%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEO199+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n010.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 22:50:24 EDT 2023

% Result   : Theorem 0.20s 0.60s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GEO199+3 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.13  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 29 23:51:03 EDT 2023
% 0.14/0.34  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.60  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qpU43uEOWV/cvc5---1.0.5_12292.p...
% 0.20/0.60  ------- get file name : TPTP file name is GEO199+3
% 0.20/0.60  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12292.smt2...
% 0.20/0.60  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.60  % SZS status Theorem for GEO199+3
% 0.20/0.60  % SZS output start Proof for GEO199+3
% 0.20/0.60  (
% 0.20/0.60  (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.convergent_lines X Y) (tptp.convergent_lines Z Y) (tptp.convergent_lines X Z) (tptp.incident_point_and_line (tptp.intersection_point X Y) Z)) (tptp.incident_point_and_line (tptp.intersection_point Y X) Z)))))) (let ((_let_2 (forall ((X $$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 $$unsorted)) (=> (tptp.distinct_lines X Y) (tptp.convergent_lines X Y))))) (let ((_let_4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z)))))) (let ((_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 $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_points X Z) (tptp.apart_point_and_line Z Y)))))) (let ((_let_7 (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_8 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.convergent_lines X Y) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) Y)))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.convergent_lines X Y) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) X)))))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z)))))) (let ((_let_11 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (or (tptp.distinct_points X Z) (tptp.distinct_points Y Z)))))) (let ((_let_13 (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))))) (let ((_let_14 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_points X Y)) (tptp.distinct_points X Z) (tptp.distinct_points Y Z))))) (let ((_let_15 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (tptp.distinct_points _let_16 _let_15))) (let ((_let_18 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_19 (tptp.distinct_points _let_18 _let_15))) (let ((_let_20 (tptp.distinct_points _let_18 _let_16))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_17))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (tptp.apart_point_and_line _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_26 (tptp.apart_point_and_line _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_20 _let_25))) (let ((_let_29 (forall ((X $$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_30 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (tptp.incident_point_and_line _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_32 (= _let_31 _let_27))) (let ((_let_33 (_let_2))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 ((tptp.incident_point_and_line X Y)))) (let ((_let_36 (tptp.incident_point_and_line _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 (not (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_39 _let_37 _let_31))) (let ((_let_43 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (not (tptp.convergent_lines Z Y)) (not (tptp.convergent_lines X Z)) (not (tptp.incident_point_and_line (tptp.intersection_point X Y) Z)) (tptp.incident_point_and_line (tptp.intersection_point Y X) Z))))) (let ((_let_44 (not _let_42))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (or))) (let ((_let_47 (not _let_43))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_45) :args (_let_47))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_43))) (REFL :args (_let_44)) :args _let_46)) _let_45 :args (_let_44 true _let_43)))) (let ((_let_49 (not _let_32))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_32)) (CONG (REFL :args (_let_49)) (REFL :args (_let_31)) (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_46)) :args ((or _let_31 _let_26 _let_49))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 4)) _let_48 :args ((not _let_31) true _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33)) _let_34 :args (_let_32 false _let_2)) :args (_let_26 true _let_31 false _let_32)))) (let ((_let_51 (not _let_25))) (let ((_let_52 (or _let_39 _let_51))) (let ((_let_53 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.convergent_lines X Y)) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) Y)))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 ((not (= (tptp.convergent_lines X Y) false))))) (let ((_let_57 (REFL :args (_let_42)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 2)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_46)) :args ((or _let_38 _let_42))) _let_48 :args (_let_38 true _let_42)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_39 _let_51 (not _let_52)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_52 false _let_53)) :args (_let_51 false _let_38 false _let_52)))) (let ((_let_60 (tptp.apart_point_and_line _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_61 (tptp.apart_point_and_line _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_62 (tptp.apart_point_and_line _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_63 (tptp.apart_point_and_line _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_64 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_65 (not _let_64))) (let ((_let_66 (not _let_19))) (let ((_let_67 (or _let_66 _let_65 _let_63 _let_62 _let_61 _let_60))) (let ((_let_68 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.distinct_lines U V)) (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V) (tptp.apart_point_and_line Y U) (tptp.apart_point_and_line Y V))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (_let_68))) (let ((_let_71 ((not (= (tptp.apart_point_and_line X V) true)) (not (= (tptp.apart_point_and_line Y V) true)) (not (= (tptp.distinct_lines U V) false))))) (let ((_let_72 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_73 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_74 _let_72 _let_64))) (let ((_let_76 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_lines X Y)) (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_79 (not _let_72))) (let ((_let_80 (or _let_79 _let_78))) (let ((_let_81 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.distinct_lines X Y)) (tptp.convergent_lines X Y))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (_let_13))) (let ((_let_84 (ASSUME :args _let_83))) (let ((_let_85 ((not (= (tptp.convergent_lines X X) false))))) (let ((_let_86 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_87 (or _let_41 _let_73 _let_86))) (let ((_let_88 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_83)) _let_84 :args ((not _let_86) false _let_13)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_46)) :args ((or _let_40 _let_42))) _let_48 :args (_let_40 true _let_42)))) (let ((_let_92 (not _let_63))) (let ((_let_93 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_94 (not _let_93))) (let ((_let_95 (or _let_94 _let_92))) (let ((_let_96 (or _let_41 _let_86 _let_93))) (let ((_let_97 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_41 _let_93 _let_86 (not _let_96)))) _let_91 _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.convergent_lines X Y) false)) (not (= (tptp.convergent_lines X Z) true))))) :args (_let_97))) _let_98 :args (_let_96 false _let_97)) :args (_let_93 false _let_40 true _let_86 false _let_96)))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_94 _let_92 (not _let_95)))) _let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.intersection_point X Y)))) :args _let_55)) _let_54 :args (_let_95 false _let_53)) :args (_let_92 false _let_93 false _let_95)))) (let ((_let_101 (not _let_60))) (let ((_let_102 (or _let_41 _let_101))) (let ((_let_103 (not _let_62))) (let ((_let_104 (or _let_94 _let_103))) (let ((_let_105 (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_106 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (_let_105))) (let ((_let_108 (not _let_61))) (let ((_let_109 (or _let_41 _let_108))) (let ((_let_110 ((not (= (tptp.convergent_lines X Y) false))))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_109)) :args ((or _let_41 _let_108 (not _let_109)))) _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_110)) :args _let_107)) _let_106 :args (_let_109 false _let_105)) :args (_let_108 false _let_40 false _let_109)))) (let ((_let_112 (tptp.apart_point_and_line _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_113 (tptp.apart_point_and_line _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_114 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_115 (not _let_114))) (let ((_let_116 (not _let_17))) (let ((_let_117 (or _let_116 _let_115 _let_25 _let_113 _let_112 _let_61))) (let ((_let_118 (or _let_27 _let_114 _let_63))) (let ((_let_119 (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_120 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (not _let_112))) (let ((_let_122 (= _let_36 _let_121))) (let ((_let_123 (not _let_113))) (let ((_let_124 (or _let_39 _let_123))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_18 _let_16 _let_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_points Y Z) true)) (not (= (tptp.distinct_points X Y) false))))) :args (_let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_17 _let_19 _let_21 _let_24))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_61 _let_113 _let_25 _let_112 _let_115 _let_116 (not _let_117)))) _let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_124)) :args ((or _let_39 _let_123 (not _let_124)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_110)) :args _let_107)) _let_106 :args (_let_124 false _let_105)) :args (_let_123 false _let_38 false _let_124)) _let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_122)) :args ((or _let_37 _let_121 (not _let_122)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 3)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_46)) :args ((or _let_36 _let_42))) _let_48 :args (_let_36 true _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33)) _let_34 :args (_let_122 false _let_2)) :args (_let_121 false _let_36 false _let_122)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_63 _let_27 _let_114 (not _let_118)))) _let_100 _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (_let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apart_point_and_line X Y) false)) (not (= (tptp.distinct_lines Y Z) true))))) :args (_let_119))) _let_120 :args (_let_118 false _let_119)) :args (_let_114 true _let_63 false _let_26 false _let_118)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (_let_16 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_71)) :args _let_70)) _let_69 :args (_let_117 false _let_68)) :args (_let_116 true _let_61 true _let_113 true _let_25 true _let_112 false _let_114 false _let_117)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_61 _let_62 _let_60 _let_63 _let_65 _let_66 (not _let_67)))) _let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_94 _let_103 (not _let_104)))) _let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.intersection_point X Y)))) :args _let_107)) _let_106 :args (_let_104 false _let_105)) :args (_let_103 false _let_93 false _let_104)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_41 _let_101 (not _let_102)))) _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_102 false _let_53)) :args (_let_101 false _let_40 false _let_102)) _let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_74 _let_72 _let_64 (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_41 _let_73 _let_86 (not _let_87)))) _let_91 _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.convergent_lines X Y) false)) (not (= (tptp.distinct_lines Y Z) true))))) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_73 false _let_40 true _let_86 false _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_78 _let_79 (not _let_80)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_83)) _let_84 :args ((not _let_78) false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X Y) true))))) :args (_let_81))) _let_82 :args (_let_80 false _let_81)) :args (_let_79 true _let_78 false _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_lines Y Z) true)) (not (= (tptp.distinct_lines X Z) true))))) :args (_let_76))) _let_77 :args (_let_75 false _let_76)) :args (_let_64 false _let_73 true _let_72 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (_let_18 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_71)) :args _let_70)) _let_69 :args (_let_67 false _let_68)) :args (_let_66 true _let_61 true _let_62 true _let_60 true _let_63 false _let_64 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_25 _let_27 _let_20 (not _let_28)))) _let_59 _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apart_point_and_line X Y) false)) (not (= (tptp.apart_point_and_line Z Y) true))))) :args (_let_29))) _let_30 :args (_let_28 false _let_29)) :args (_let_20 true _let_25 false _let_26 false _let_28)) :args (_let_24 true _let_17 true _let_19 false _let_20)) _let_23 :args (false true _let_22 false _let_14)) :args ((forall ((X $$unsorted)) (not (tptp.distinct_points X X))) (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))) _let_13 _let_12 _let_11 _let_10 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line X (tptp.line_connecting X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line Y (tptp.line_connecting X Y))))) _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 (forall ((X $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.61  )
% 0.20/0.61  % SZS output end Proof for GEO199+3
% 0.20/0.61  % cvc5---1.0.5 exiting
% 0.20/0.61  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------