%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRA002+3 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.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 : Thu Aug 31 00:00:30 EDT 2023

% Result   : Theorem 25.60s 25.81s
% Output   : Proof 25.60s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRA002+3 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n026.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   : Sun Aug 27 04:04:34 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 25.60/25.81  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.rsbMhFKZcX/cvc5---1.0.5_1276.p...
% 25.60/25.81  ------- get file name : TPTP file name is GRA002+3
% 25.60/25.81  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1276.smt2...
% 25.60/25.81  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.60/25.81  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.60/25.81  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.60/25.81  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.60/25.81  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.60/25.81  % SZS status Theorem for GRA002+3
% 25.60/25.81  % SZS output start Proof for GRA002+3
% 25.60/25.81  (
% 25.60/25.81  (let ((_let_1 (not (=> tptp.complete (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.shortest_path V1 V2 P) (tptp.less_or_equal (tptp.minus (tptp.length_of P) tptp.n1) (tptp.number_of_in tptp.triangles tptp.graph)))))))) (let ((_let_2 (=> tptp.complete (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (=> (and (tptp.shortest_path V1 V2 P) (tptp.precedes E1 E2 P) (tptp.sequential E1 E2)) (exists ((E3 $$unsorted)) (tptp.triangle E1 E2 E3))))))) (let ((_let_3 (forall ((Things $$unsorted) (InThese $$unsorted)) (tptp.less_or_equal (tptp.number_of_in Things InThese) (tptp.number_of_in Things tptp.graph))))) (let ((_let_4 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (and (tptp.path V1 V2 P) (forall ((E1 $$unsorted) (E2 $$unsorted)) (=> (and (tptp.on_path E1 P) (tptp.on_path E2 P) (tptp.sequential E1 E2)) (exists ((E3 $$unsorted)) (tptp.triangle E1 E2 E3))))) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.number_of_in tptp.triangles P)))))) (let ((_let_5 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.minus (tptp.length_of P) tptp.n1)))))) (let ((_let_6 (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (=> (tptp.path V1 V2 P) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))))) (let ((_let_7 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.path V1 V2 P) (forall ((E1 $$unsorted) (E2 $$unsorted)) (=> (and (tptp.on_path E1 P) (tptp.on_path E2 P) (or (tptp.sequential E1 E2) (exists ((E3 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))) (tptp.precedes E1 E2 P))))))) (let ((_let_8 (tptp.number_of_in tptp.triangles tptp.graph))) (let ((_let_9 (tptp.minus (tptp.length_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) tptp.n1))) (let ((_let_10 (tptp.less_or_equal _let_9 _let_8))) (let ((_let_11 (tptp.number_of_in tptp.sequential_pairs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (= _let_9 _let_11))) (let ((_let_13 (tptp.number_of_in tptp.triangles SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (tptp.less_or_equal _let_13 _let_8))) (let ((_let_15 (= _let_11 _let_13))) (let ((_let_16 (tptp.shortest_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_10))) (let ((_let_19 (not _let_10))) (let ((_let_20 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (tptp.less_or_equal (tptp.minus (tptp.length_of P) tptp.n1) (tptp.number_of_in tptp.triangles tptp.graph)))))) (let ((_let_21 (not _let_18))) (let ((_let_22 (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_23 (ASSUME :args (_let_1)))) (let ((_let_24 (MACRO_SR_PRED_TRANSFORM (NOT_IMPLIES_ELIM1 (EQ_RESOLVE _let_23 _let_22)) :args ((= tptp.complete true))))) (let ((_let_25 (EQ_RESOLVE _let_23 (TRANS _let_22 (MACRO_SR_EQ_INTRO _let_24 :args ((not (=> tptp.complete _let_20)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_26 (or))) (let ((_let_27 (not _let_20))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_25) :args (_let_27))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_20))) (REFL :args (_let_21)) :args _let_26)) _let_25 :args (_let_21 true _let_20)))) (let ((_let_29 (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_12))) (let ((_let_32 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (tptp.path V1 V2 P)) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.minus (tptp.length_of P) tptp.n1)))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (and _let_29 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (forall ((P $$unsorted)) (or (not (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 P)) (tptp.less_or_equal (tptp.length_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.length_of P))))))) (let ((_let_35 (= _let_16 _let_34))) (let ((_let_36 (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (or (not (tptp.path V1 V2 P)) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG (REFL :args (_let_18)) (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_26)) :args ((or _let_16 _let_18))) _let_28 :args (_let_16 true _let_18)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_29 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_35)) :args ((or _let_17 _let_34 (not _let_35)))) _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.shortest_path V1 V2 SP)))) :args (_let_36))) _let_37 :args (_let_35 false _let_36)) :args (_let_34 false _let_16 false _let_35)) :args (_let_29 false _let_34)))) (let ((_let_40 (_let_3))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (tptp.on_path E1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.on_path E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.sequential E1 E2)) (not (forall ((E3 $$unsorted)) (not (tptp.triangle E1 E2 E3)))))))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_30 _let_43 _let_15))) (let ((_let_45 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (tptp.on_path E1 P)) (not (tptp.on_path E2 P)) (not (tptp.sequential E1 E2)) (not (forall ((E3 $$unsorted)) (not (tptp.triangle E1 E2 E3))))))) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.number_of_in tptp.triangles P)))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (forall ((E3 $$unsorted)) (not (tptp.triangle SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 E3))))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_52 _let_50 _let_48))) (let ((_let_56 (and _let_50 (or (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_57 (forall ((E3 $$unsorted)) (not (tptp.triangle SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 E3))))) (let ((_let_58 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_59 (or _let_30 _let_54 _let_52 _let_56 _let_58))) (let ((_let_60 (not _let_57))) (let ((_let_61 (not _let_58))) (let ((_let_62 (or _let_17 _let_61 _let_50 _let_60))) (let ((_let_63 (REFL :args (_let_55)))) (let ((_let_64 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1156 $$unsorted) (BOUND_VARIABLE_1154 $$unsorted) (BOUND_VARIABLE_1152 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.on_path BOUND_VARIABLE_1152 P)) (not (tptp.on_path BOUND_VARIABLE_1154 P)) (and (not (tptp.sequential BOUND_VARIABLE_1152 BOUND_VARIABLE_1154)) (or (not (tptp.sequential BOUND_VARIABLE_1152 BOUND_VARIABLE_1156)) (not (tptp.precedes BOUND_VARIABLE_1156 BOUND_VARIABLE_1154 P)))) (tptp.precedes BOUND_VARIABLE_1152 BOUND_VARIABLE_1154 P))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (not (tptp.precedes E1 E2 P)) (not (tptp.sequential E1 E2)) (not (forall ((E3 $$unsorted)) (not (tptp.triangle E1 E2 E3)))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_24 :args ((=> tptp.complete _let_66) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_68 (_let_43))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (ASSUME :args (_let_14)))) (CONG (TRANS (SYMM (ASSUME :args (_let_15))) (SYMM (ASSUME :args (_let_12)))) (REFL :args (_let_8)) :args (APPLY_UF tptp.less_or_equal)) (FALSE_INTRO (ASSUME :args (_let_19))))) :args (_let_19 _let_12 _let_15 _let_14))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_10))) (REFL :args ((not _let_12))) (REFL :args ((not _let_15))) (REFL :args ((not _let_14))) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_30 _let_43 _let_15 (not _let_44)))) _let_39 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_68)) :args _let_68)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) (REFL :args ((not _let_55))) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_17 _let_50 _let_61 _let_60 (not _let_62)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.shortest_path V1 V2 P) false)) (not (= (tptp.precedes E1 E2 P) false))))) :args (_let_66))) _let_67 :args (_let_62 false _let_66)) _let_38 (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_30 _let_54 _let_52 _let_58 _let_56 (not _let_59)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_64))) _let_65 :args (_let_59 false _let_64)) _let_39 (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_47 (= E3 E3)))) (REORDERING (CNF_AND_POS :args (_let_56 0)) :args ((or _let_50 (not _let_56)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 3)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_26)) :args ((or _let_47 _let_55))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 2)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_26)) :args ((or _let_49 _let_55))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 1)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_26)) :args ((or _let_51 _let_55))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 0)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_26)) :args ((or _let_53 _let_55))) :args (_let_55 false _let_62 false _let_16 false _let_58 false _let_59 false _let_29 false _let_57 true _let_56 false _let_47 false _let_49 false _let_51 false _let_53)) :args (_let_42 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.path V1 V2 P) false))))) :args (_let_45))) _let_46 :args (_let_44 false _let_45)) :args (_let_15 false _let_29 false _let_42 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.triangles SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.number_of_in Things InThese)))) :args _let_40)) _let_41 :args (_let_14 false _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_12 (not _let_31)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.path V1 V2 P) false))))) :args (_let_32)))) _let_33 :args (_let_31 false _let_32)) :args (_let_12 false _let_29 false _let_31)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_18 1)) _let_28 :args (_let_19 true _let_18)) :args (false false _let_15 false _let_14 false _let_12 true _let_10)) :args ((forall ((E $$unsorted)) (=> (tptp.edge E) (not (= (tptp.head_of E) (tptp.tail_of E))))) (forall ((E $$unsorted)) (=> (tptp.edge E) (and (tptp.vertex (tptp.head_of E)) (tptp.vertex (tptp.tail_of E))))) (=> tptp.complete (forall ((V1 $$unsorted) (V2 $$unsorted)) (=> (and (tptp.vertex V1) (tptp.vertex V2) (not (= V1 V2))) (exists ((E $$unsorted)) (let ((_let_1 (tptp.tail_of E))) (let ((_let_2 (tptp.head_of E))) (and (tptp.edge E) (xor (and (= V1 _let_2) (= V2 _let_1)) (and (= V2 _let_2) (= V1 _let_1)))))))))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (and (tptp.vertex V1) (tptp.vertex V2) (exists ((E $$unsorted)) (and (tptp.edge E) (= V1 (tptp.tail_of E)) (or (and (= V2 (tptp.head_of E)) (= P (tptp.path_cons E tptp.empty))) (exists ((TP $$unsorted)) (and (tptp.path (tptp.head_of E) V2 TP) (= P (tptp.path_cons E TP)))))))) (tptp.path V1 V2 P))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (and (tptp.vertex V1) (tptp.vertex V2) (exists ((E $$unsorted)) (and (tptp.edge E) (= V1 (tptp.tail_of E)) (xor (and (= V2 (tptp.head_of E)) (= P (tptp.path_cons E tptp.empty))) (exists ((TP $$unsorted)) (and (tptp.path (tptp.head_of E) V2 TP) (= P (tptp.path_cons E TP)))))))))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (E $$unsorted)) (=> (and (tptp.path V1 V2 P) (tptp.on_path E P)) (and (tptp.edge E) (tptp.in_path (tptp.head_of E) P) (tptp.in_path (tptp.tail_of E) P)))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (V $$unsorted)) (=> (and (tptp.path V1 V2 P) (tptp.in_path V P)) (and (tptp.vertex V) (exists ((E $$unsorted)) (and (tptp.on_path E P) (or (= V (tptp.head_of E)) (= V (tptp.tail_of E)))))))) (forall ((E1 $$unsorted) (E2 $$unsorted)) (= (tptp.sequential E1 E2) (and (tptp.edge E1) (tptp.edge E2) (not (= E1 E2)) (= (tptp.head_of E1) (tptp.tail_of E2))))) _let_7 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.path V1 V2 P) (forall ((E1 $$unsorted) (E2 $$unsorted)) (=> (tptp.precedes E1 E2 P) (and (tptp.on_path E1 P) (tptp.on_path E2 P) (xor (tptp.sequential E1 E2) (exists ((E3 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))))))) _let_6 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (=> (and (tptp.shortest_path V1 V2 P) (tptp.precedes E1 E2 P)) (and (not (exists ((E3 $$unsorted)) (and (= (tptp.tail_of E3) (tptp.tail_of E1)) (= (tptp.head_of E3) (tptp.head_of E2))))) (not (tptp.precedes E2 E1 P))))) (forall ((E1 $$unsorted) (E2 $$unsorted) (E3 $$unsorted)) (= (tptp.triangle E1 E2 E3) (and (tptp.edge E1) (tptp.edge E2) (tptp.edge E3) (tptp.sequential E1 E2) (tptp.sequential E2 E3) (tptp.sequential E3 E1)))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (= (tptp.length_of P) (tptp.number_of_in tptp.edges P)))) _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.60/25.81  )
% 25.60/25.81  % SZS output end Proof for GRA002+3
% 25.60/25.81  % cvc5---1.0.5 exiting
% 25.60/25.82  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------