TSTP Solution File: GEO175+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEO175+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 22:50:07 EDT 2023
% Result : Theorem 0.19s 0.67s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : GEO175+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 22:46:14 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.19/0.47 %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.67 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.U8Tem4qgB4/cvc5---1.0.5_3415.p...
% 0.19/0.67 ------- get file name : TPTP file name is GEO175+3
% 0.19/0.67 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3415.smt2...
% 0.19/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.67 % SZS status Theorem for GEO175+3
% 0.19/0.67 % SZS output start Proof for GEO175+3
% 0.19/0.67 (
% 0.19/0.67 (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (=> (and (tptp.distinct_points X Y) (tptp.convergent_lines U V) (tptp.distinct_points X (tptp.intersection_point U V))) (or (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V))))))) (let ((_let_2 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_lines X Y) (tptp.convergent_lines 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 $$unsorted) (U $$unsorted) (V $$unsorted)) (=> (and (tptp.distinct_points X Y) (tptp.distinct_lines U V)) (or (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V) (tptp.apart_point_and_line Y U) (tptp.apart_point_and_line Y V)))))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.convergent_lines X Y) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) Y)))))) (let ((_let_6 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.convergent_lines X Y) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) X)))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (or (tptp.distinct_points X Z) (tptp.distinct_points Y Z)))))) (let ((_let_9 (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))))) (let ((_let_10 (forall ((X $$unsorted)) (not (tptp.distinct_points X X))))) (let ((_let_11 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_12 (_let_9))) (let ((_let_13 (ASSUME :args _let_12))) (let ((_let_14 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14 _let_11))) (let ((_let_18 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z))))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_20 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (not _let_14))) (let ((_let_23 (or _let_22 _let_21 _let_20))) (let ((_let_24 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_lines X Y)) (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_27 (tptp.apart_point_and_line SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_28 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_29 (tptp.apart_point_and_line _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_30 (tptp.apart_point_and_line _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_31 (not _let_20))) (let ((_let_32 (tptp.distinct_points _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31 _let_30 _let_29 _let_27 _let_26))) (let ((_let_35 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.distinct_lines U V)) (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V) (tptp.apart_point_and_line Y U) (tptp.apart_point_and_line Y V))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_38 (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_28))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37 _let_32))) (let ((_let_41 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.distinct_points X Y)) (tptp.distinct_points X Z) (tptp.distinct_points Y Z))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_10))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 (or (not (tptp.distinct_points SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_16 _let_39 _let_27 _let_26))) (let ((_let_46 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.convergent_lines U V)) (not (tptp.distinct_points X (tptp.intersection_point U V))) (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or))) (let ((_let_50 (not _let_46))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_48) :args (_let_50))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_46))) (REFL :args (_let_47)) :args _let_49)) _let_48 :args (_let_47 true _let_46)))) (let ((_let_52 (REFL :args (_let_45)))) (let ((_let_53 (not _let_29))) (let ((_let_54 (or _let_16 _let_53))) (let ((_let_55 (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_56 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 1)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_49)) :args ((or _let_15 _let_45))) _let_51 :args (_let_15 true _let_45)))) (let ((_let_58 (not _let_30))) (let ((_let_59 (or _let_16 _let_58))) (let ((_let_60 (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_61 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_63 (not _let_21))) (let ((_let_64 (or _let_63 _let_62))) (let ((_let_65 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.distinct_lines X Y)) (tptp.convergent_lines X Y))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 ((not (= (tptp.convergent_lines X X) false))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_12)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_16 _let_11 _let_14 (not _let_17)))) _let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_21 _let_20 _let_22 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_62 _let_63 (not _let_64)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_12)) _let_13 :args ((not _let_62) false _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X Y) true))))) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_63 true _let_62 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_27 _let_26 _let_30 _let_29 _let_33 _let_31 (not _let_34)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_45 3)) _let_51 :args ((not _let_27) true _let_45)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_45 4)) _let_51 :args ((not _let_26) true _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_16 _let_58 (not _let_59)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X Y) false))))) :args (_let_60))) _let_61 :args (_let_59 false _let_60)) :args (_let_58 false _let_15 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_16 _let_53 (not _let_54)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X Y) false))))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_53 false _let_15 false _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 _let_32 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 2)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_49)) :args ((or _let_38 _let_45))) _let_51 :args (_let_38 true _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.distinct_points X X) false))))) :args _let_43)) _let_44 :args ((not _let_37) false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_points X Y) false)) (not (= (tptp.distinct_points X Z) true))))) :args (_let_41))) _let_42 :args (_let_40 false _let_41)) :args (_let_32 false _let_38 true _let_37 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apart_point_and_line Y V) true)) (not (= (tptp.apart_point_and_line X U) true))))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_31 true _let_27 true _let_26 true _let_30 true _let_29 false _let_32 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.distinct_lines X Y) false)) (not (= (tptp.distinct_lines X Z) true))))) :args (_let_24))) _let_25 :args (_let_23 false _let_24)) :args (_let_22 true _let_21 true _let_20 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :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_18))) _let_19 :args (_let_17 false _let_18)) :args (_let_11 false _let_15 true _let_14 false _let_17)) _let_13 :args (false false _let_11 false _let_9)) :args (_let_10 (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))) _let_9 _let_8 _let_7 (forall ((X $$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_6 _let_5 _let_4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.apart_point_and_line X Y) (or (tptp.distinct_points X Z) (tptp.apart_point_and_line Z Y)))) (forall ((X $$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 _let_2 (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)))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.67 )
% 0.19/0.67 % SZS output end Proof for GEO175+3
% 0.19/0.67 % cvc5---1.0.5 exiting
% 0.19/0.67 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------