TSTP Solution File: GEO191+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEO191+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 22:50:18 EDT 2023
% Result : Theorem 0.90s 1.13s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : GEO191+3 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.12 % Command : do_cvc5 %s %d
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 29 22:01:20 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.44 %----Proving TF0_NAR, FOF, or CNF
% 0.90/1.13 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.TTD6lkIRr3/cvc5---1.0.5_17945.p...
% 0.90/1.13 ------- get file name : TPTP file name is GEO191+3
% 0.90/1.13 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_17945.smt2...
% 0.90/1.13 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.90/1.13 % SZS status Theorem for GEO191+3
% 0.90/1.13 % SZS output start Proof for GEO191+3
% 0.90/1.13 (
% 0.90/1.13 (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.intersection_point U V))) (let ((_let_2 (tptp.intersection_point X Y))) (=> (and (tptp.convergent_lines X Y) (tptp.convergent_lines U V) (or (tptp.apart_point_and_line _let_2 U) (tptp.apart_point_and_line _let_2 V))) (or (tptp.apart_point_and_line _let_1 X) (tptp.apart_point_and_line _let_1 Y))))))))) (let ((_let_2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z)))))) (let ((_let_3 (forall ((X $$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 ((_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 $$unsorted)) (=> (tptp.convergent_lines X Y) (or (tptp.convergent_lines X Z) (tptp.convergent_lines Y Z)))))) (let ((_let_8 (forall ((X $$unsorted)) (not (tptp.convergent_lines X X))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.convergent_lines X Y)) (tptp.distinct_lines Y Z) (tptp.convergent_lines X Z))))) (let ((_let_10 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_11 (tptp.distinct_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_11 _let_10))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_16 (not _let_14))) (let ((_let_17 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (tptp.apart_point_and_line _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (tptp.apart_point_and_line _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_20 (tptp.intersection_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (tptp.apart_point_and_line _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_22 (tptp.apart_point_and_line _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (not _let_11))) (let ((_let_24 (tptp.distinct_points _let_20 _let_17))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_22 _let_21 _let_19 _let_18))) (let ((_let_27 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.distinct_points X Y)) (not (tptp.distinct_lines U V)) (tptp.apart_point_and_line X U) (tptp.apart_point_and_line X V) (tptp.apart_point_and_line Y U) (tptp.apart_point_and_line Y V))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (tptp.apart_point_and_line _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_30 (tptp.apart_point_and_line _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_24 _let_29))) (let ((_let_33 (tptp.apart_point_and_line _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_34 (tptp.apart_point_and_line _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_24 _let_33))) (let ((_let_37 (and _let_35 _let_31))) (let ((_let_38 (not _let_29))) (let ((_let_39 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38))) (let ((_let_42 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.convergent_lines X Y)) (not (tptp.apart_point_and_line (tptp.intersection_point X Y) Y)))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (_let_42))) (let ((_let_45 ((not (= (tptp.convergent_lines X Y) false))))) (let ((_let_46 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_40 _let_37 _let_19 _let_18))) (let ((_let_49 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.intersection_point U V))) (let ((_let_2 (tptp.intersection_point X Y))) (or (not (tptp.convergent_lines X Y)) (not (tptp.convergent_lines U V)) (and (not (tptp.apart_point_and_line _let_2 U)) (not (tptp.apart_point_and_line _let_2 V))) (tptp.apart_point_and_line _let_1 X) (tptp.apart_point_and_line _let_1 Y))))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (REFL :args (_let_48)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_52)) :args ((or _let_39 _let_48))) _let_54 :args (_let_39 true _let_48)))) (let ((_let_57 (forall ((X $$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_58 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (_let_57))) (let ((_let_60 ((not (= (tptp.apart_point_and_line X Y) false)) (not (= (tptp.apart_point_and_line Z Y) true))))) (let ((_let_61 (not _let_33))) (let ((_let_62 (or _let_40 _let_61))) (let ((_let_63 (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_64 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 ((not (= (tptp.convergent_lines X Y) false))))) (let ((_let_67 (_let_37))) (let ((_let_68 (not _let_21))) (let ((_let_69 (or _let_47 _let_68))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_52)) :args ((or _let_46 _let_48))) _let_54 :args (_let_46 true _let_48)))) (let ((_let_71 (not _let_22))) (let ((_let_72 (or _let_47 _let_71))) (let ((_let_73 (tptp.convergent_lines SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_74 (or _let_47 _let_73 _let_12))) (let ((_let_75 (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_76 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (_let_8))) (let ((_let_78 (ASSUME :args _let_77))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_15 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.convergent_lines X Y) false)) (not (= (tptp.convergent_lines X Z) true))))) :args (_let_9))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_10 _let_13 _let_11 _let_16))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.convergent_lines X X) false))))) :args _let_77)) _let_78 :args ((not _let_10) false _let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_47 _let_73 _let_12 (not _let_74)))) _let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM)) :args _let_77)) _let_78 :args ((not _let_73) false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :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 Z) true)) (not (= (tptp.convergent_lines Y Z) true))))) :args (_let_75))) _let_76 :args (_let_74 false _let_75)) :args (_let_12 false _let_46 true _let_73 false _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_19 _let_18 _let_22 _let_21 _let_25 _let_23 (not _let_26)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 3)) _let_54 :args ((not _let_19) true _let_48)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 4)) _let_54 :args ((not _let_18) true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_47 _let_71 (not _let_72)))) _let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_72 false _let_63)) :args (_let_71 false _let_46 false _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_47 _let_68 (not _let_69)))) _let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_44)) _let_43 :args (_let_69 false _let_42)) :args (_let_68 false _let_46 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_67) (CONG (REFL :args _let_67) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_52)) :args ((or _let_34 _let_30 _let_37))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 2)) _let_54 :args ((not _let_37) true _let_48)) (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_33 _let_24 (not _let_36)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (_let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17 QUANTIFIERS_INST_E_MATCHING _let_60)) :args _let_59)) _let_58 :args (_let_36 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_40 _let_61 (not _let_62)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_62 false _let_63)) :args (_let_61 false _let_39 false _let_62)) (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_29 _let_24 (not _let_32)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (_let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_17 QUANTIFIERS_INST_E_MATCHING _let_60)) :args _let_59)) _let_58 :args (_let_32 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_38 (not _let_41)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_44)) _let_43 :args (_let_41 false _let_42)) :args (_let_38 false _let_39 false _let_41)) :args (_let_24 true _let_37 true _let_34 false _let_36 true _let_33 true _let_30 false _let_32 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_20 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apart_point_and_line Y V) true)) (not (= (tptp.apart_point_and_line X U) true))))) :args (_let_27))) _let_28 :args (_let_26 false _let_27)) :args (_let_23 true _let_19 true _let_18 true _let_22 true _let_21 false _let_24 false _let_26)) :args (_let_16 true _let_10 false _let_12 true _let_11)) _let_15 :args (false true _let_14 false _let_9)) :args ((forall ((X $$unsorted)) (not (tptp.distinct_points X X))) (forall ((X $$unsorted)) (not (tptp.distinct_lines X X))) _let_8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_points X Y) (or (tptp.distinct_points X Z) (tptp.distinct_points Y Z)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.distinct_lines X Y) (or (tptp.distinct_lines X Z) (tptp.distinct_lines Y Z)))) _let_7 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line X (tptp.line_connecting X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_points X Y) (not (tptp.apart_point_and_line Y (tptp.line_connecting X Y))))) _let_6 _let_5 _let_4 _let_3 (forall ((X $$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_2 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.distinct_lines X Y) (tptp.convergent_lines X Y))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.90/1.14 )
% 0.90/1.14 % SZS output end Proof for GEO191+3
% 0.90/1.14 % cvc5---1.0.5 exiting
% 0.90/1.14 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------