%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEO205+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.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 22:50:28 EDT 2023

% Result   : Theorem 0.21s 0.62s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem    : GEO205+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n017.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Aug 29 20:04:13 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.62  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.E40VQrtxZc/cvc5---1.0.5_22669.p...
% 0.21/0.62  ------- get file name : TPTP file name is GEO205+3
% 0.21/0.62  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22669.smt2...
% 0.21/0.62  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.62  % SZS status Theorem for GEO205+3
% 0.21/0.62  % SZS output start Proof for GEO205+3
% 0.21/0.62  (
% 0.21/0.62  (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.convergent_lines X Y) (tptp.equal_lines Y Z)) (and (tptp.convergent_lines X Z) (tptp.equal_points (tptp.intersection_point X Y) (tptp.intersection_point X Z)))))))) (let ((_let_2 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.equal_lines X Y) (not (tptp.distinct_lines X Y)))))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.equal_points X Y) (not (tptp.distinct_points X Y)))))) (let ((_let_4 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_lines X Y) (tptp.convergent_lines X Y))))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z)))))) (let ((_let_6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_lines Y Z) (tptp.apart_point_and_line X Z)))))) (let ((_let_7 (forall ((X $$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 $$unsorted)) (not (tptp.convergent_lines X X))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z))))) (let ((_let_13 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14 _let_13))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 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 ((not (= (tptp.convergent_lines X X) false))))) (let ((_let_23 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_24 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (not _let_13))) (let ((_let_26 (or _let_25 _let_24 _let_23))) (let ((_let_27 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (_let_27))) (let ((_let_30 ((not (= (tptp.convergent_lines X Y) false)) (not (= (tptp.distinct_lines Y Z) true))))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_22)) :args _let_20)) _let_21 :args ((not _let_23) false _let_11)))) (let ((_let_32 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (tptp.apart_point_and_line _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_34 (tptp.apart_point_and_line _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_36 (tptp.apart_point_and_line _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (tptp.apart_point_and_line _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_38 (not _let_24))) (let ((_let_39 (tptp.distinct_points _let_35 _let_32))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38 _let_37 _let_36 _let_34 _let_33))) (let ((_let_42 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.distinct_lines U V)) (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V) (tptp.apart_point_and_line Y U) (tptp.apart_point_and_line Y V))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.apart_point_and_line _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_45 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_46 (not _let_36))) (let ((_let_47 (or _let_46 _let_45 _let_44))) (let ((_let_48 (forall ((X $$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_49 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_51 (not _let_45))) (let ((_let_52 (or _let_51 _let_50))) (let ((_let_53 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.distinct_lines X Y)) (tptp.convergent_lines X Y))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_56 (not _let_50))) (let ((_let_57 (or _let_56 _let_55 _let_23))) (let ((_let_58 (not _let_55))) (let ((_let_59 (tptp.equal_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_60 (= _let_59 _let_58))) (let ((_let_61 (_let_2))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (tptp.equal_points _let_35 _let_32))) (let ((_let_64 (and _let_15 _let_63))) (let ((_let_65 (not _let_59))) (let ((_let_66 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_65 _let_64))) (let ((_let_69 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (not (tptp.equal_lines Y Z)) (and (tptp.convergent_lines X Z) (tptp.equal_points (tptp.intersection_point X Y) (tptp.intersection_point X Z))))))) (let ((_let_70 (not _let_68))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (or))) (let ((_let_73 (not _let_69))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_71) :args (_let_73))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_69))) (REFL :args (_let_70)) :args _let_72)) _let_71 :args (_let_70 true _let_69)))) (let ((_let_75 (REFL :args (_let_68)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_50 _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_23 _let_55 _let_56 (not _let_57)))) _let_31 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_60)) :args ((or _let_65 _let_58 (not _let_60)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 1)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_59))) :args _let_72)) :args ((or _let_59 _let_68))) _let_74 :args (_let_59 true _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_lines X Y)))) :args _let_61)) _let_62 :args (_let_60 false _let_2)) :args (_let_58 false _let_59 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_30)) :args _let_29)) _let_28 :args (_let_57 false _let_27)) :args (_let_56 true _let_23 true _let_55 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X Y) true))))) :args (_let_53))) _let_54 :args (_let_52 false _let_53)) :args (_let_51 true _let_50 false _let_52)))) (let ((_let_77 (not _let_44))) (let ((_let_78 (or _let_67 _let_77))) (let ((_let_79 (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_80 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_79))) (let ((_let_82 ((not (= (tptp.convergent_lines X Y) false))))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 0)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_72)) :args ((or _let_66 _let_68))) _let_74 :args (_let_66 true _let_68)))) (let ((_let_84 (not _let_33))) (let ((_let_85 (or _let_16 _let_84))) (let ((_let_86 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_87 (or _let_67 _let_15 _let_86))) (let ((_let_88 (_let_12))) (let ((_let_89 (not (= (tptp.convergent_lines X Z) true)))) (let ((_let_90 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_91 (not _let_86))) (let ((_let_92 (or _let_91 _let_45 _let_90))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_67 _let_15 _let_86 (not _let_87)))) _let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_90 _let_91 _let_45 (not _let_92)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_22)) :args _let_20)) _let_21 :args ((not _let_90) false _let_11)) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_30)) :args _let_29)) _let_28 :args (_let_92 false _let_27)) :args (_let_91 true _let_90 true _let_45 false _let_92)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.convergent_lines X Y) false)) _let_89))) :args _let_88)) _let_18 :args (_let_87 false _let_12)) :args (_let_15 false _let_66 true _let_86 false _let_87)))) (let ((_let_94 (not _let_34))) (let ((_let_95 (or _let_16 _let_94))) (let ((_let_96 (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_97 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (_let_96))) (let ((_let_99 ((not (= (tptp.convergent_lines X Y) false))))) (let ((_let_100 (= _let_63 _let_40))) (let ((_let_101 (_let_3))) (let ((_let_102 (ASSUME :args _let_101))) (let ((_let_103 (not _let_100))) (let ((_let_104 (not _let_37))) (let ((_let_105 (or _let_67 _let_104))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING (_let_89 (not (= (tptp.convergent_lines Y Z) true))))) :args _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_16 _let_13 _let_14 _let_19))) _let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_24 _let_23 _let_25 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_37 _let_38 _let_40 _let_34 _let_33 _let_36 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_67 _let_104 (not _let_105)))) _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_99)) :args _let_98)) _let_97 :args (_let_105 false _let_96)) :args (_let_104 false _let_66 false _let_105)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_100)) (CONG (REFL :args (_let_103)) (REFL :args (_let_63)) (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_72)) :args ((or _let_63 _let_39 _let_103))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_64)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_68 2)) _let_74 :args ((not _let_64) true _let_68)) _let_93 :args ((not _let_63) true _let_64 false _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (_let_35 _let_32 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_points X Y)))) :args _let_101)) _let_102 :args (_let_100 false _let_3)) :args (_let_39 true _let_63 false _let_100)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_16 _let_94 (not _let_95)))) _let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_99)) :args _let_98)) _let_97 :args (_let_95 false _let_96)) :args (_let_94 false _let_15 false _let_95)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_16 _let_84 (not _let_85)))) _let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_82)) :args _let_81)) _let_80 :args (_let_85 false _let_79)) :args (_let_84 false _let_15 false _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_44 _let_45 _let_46 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_67 _let_77 (not _let_78)))) _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_82)) :args _let_81)) _let_80 :args (_let_78 false _let_79)) :args (_let_77 false _let_66 false _let_78)) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apart_point_and_line X Y) false)) (not (= (tptp.distinct_lines Y Z) true))))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_46 true _let_44 true _let_45 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_35 _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_points X Y) false)) (not (= (tptp.distinct_lines U V) false))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_38 true _let_37 false _let_39 true _let_34 true _let_33 true _let_36 false _let_41)) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_30)) :args _let_29)) _let_28 :args (_let_26 false _let_27)) :args (_let_25 true _let_24 true _let_23 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_22)) :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 ((forall ((X $$unsorted)) (not (tptp.distinct_points X X))) (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))) _let_11 (forall ((X $$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 $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))) _let_10 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line X (tptp.line_connecting X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line Y (tptp.line_connecting X Y))))) _let_9 _let_8 _let_7 (forall ((X $$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_6 _let_5 _let_4 (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)))) _let_3 _let_2 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.62  )
% 0.21/0.62  % SZS output end Proof for GEO205+3
% 0.21/0.62  % cvc5---1.0.5 exiting
% 0.21/0.63  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------