%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEO181+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n004.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 22:50:11 EDT 2023

% Result   : Theorem 0.22s 0.67s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem    : GEO181+2 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n004.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 22:35:37 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.67  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.PyRTno9R16/cvc5---1.0.5_5483.p...
% 0.22/0.67  ------- get file name : TPTP file name is GEO181+2
% 0.22/0.67  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_5483.smt2...
% 0.22/0.67  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.67  % SZS status Theorem for GEO181+2
% 0.22/0.67  % SZS output start Proof for GEO181+2
% 0.22/0.67  (
% 0.22/0.67  (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (=> (tptp.apart_point_and_line Z (tptp.line_connecting X Y)) (tptp.apart_point_and_line Y (tptp.line_connecting X Z)))))))) (let ((_let_2 (forall ((X $$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_3 (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_4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (=> (tptp.apart_point_and_line Z (tptp.line_connecting X Y)) (and (tptp.distinct_points Z X) (tptp.distinct_points Z Y))))))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (or (tptp.distinct_points X Z) (tptp.distinct_points Y Z)))))) (let ((_let_6 (forall ((X $$unsorted)) (not (tptp.distinct_points X X))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.distinct_lines U V)) (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V) (tptp.apart_point_and_line Y U) (tptp.apart_point_and_line Y V))))) (let ((_let_8 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_8))) (let ((_let_10 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_10))) (let ((_let_12 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8))) (let ((_let_13 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10))) (let ((_let_14 (tptp.distinct_lines _let_10 _let_8))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15 _let_13 _let_12 _let_11 _let_9))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8))) (let ((_let_22 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_10))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_14 _let_21))) (let ((_let_25 (forall ((X $$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_26 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (_let_25))) (let ((_let_28 ((not (= (tptp.apart_point_and_line X Z) true)) (not (= (tptp.apart_point_and_line X Y) false))))) (let ((_let_29 (tptp.line_connecting SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_30 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_29))) (let ((_let_31 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_29))) (let ((_let_32 (tptp.distinct_lines _let_29 _let_10))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_31 _let_13 _let_30 _let_22))) (let ((_let_37 (_let_7))) (let ((_let_38 (not (= (tptp.apart_point_and_line Y U) true)))) (let ((_let_39 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_29))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_32 _let_11))) (let ((_let_42 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_43 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_44 (and _let_43 _let_42))) (let ((_let_45 (not _let_11))) (let ((_let_46 (not _let_42))) (let ((_let_47 (or _let_46 _let_45 _let_44))) (let ((_let_48 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.apart_point_and_line Z (tptp.line_connecting X Y))) (and (tptp.distinct_points Z X) (tptp.distinct_points Z Y)))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_48))) (let ((_let_51 ((not (= (tptp.distinct_points X Y) false)) (tptp.distinct_points Z Y)))) (let ((_let_52 (not _let_44))) (let ((_let_53 (_let_6))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 ((not (= (tptp.distinct_points X X) false))))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_53)) _let_54 :args ((not _let_43) false _let_6)))) (let ((_let_57 (and _let_42 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_58 (or _let_35 _let_40 _let_57))) (let ((_let_59 (tptp.line_connecting X Y))) (let ((_let_60 ((not (= (tptp.apart_point_and_line Z _let_59) false))))) (let ((_let_61 (or _let_35 _let_40 _let_21))) (let ((_let_62 (forall ((X $$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 Y (tptp.line_connecting X Z)))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (or))) (let ((_let_66 (not _let_62))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_64) :args (_let_66))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_62))) (REFL :args (_let_63)) :args _let_65)) _let_64 :args (_let_63 true _let_62)))) (let ((_let_68 (REFL :args (_let_61)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 1)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_65)) :args ((or _let_39 _let_61))) _let_67 :args (_let_39 true _let_61)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_65)) :args ((or _let_34 _let_61))) _let_67 :args (_let_34 true _let_61)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_57 0)) :args ((or _let_42 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_35 _let_40 _let_57 (not _let_58)))) _let_70 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_60)) :args _let_50)) _let_49 :args (_let_58 false _let_48)) :args (_let_57 false _let_34 false _let_39 false _let_58)) :args (_let_42 false _let_57)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_45 _let_44 (not _let_47)))) _let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 0)) :args ((or _let_43 _let_52))) _let_56 :args (_let_52 true _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_51)) :args _let_50)) _let_49 :args (_let_47 false _let_48)) :args (_let_45 false _let_42 true _let_44 false _let_47)))) (let ((_let_73 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_74 (and (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_73))) (let ((_let_75 (not _let_30))) (let ((_let_76 (or _let_35 _let_75 _let_74))) (let ((_let_77 (not _let_74))) (let ((_let_78 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_79 (and _let_16 _let_78))) (let ((_let_80 (not _let_13))) (let ((_let_81 (or _let_46 _let_80 _let_79))) (let ((_let_82 (not _let_79))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM)) :args _let_53)) _let_54 :args ((not _let_78) false _let_6)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_46 _let_80 _let_79 (not _let_81)))) _let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 1)) :args ((or _let_78 _let_82))) _let_83 :args (_let_82 true _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_51)) :args _let_50)) _let_49 :args (_let_81 false _let_48)) :args (_let_80 false _let_42 true _let_79 false _let_81)))) (let ((_let_85 (and _let_78 _let_34))) (let ((_let_86 (not _let_31))) (let ((_let_87 (or _let_35 _let_86 _let_85))) (let ((_let_88 (not _let_85))) (let ((_let_89 (and _let_42 _let_43))) (let ((_let_90 (not _let_9))) (let ((_let_91 (or _let_17 _let_90 _let_89))) (let ((_let_92 (not _let_89))) (let ((_let_93 (or _let_46 _let_43 _let_16))) (let ((_let_94 (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_95 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_46 _let_43 _let_16 (not _let_93)))) _let_71 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 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_94))) _let_95 :args (_let_93 false _let_94)) :args (_let_16 false _let_42 true _let_43 false _let_93)))) (let ((_let_97 (and _let_78 _let_16))) (let ((_let_98 (not _let_12))) (let ((_let_99 (or _let_17 _let_98 _let_97))) (let ((_let_100 (not _let_97))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_10 _let_8 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apart_point_and_line X V) true)) _let_38))) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_11 _let_17 _let_13 _let_12 _let_9 _let_15 _let_20))) _let_72 _let_96 _let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_17 _let_98 _let_97 (not _let_99)))) _let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 0)) :args ((or _let_78 _let_100))) _let_83 :args (_let_100 true _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_51)) :args _let_50)) _let_49 :args (_let_99 false _let_48)) :args (_let_98 false _let_16 true _let_97 false _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_17 _let_90 _let_89 (not _let_91)))) _let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_89 1)) :args ((or _let_43 _let_92))) _let_56 :args (_let_92 true _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING (_let_59 (tptp.distinct_points Z X)))) :args _let_50)) _let_49 :args (_let_91 false _let_48)) :args (_let_90 false _let_16 true _let_89 false _let_91)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_21 _let_23 _let_14 (not _let_24)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_61 2)) _let_67 :args ((not _let_21) true _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_31 _let_13 _let_30 _let_22 _let_33 (not _let_36)))) _let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_35 _let_86 _let_85 (not _let_87)))) _let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_85 0)) :args ((or _let_78 _let_88))) _let_83 :args (_let_88 true _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_60)) :args _let_50)) _let_49 :args (_let_87 false _let_48)) :args (_let_86 false _let_34 true _let_85 false _let_87)) _let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_35 _let_75 _let_74 (not _let_76)))) _let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_74 1)) :args ((or _let_73 _let_77))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_53)) _let_54 :args ((not _let_73) false _let_6)) :args (_let_77 true _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_51)) :args _let_50)) _let_49 :args (_let_76 false _let_48)) :args (_let_75 false _let_34 true _let_74 false _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_11 _let_32 (not _let_41)))) _let_69 _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_29 _let_10 QUANTIFIERS_INST_E_MATCHING _let_28)) :args _let_27)) _let_26 :args (_let_41 false _let_25)) :args (_let_32 false _let_39 true _let_11 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_29 _let_10 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_lines U V) false)) (not (= (tptp.apart_point_and_line X U) true)) _let_38))) :args _let_37)) _let_19 :args (_let_36 false _let_7)) :args (_let_22 false _let_34 true _let_31 true _let_13 true _let_30 false _let_32 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_10 _let_8 QUANTIFIERS_INST_E_MATCHING _let_28)) :args _let_27)) _let_26 :args (_let_24 false _let_25)) :args (_let_14 true _let_21 false _let_22 false _let_24)) :args (_let_20 true _let_11 false _let_16 true _let_13 true _let_12 true _let_9 false _let_14)) _let_19 :args (false true _let_18 false _let_7)) :args (_let_6 (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))) (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))) _let_5 (forall ((X $$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 $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z)))) _let_4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (=> (or (tptp.apart_point_and_line Z X) (tptp.apart_point_and_line Z Y)) (tptp.distinct_points Z (tptp.intersection_point X Y))))) _let_3 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_points X Z) (tptp.apart_point_and_line Z Y)))) _let_2 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.convergent_lines X Y) (tptp.distinct_lines X Y))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.67  )
% 0.22/0.67  % SZS output end Proof for GEO181+2
% 0.22/0.67  % cvc5---1.0.5 exiting
% 0.22/0.68  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------