let_61 (tptp.distinct_lines _let_59 _let_22))) (let ((_let_62 (not _let_61))) (let ((_let_63 (or _let_62 _let_60 _let_33))) (let ((_let_64 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_lines X Y)) (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (_let_64))) (let ((_let_67 (not (= (tptp.distinct_lines X Z) true)))) (let ((_let_68 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_59))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_61 _let_45))) (let ((_let_71 (forall ((X $$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_72 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (_let_71))) (let ((_let_74 ((not (= (tptp.apart_point_and_line X Y) false)) (not (= (tptp.distinct_lines Y Z) true))))) (let ((_let_75 (tptp.distinct_lines _let_30 _let_59))) (let ((_let_76 (or _let_47 _let_75 _let_68))) (let ((_let_77 (tptp.distinct_lines _let_30 _let_30))) (let ((_let_78 (not _let_75))) (let ((_let_79 (or _let_78 _let_77 _let_60))) (let ((_let_80 (tptp.convergent_lines _let_59 _let_30))) (let ((_let_81 (not _let_60))) (let ((_let_82 (or _let_81 _let_80))) (let ((_let_83 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.distinct_lines X Y)) (tptp.convergent_lines X Y))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (_let_2))) (let ((_let_86 (ASSUME :args _let_85))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_80 _let_81 (not _let_82)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_30 QUANTIFIERS_INST_ENUM)) :args _let_85)) _let_86 :args ((not _let_80) false _let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (_let_59 _let_30 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X Y) true))))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_81 true _let_80 false _let_82)))) (let ((_let_88 (_let_10))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 (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_91 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_points Y Z) true)) (not (= (tptp.distinct_points X Y) false))))) :args (_let_12))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_16 _let_13 _let_14 _let_19))) _let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_31 _let_25 _let_23 _let_32 _let_27 _let_34 (not _let_35)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_22 _let_30 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apart_point_and_line Y V) true)) (not (= (tptp.apart_point_and_line X U) true))))) :args (_let_90))) _let_91 :args (_let_35 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_60 _let_33 _let_62 (not _let_63)))) _let_87 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_45 _let_69 _let_61 (not _let_70)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 2)) _let_54 :args ((not _let_45) true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_47 _let_75 _let_68 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_52)) :args ((or _let_46 _let_48))) _let_54 :args (_let_46 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_77 _let_60 _let_78 (not _let_79)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (_let_30 QUANTIFIERS_INST_ENUM)) :args _let_88)) _let_89 :args ((not _let_77) false _let_10)) _let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_30 _let_59 _let_30 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_lines Y Z) true)) _let_67))) :args _let_66)) _let_65 :args (_let_79 false _let_64)) :args (_let_78 true _let_77 true _let_60 false _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_30 _let_59 QUANTIFIERS_INST_E_MATCHING _let_74)) :args _let_73)) _let_72 :args (_let_76 false _let_71)) :args (_let_68 false _let_46 true _let_75 false _let_76)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_59 _let_22 QUANTIFIERS_INST_E_MATCHING _let_74)) :args _let_73)) _let_72 :args (_let_70 false _let_71)) :args (_let_61 true _let_45 false _let_68 false _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_59 _let_22 _let_30 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_lines X Y) false)) _let_67))) :args _let_66)) _let_65 :args (_let_63 false _let_64)) :args (_let_33 true _let_60 false _let_61 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_16 _let_57 (not _let_58)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_42)) :args _let_41)) _let_40 :args (_let_58 false _let_39)) :args (_let_57 false _let_15 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_16 _let_43 (not _let_44)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.distinct_points X Y) false))))) :args _let_38)) _let_37 :args (_let_44 false _let_36)) :args (_let_43 false _let_15 false _let_44)) (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_25 _let_28 (not _let_29)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_42)) :args _let_41)) _let_40 :args (_let_29 false _let_39)) (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_24 (not _let_26)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.line_connecting X Y)))) :args _let_38)) _let_37 :args (_let_26 false _let_36)) :args (_let_25 false _let_35 false _let_33 true _let_32 true _let_31 true _let_27 false _let_29 true _let_23 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM)) :args _let_20)) _let_21 :args ((not _let_14) false _let_11)) :args (_let_19 false _let_15 true _let_13 true _let_14)) _let_18 :args (false true _let_17 false _let_12)) :args (_let_11 _let_10 (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))) _let_9 _let_8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z)))) _let_7 _let_6 (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_5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_points X Z) (tptp.apart_point_and_line Z Y)))) _let_4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z)))) _let_3 _let_2 (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.apart_point_and_line X (tptp.parallel_through_point Y X)))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.86/1.06  )
% 0.86/1.06  % SZS output end Proof for GEO182+3
% 0.86/1.06  % cvc5---1.0.5 exiting
% 0.86/1.06  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------