%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEO196+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n022.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 22:50:22 EDT 2023

% Result   : Theorem 0.34s 0.67s
% Output   : Proof 0.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : GEO196+3 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Aug 29 22:26:53 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.34/0.67  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.krwvzPM4ml/cvc5---1.0.5_15318.p...
% 0.34/0.67  ------- get file name : TPTP file name is GEO196+3
% 0.34/0.67  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15318.smt2...
% 0.34/0.67  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.34/0.67  % SZS status Theorem for GEO196+3
% 0.34/0.67  % SZS output start Proof for GEO196+3
% 0.34/0.67  (
% 0.34/0.67  (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.intersection_point U V))) (let ((_let_2 (tptp.intersection_point X Y))) (=> (and (tptp.convergent_lines X Y) (tptp.convergent_lines U V) (tptp.incident_point_and_line _let_2 U) (tptp.incident_point_and_line _let_2 V)) (and (tptp.incident_point_and_line _let_1 X) (tptp.incident_point_and_line _let_1 Y))))))))) (let ((_let_2 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.incident_point_and_line X Y) (not (tptp.apart_point_and_line X Y)))))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z)))))) (let ((_let_4 (forall ((X $$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 ((_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.convergent_lines X Y) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) Y)))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.convergent_lines X Y) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) X)))))) (let ((_let_8 (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))))) (let ((_let_9 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_10 (tptp.incident_point_and_line _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_11 (tptp.incident_point_and_line _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (and _let_11 _let_10))) (let ((_let_13 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_14 (tptp.incident_point_and_line _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.incident_point_and_line _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_17 _let_15 _let_12))) (let ((_let_23 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.intersection_point U V))) (let ((_let_2 (tptp.intersection_point X Y))) (or (not (tptp.convergent_lines X Y)) (not (tptp.convergent_lines U V)) (not (tptp.incident_point_and_line _let_2 U)) (not (tptp.incident_point_and_line _let_2 V)) (and (tptp.incident_point_and_line _let_1 X) (tptp.incident_point_and_line _let_1 Y)))))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (or))) (let ((_let_27 (not _let_23))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_25) :args (_let_27))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_23))) (REFL :args (_let_24)) :args _let_26)) _let_25 :args (_let_24 true _let_23)))) (let ((_let_29 (tptp.apart_point_and_line _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_30 (not _let_29))) (let ((_let_31 (= _let_10 _let_30))) (let ((_let_32 (_let_2))) (let ((_let_33 (ASSUME :args _let_32))) (let ((_let_34 ((tptp.incident_point_and_line X Y)))) (let ((_let_35 (tptp.apart_point_and_line _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_36 (tptp.distinct_points _let_9 _let_13))) (let ((_let_37 (or _let_30 _let_36 _let_35))) (let ((_let_38 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.apart_point_and_line X Y)) (tptp.distinct_points X Z) (tptp.apart_point_and_line Z Y))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 ((not (= (tptp.apart_point_and_line X Y) false)) (not (= (tptp.apart_point_and_line Z Y) true))))) (let ((_let_42 (tptp.apart_point_and_line _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_43 (tptp.apart_point_and_line _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_44 (tptp.apart_point_and_line _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_45 (tptp.apart_point_and_line _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_46 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_47 (not _let_46))) (let ((_let_48 (not _let_36))) (let ((_let_49 (or _let_48 _let_47 _let_45 _let_44 _let_43 _let_42))) (let ((_let_50 (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_51 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_53 (or _let_19 _let_46 _let_52))) (let ((_let_54 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (_let_8))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 (REFL :args (_let_22)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 1)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_26)) :args ((or _let_18 _let_22))) _let_28 :args (_let_18 true _let_22)))) (let ((_let_60 (not _let_43))) (let ((_let_61 (= _let_14 _let_60))) (let ((_let_62 (not _let_42))) (let ((_let_63 (= _let_16 _let_62))) (let ((_let_64 (not _let_45))) (let ((_let_65 (or _let_19 _let_64))) (let ((_let_66 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.convergent_lines X Y)) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) Y)))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (_let_66))) (let ((_let_69 ((not (= (tptp.convergent_lines X Y) false))))) (let ((_let_70 (not _let_44))) (let ((_let_71 (or _let_19 _let_70))) (let ((_let_72 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.convergent_lines X Y)) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) X)))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (_let_72))) (let ((_let_75 ((not (= (tptp.convergent_lines X Y) false))))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_44 _let_45 _let_42 _let_43 _let_47 _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_19 _let_70 (not _let_71)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74)) _let_73 :args (_let_71 false _let_72)) :args (_let_70 false _let_18 false _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_19 _let_64 (not _let_65)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_69)) :args _let_68)) _let_67 :args (_let_65 false _let_66)) :args (_let_64 false _let_18 false _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_63)) :args ((or _let_17 _let_62 (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 2)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_26)) :args ((or _let_16 _let_22))) _let_28 :args (_let_16 true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (_let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_32)) _let_33 :args (_let_63 false _let_2)) :args (_let_62 false _let_16 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_61)) :args ((or _let_15 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 3)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_26)) :args ((or _let_14 _let_22))) _let_28 :args (_let_14 true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (_let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_32)) _let_33 :args (_let_61 false _let_2)) :args (_let_60 false _let_14 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_19 _let_46 _let_52 (not _let_53)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X X) false))))) :args _let_56)) _let_57 :args ((not _let_52) false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.convergent_lines X Y) false)) (not (= (tptp.distinct_lines Y Z) true))))) :args (_let_54))) _let_55 :args (_let_53 false _let_54)) :args (_let_46 false _let_18 true _let_52 false _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (_let_9 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apart_point_and_line Y V) true)) (not (= (tptp.apart_point_and_line X U) true))))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_48 true _let_44 true _let_45 true _let_42 true _let_43 false _let_46 false _let_49)))) (let ((_let_77 (not _let_35))) (let ((_let_78 (or _let_21 _let_77))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_26)) :args ((or _let_20 _let_22))) _let_28 :args (_let_20 true _let_22)))) (let ((_let_80 (not _let_31))) (let ((_let_81 (tptp.apart_point_and_line _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_82 (not _let_81))) (let ((_let_83 (= _let_11 _let_82))) (let ((_let_84 (tptp.apart_point_and_line _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_85 (or _let_82 _let_36 _let_84))) (let ((_let_86 (not _let_84))) (let ((_let_87 (or _let_21 _let_86))) (let ((_let_88 (not _let_83))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_12)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_83)) (CONG (REFL :args (_let_88)) (REFL :args (_let_11)) (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_81))) :args _let_26)) :args ((or _let_11 _let_81 _let_88))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_84 _let_82 _let_36 (not _let_85)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_21 _let_86 (not _let_87)))) _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74)) _let_73 :args (_let_87 false _let_72)) :args (_let_86 false _let_20 false _let_87)) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13 QUANTIFIERS_INST_E_MATCHING _let_41)) :args _let_40)) _let_39 :args (_let_85 false _let_38)) :args (_let_82 true _let_84 true _let_36 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_32)) _let_33 :args (_let_83 false _let_2)) :args (_let_11 true _let_81 false _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_31)) (CONG (REFL :args (_let_80)) (REFL :args (_let_10)) (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_26)) :args ((or _let_10 _let_29 _let_80))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_35 _let_30 _let_36 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_21 _let_77 (not _let_78)))) _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_69)) :args _let_68)) _let_67 :args (_let_78 false _let_66)) :args (_let_77 false _let_20 false _let_78)) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13 QUANTIFIERS_INST_E_MATCHING _let_41)) :args _let_40)) _let_39 :args (_let_37 false _let_38)) :args (_let_30 true _let_35 true _let_36 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_32)) _let_33 :args (_let_31 false _let_2)) :args (_let_10 true _let_29 false _let_31)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 4)) _let_28 :args ((not _let_12) true _let_22)) :args (false false _let_11 false _let_10 true _let_12)) :args ((forall ((X $$unsorted)) (not (tptp.distinct_points X X))) (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))) _let_8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (or (tptp.distinct_points X Z) (tptp.distinct_points Y Z)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line X (tptp.line_connecting X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line Y (tptp.line_connecting X Y))))) _let_7 _let_6 _let_5 _let_4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_lines Y Z) (tptp.apart_point_and_line X Z)))) _let_3 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_lines X Y) (tptp.convergent_lines X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.convergent_lines (tptp.parallel_through_point Y X) Y))) (forall ((X $$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 $$unsorted)) (= (tptp.parallel_lines X Y) (not (tptp.convergent_lines X Y)))) _let_2 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.orthogonal_lines X Y) (not (tptp.unorthogonal_lines X Y)))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.34/0.67  )
% 0.34/0.67  % SZS output end Proof for GEO196+3
% 0.34/0.68  % cvc5---1.0.5 exiting
% 0.52/0.68  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------