%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEO049-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n020.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 22:49:25 EDT 2023

% Result   : Unsatisfiable 8.56s 8.90s
% Output   : Proof 8.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14  % Problem    : GEO049-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.36  % Computer : n020.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Tue Aug 29 22:26:43 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.23/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.52  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.N4ZqywlgNV/cvc5---1.0.5_9297.p...
% 0.23/0.54  ------- get file name : TPTP file name is GEO049-3
% 0.23/0.54  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9297.smt2...
% 0.23/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 8.56/8.90  % SZS status Unsatisfiable for GEO049-3
% 8.56/8.90  % SZS output start Proof for GEO049-3
% 8.56/8.91  (
% 8.56/8.91  (let ((_let_1 (tptp.between tptp.u1 tptp.v1 tptp.w1))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.between tptp.u tptp.v tptp.w))) (let ((_let_4 (tptp.equidistant tptp.u tptp.w tptp.u1 tptp.w1))) (let ((_let_5 (tptp.equidistant tptp.v tptp.w tptp.v1 tptp.w1))) (let ((_let_6 (tptp.equidistant tptp.u tptp.v tptp.u1 tptp.v1))) (let ((_let_7 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (U1 $$unsorted) (W1 $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.equidistant U W U1 W1)) (tptp.between U1 (tptp.insertion U1 W1 U V) W1))))) (let ((_let_8 (forall ((U $$unsorted) (V $$unsorted) (U1 $$unsorted) (W1 $$unsorted)) (tptp.equidistant U V U1 (tptp.insertion U1 W1 U V))))) (let ((_let_9 (forall ((U $$unsorted) (V $$unsorted) (U1 $$unsorted) (V1 $$unsorted) (W $$unsorted) (W1 $$unsorted) (X $$unsorted) (X1 $$unsorted)) (or (not (tptp.equidistant U V U1 V1)) (not (tptp.equidistant U W U1 W1)) (not (tptp.equidistant U X U1 X1)) (not (tptp.equidistant W X W1 X1)) (not (tptp.between U V W)) (not (tptp.between U1 V1 W1)) (tptp.equidistant V X V1 X1))))) (let ((_let_10 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between U W X)) (tptp.between U V X))))) (let ((_let_11 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.between U V W)) (tptp.between W V U))))) (let ((_let_12 (forall ((U $$unsorted) (V $$unsorted)) (tptp.between U V V)))) (let ((_let_13 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.equidistant U V W X)) (tptp.equidistant X W U V))))) (let ((_let_14 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.equidistant U V W X)) (tptp.equidistant V U X W))))) (let ((_let_15 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.equidistant X Y Z Z)) (= X Y))))) (let ((_let_16 (tptp.between tptp.w1 tptp.v1 tptp.v1))) (let ((_let_17 (tptp.insertion tptp.u1 tptp.w1 tptp.u tptp.v))) (let ((_let_18 (= tptp.v1 _let_17))) (let ((_let_19 (tptp.between tptp.w1 tptp.v1 _let_17))) (let ((_let_20 (_let_12))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (tptp.equidistant tptp.v1 _let_17 tptp.v tptp.v))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_18))) (let ((_let_25 (_let_15))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (tptp.equidistant tptp.v tptp.v _let_17 tptp.v1))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_22))) (let ((_let_30 (_let_13))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (tptp.between tptp.u1 _let_17 tptp.w1))) (let ((_let_33 (not _let_32))) (let ((_let_34 (not _let_3))) (let ((_let_35 (tptp.equidistant tptp.w tptp.v tptp.w1 tptp.v1))) (let ((_let_36 (not _let_35))) (let ((_let_37 (not _let_6))) (let ((_let_38 (not _let_4))) (let ((_let_39 (tptp.equidistant tptp.u tptp.v tptp.u1 _let_17))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38 _let_37 _let_36 _let_34 _let_33 _let_27))) (let ((_let_42 (_let_9))) (let ((_let_43 (ASSUME :args _let_42))) (let ((_let_44 (_let_8))) (let ((_let_45 (ASSUME :args _let_44))) (let ((_let_46 (or _let_34 _let_38 _let_32))) (let ((_let_47 (_let_7))) (let ((_let_48 (ASSUME :args _let_47))) (let ((_let_49 (ASSUME :args (_let_3)))) (let ((_let_50 (ASSUME :args (_let_4)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_38 _let_34 _let_32 (not _let_46)))) _let_50 _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.u tptp.v tptp.w tptp.u1 tptp.w1 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.between U V W) false)) (not (= (tptp.equidistant U W U1 W1) false))))) :args _let_47)) _let_48 :args (_let_46 false _let_7)) :args (_let_32 false _let_4 false _let_3 false _let_46)))) (let ((_let_52 (not _let_5))) (let ((_let_53 (or _let_52 _let_35))) (let ((_let_54 (_let_14))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 (tptp.between tptp.w1 tptp.v1 tptp.u1))) (let ((_let_57 (tptp.between tptp.w1 _let_17 tptp.u1))) (let ((_let_58 (not _let_57))) (let ((_let_59 (not _let_19))) (let ((_let_60 (or _let_59 _let_58 _let_56))) (let ((_let_61 (_let_10))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (or _let_33 _let_57))) (let ((_let_64 (_let_11))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (not _let_56))) (let ((_let_67 (or _let_66 _let_1))) (let ((_let_68 (and _let_16 _let_18))) (let ((_let_69 (_let_16 _let_18))) (let ((_let_70 (ASSUME :args (_let_16)))) (let ((_let_71 (ASSUME :args (_let_18)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_68)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_70 _let_71) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (tptp.w1)) (REFL :args (tptp.v1)) (SYMM _let_71) :args (APPLY_UF tptp.between)) (TRUE_INTRO _let_70))) :args _let_69)) :args _let_69)) :args (true _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_56 _let_58 _let_59 (not _let_60)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_1 _let_66 (not _let_67)))) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.w1 tptp.v1 tptp.u1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.between W V U) true))))) :args _let_64)) _let_65 :args (_let_67 false _let_11)) :args (_let_66 true _let_1 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_33 _let_57 (not _let_63)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.u1 _let_17 tptp.w1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.between U V W) false))))) :args _let_64)) _let_65 :args (_let_63 false _let_11)) :args (_let_57 false _let_32 false _let_63)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.w1 tptp.v1 _let_17 tptp.u1 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.between U V X) true)) (not (= (tptp.between U W X) false))))) :args _let_61)) _let_62 :args (_let_60 false _let_10)) :args (_let_59 true _let_56 false _let_57 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_18 _let_23 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_22 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_37 _let_38 _let_34 _let_36 _let_33 _let_40 _let_27 (not _let_41)))) (ASSUME :args (_let_6)) _let_50 _let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_52 _let_35 (not _let_53)))) (ASSUME :args (_let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (tptp.v tptp.w tptp.v1 tptp.w1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.equidistant U V W X) false))))) :args _let_54)) _let_55 :args (_let_53 false _let_14)) :args (_let_35 false _let_5 false _let_53)) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (tptp.u tptp.v tptp.u1 tptp.w1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.insertion U1 W1 U V)))) :args _let_44)) _let_45 :args (_let_39 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.u tptp.v tptp.u1 _let_17 tptp.w tptp.w1 tptp.v tptp.v1 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.equidistant U V U1 V1) false)) (not (= (tptp.equidistant U W U1 W1) false)) (not (= (tptp.equidistant U X U1 X1) false))))) :args _let_42)) _let_43 :args (_let_41 false _let_9)) :args (_let_27 false _let_6 false _let_4 false _let_3 false _let_35 false _let_32 false _let_39 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (tptp.v tptp.v _let_17 tptp.v1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.equidistant U V W X) false))))) :args _let_30)) _let_31 :args (_let_29 false _let_13)) :args (_let_22 false _let_27 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (tptp.v1 _let_17 tptp.v QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.equidistant X Y Z Z) false))))) :args _let_25)) _let_26 :args (_let_24 false _let_15)) :args (_let_18 false _let_22 false _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (tptp.w1 tptp.v1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.between U V V) true))))) :args _let_20)) _let_21 :args (_let_16 false _let_12)) :args (false true _let_19 false _let_18 false _let_16)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (tptp.equidistant X Y Y X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (V $$unsorted) (V2 $$unsorted) (W $$unsorted)) (or (not (tptp.equidistant X Y Z V)) (not (tptp.equidistant X Y V2 W)) (tptp.equidistant Z V V2 W))) _let_15 (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (V $$unsorted)) (tptp.between X Y (tptp.extension X Y W V))) (forall ((Y $$unsorted) (X $$unsorted) (W $$unsorted) (V $$unsorted)) (tptp.equidistant Y (tptp.extension X Y W V) W V)) (forall ((X $$unsorted) (Y $$unsorted) (X1 $$unsorted) (Y1 $$unsorted) (Z $$unsorted) (Z1 $$unsorted) (V $$unsorted) (V1 $$unsorted)) (or (not (tptp.equidistant X Y X1 Y1)) (not (tptp.equidistant Y Z Y1 Z1)) (not (tptp.equidistant X V X1 V1)) (not (tptp.equidistant Y V Y1 V1)) (not (tptp.between X Y Z)) (not (tptp.between X1 Y1 Z1)) (= X Y) (tptp.equidistant Z V Z1 V1))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.between X Y X)) (= X Y))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (Y $$unsorted) (X $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between Y X W)) (tptp.between V (tptp.inner_pasch U V W X Y) Y))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (Y $$unsorted) (X $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between Y X W)) (tptp.between X (tptp.inner_pasch U V W X Y) U))) (not (tptp.between tptp.lower_dimension_point_1 tptp.lower_dimension_point_2 tptp.lower_dimension_point_3)) (not (tptp.between tptp.lower_dimension_point_2 tptp.lower_dimension_point_3 tptp.lower_dimension_point_1)) (not (tptp.between tptp.lower_dimension_point_3 tptp.lower_dimension_point_1 tptp.lower_dimension_point_2)) (forall ((X $$unsorted) (W $$unsorted) (V $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.equidistant X W X V)) (not (tptp.equidistant Y W Y V)) (not (tptp.equidistant Z W Z V)) (tptp.between X Y Z) (tptp.between Y Z X) (tptp.between Z X Y) (= W V))) (forall ((U $$unsorted) (W $$unsorted) (Y $$unsorted) (V $$unsorted) (X $$unsorted)) (or (not (tptp.between U W Y)) (not (tptp.between V W X)) (= U W) (tptp.between U V (tptp.euclid1 U V W X Y)))) (forall ((U $$unsorted) (W $$unsorted) (Y $$unsorted) (V $$unsorted) (X $$unsorted)) (or (not (tptp.between U W Y)) (not (tptp.between V W X)) (= U W) (tptp.between U X (tptp.euclid2 U V W X Y)))) (forall ((U $$unsorted) (W $$unsorted) (Y $$unsorted) (V $$unsorted) (X $$unsorted)) (or (not (tptp.between U W Y)) (not (tptp.between V W X)) (= U W) (tptp.between (tptp.euclid1 U V W X Y) Y (tptp.euclid2 U V W X Y)))) (forall ((U $$unsorted) (V $$unsorted) (V1 $$unsorted) (X $$unsorted) (X1 $$unsorted) (W $$unsorted)) (or (not (tptp.equidistant U V U V1)) (not (tptp.equidistant U X U X1)) (not (tptp.between U V X)) (not (tptp.between V W X)) (tptp.between V1 (tptp.continuous U V V1 W X X1) X1))) (forall ((U $$unsorted) (V $$unsorted) (V1 $$unsorted) (X $$unsorted) (X1 $$unsorted) (W $$unsorted)) (or (not (tptp.equidistant U V U V1)) (not (tptp.equidistant U X U X1)) (not (tptp.between U V X)) (not (tptp.between V W X)) (tptp.equidistant U W U (tptp.continuous U V V1 W X X1)))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.reflection U V) (tptp.extension U V U V))) (forall ((U1 $$unsorted) (W1 $$unsorted) (U $$unsorted) (V $$unsorted)) (= (tptp.insertion U1 W1 U V) (tptp.extension (tptp.extension W1 U1 tptp.lower_dimension_point_1 tptp.lower_dimension_point_2) U1 U V))) (forall ((U $$unsorted) (V $$unsorted)) (tptp.equidistant U V U V)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.equidistant U V W X)) (tptp.equidistant W X U V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.equidistant U V W X)) (tptp.equidistant V U W X))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.equidistant U V W X)) (tptp.equidistant U V X W))) _let_14 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.equidistant U V W X)) (tptp.equidistant W X V U))) _let_13 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.equidistant U V W X)) (tptp.equidistant X W V U))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.equidistant U V W X)) (not (tptp.equidistant W X Y Z)) (tptp.equidistant U V Y Z))) (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted)) (= V (tptp.extension U V W W))) (forall ((Y $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= Y (tptp.extension U V W X))) (tptp.between U V Y))) (forall ((U $$unsorted) (V $$unsorted)) (tptp.between U V (tptp.reflection U V))) (forall ((V $$unsorted) (U $$unsorted)) (tptp.equidistant V (tptp.reflection U V) U V)) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= U V)) (= V (tptp.reflection U V)))) (forall ((U $$unsorted)) (= U (tptp.reflection U U))) (forall ((V $$unsorted) (U $$unsorted)) (or (not (= V (tptp.reflection U V))) (= U V))) (forall ((U $$unsorted) (V $$unsorted)) (tptp.equidistant U U V V)) (forall ((U $$unsorted) (V $$unsorted) (U1 $$unsorted) (V1 $$unsorted) (W $$unsorted) (W1 $$unsorted)) (or (not (tptp.equidistant U V U1 V1)) (not (tptp.equidistant V W V1 W1)) (not (tptp.between U V W)) (not (tptp.between U1 V1 W1)) (tptp.equidistant U W U1 W1))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between U V X)) (not (tptp.equidistant V W V X)) (= U V) (= W X))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.between U V W)) (= U V) (= W (tptp.extension U V V W)))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.equidistant W X Y Z)) (= (tptp.extension U V W X) (tptp.extension U V Y Z)) (= U V))) (forall ((U $$unsorted) (V $$unsorted)) (or (= (tptp.extension U V U V) (tptp.extension U V V U)) (= U V))) (forall ((V $$unsorted) (U $$unsorted)) (tptp.equidistant V U V (tptp.reflection (tptp.reflection U V) V))) (forall ((U $$unsorted) (V $$unsorted)) (= U (tptp.reflection (tptp.reflection U V) V))) _let_12 (forall ((U $$unsorted) (W $$unsorted) (X $$unsorted) (V $$unsorted)) (or (not (tptp.between U W X)) (not (= U X)) (tptp.between V W X))) _let_11 (forall ((U $$unsorted) (V $$unsorted)) (tptp.between U U V)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between V U W)) (= U V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between U W V)) (= V W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between V U W)) (= U V) (= V W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between U W V)) (= U V) (= V W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.between U V W))) (or (not _let_1) (not (tptp.between V W X)) _let_1))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between U W X)) (tptp.between V W X))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between V W X)) (tptp.between U W X) (= V W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between V W X)) (tptp.between U V X) (= V W))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (W $$unsorted)) (or (not (tptp.between U V X)) (not (tptp.between V W X)) (tptp.between U W X))) _let_10 (not (= tptp.lower_dimension_point_1 tptp.lower_dimension_point_2)) (not (= tptp.lower_dimension_point_2 tptp.lower_dimension_point_3)) (not (= tptp.lower_dimension_point_1 tptp.lower_dimension_point_3)) (forall ((V $$unsorted) (U $$unsorted)) (not (= V (tptp.extension U V tptp.lower_dimension_point_1 tptp.lower_dimension_point_2)))) (forall ((V $$unsorted) (U $$unsorted) (X $$unsorted) (W $$unsorted)) (tptp.equidistant V (tptp.extension U V tptp.lower_dimension_point_1 tptp.lower_dimension_point_2) X (tptp.extension W X tptp.lower_dimension_point_1 tptp.lower_dimension_point_2))) (forall ((U $$unsorted) (V $$unsorted)) (tptp.between U V (tptp.extension U V tptp.lower_dimension_point_1 tptp.lower_dimension_point_2))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (U1 $$unsorted) (V1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.inner_pasch V1 (tptp.inner_pasch U X U1 V1 W) U V W))) (or (not (tptp.between U V W)) (not (tptp.between U1 V1 W)) (not (tptp.between U X U1)) (tptp.between X _let_1 W) (tptp.between V _let_1 V1)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (W1 $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.equidistant U W U W1)) (not (tptp.equidistant V W V W1)) (= U V) (= W W1))) _let_9 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (U1 $$unsorted) (V1 $$unsorted) (W1 $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.between U1 V1 W1)) (not (tptp.equidistant U V U1 V1)) (not (tptp.equidistant U W U1 W1)) (tptp.equidistant V W V1 W1))) (forall ((U $$unsorted) (V $$unsorted) (U1 $$unsorted) (V1 $$unsorted) (W $$unsorted) (W1 $$unsorted) (X $$unsorted) (X1 $$unsorted)) (or (not (tptp.equidistant U V U1 V1)) (not (tptp.equidistant V W V1 W1)) (not (tptp.equidistant U X U1 X1)) (not (tptp.equidistant W X W1 X1)) (not (tptp.between U V W)) (not (tptp.between U1 V1 W1)) (tptp.equidistant V X V1 X1))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.equidistant U V U X)) (not (tptp.equidistant W V W X)) (= V X))) _let_8 _let_7 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (U1 $$unsorted) (W1 $$unsorted)) (or (not (tptp.between U V W)) (not (tptp.equidistant U W U1 W1)) (tptp.equidistant V W (tptp.insertion U1 W1 U V) W1))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.between U V W)) (= V (tptp.insertion U W U V)))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.equidistant W X Y Z)) (= (tptp.insertion U V W X) (tptp.insertion U V Y Z)))) _let_6 _let_5 _let_4 _let_3 _let_2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 8.69/8.91  )
% 8.69/8.92  % SZS output end Proof for GEO049-3
% 8.69/8.92  % cvc5---1.0.5 exiting
% 8.69/8.92  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------