%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRA003+1 : 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 0.20s 0.56s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun Aug 27 04:01:04 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.56  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Wb4nxIaYD7/cvc5---1.0.5_16349.p...
% 0.20/0.56  ------- get file name : TPTP file name is GRA003+1
% 0.20/0.56  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16349.smt2...
% 0.20/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.56  % SZS status Theorem for GRA003+1
% 0.20/0.56  % SZS output start Proof for GRA003+1
% 0.20/0.56  (
% 0.20/0.56  (let ((_let_1 (not (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (=> (and (tptp.shortest_path V1 V2 P) (tptp.precedes E1 E2 P)) (and (tptp.vertex V1) (tptp.vertex V2) (not (= V1 V2)) (tptp.edge E1) (tptp.edge E2) (not (= E1 E2)) (tptp.path V1 V2 P))))))) (let ((_let_2 (forall ((V1 $$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 $$unsorted)) (and (= (tptp.tail_of E3) (tptp.tail_of E1)) (= (tptp.head_of E3) (tptp.head_of E2))))) (not (tptp.precedes E2 E1 P))))))) (let ((_let_3 (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (=> (tptp.path V1 V2 P) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))))) (let ((_let_4 (forall ((P $$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 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))))))))) (let ((_let_5 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (E $$unsorted)) (=> (and (tptp.path V1 V2 P) (tptp.on_path E P)) (and (tptp.edge E) (tptp.in_path (tptp.head_of E) P) (tptp.in_path (tptp.tail_of E) P)))))) (let ((_let_6 (forall ((V1 $$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)))))))))))) (let ((_let_7 (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (and _let_10 (tptp.in_path (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in_path _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_12 (not _let_8))) (let ((_let_13 (not _let_7))) (let ((_let_14 (or _let_13 _let_12 _let_11))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (not _let_15))) (let ((_let_17 (and _let_7 _let_16 (forall ((P $$unsorted)) (or (not (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 P)) (tptp.less_or_equal (tptp.length_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.length_of P))))))) (let ((_let_18 (tptp.shortest_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_19 (= _let_18 _let_17))) (let ((_let_20 (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (or (not (tptp.path V1 V2 P)) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_25 (tptp.vertex SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_26 (tptp.vertex SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (and _let_26 _let_25 _let_16 _let_10 _let_24 _let_23 _let_7))) (let ((_let_28 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_29 (not _let_28))) (let ((_let_30 (not _let_18))) (let ((_let_31 (or _let_30 _let_29 _let_27))) (let ((_let_32 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (not (tptp.precedes E1 E2 P)) (and (tptp.vertex V1) (tptp.vertex V2) (not (= V1 V2)) (tptp.edge E1) (tptp.edge E2) (not (= E1 E2)) (tptp.path V1 V2 P)))))) (let ((_let_33 (not _let_31))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (or))) (let ((_let_36 (not _let_32))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_34) :args (_let_36))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_32))) (REFL :args (_let_33)) :args _let_35)) _let_34 :args (_let_33 true _let_32)))) (let ((_let_38 (REFL :args (_let_31)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_18))) :args _let_35)) :args ((or _let_18 _let_31))) _let_37 :args (_let_18 true _let_31)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_19)) :args ((or _let_30 _let_17 (not _let_19)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.shortest_path V1 V2 SP)))) :args (_let_20))) _let_21 :args (_let_19 false _let_20)) :args (_let_17 false _let_18 false _let_19)))) (let ((_let_41 (not _let_17))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_17 0)) :args ((or _let_7 _let_41))) _let_40 :args (_let_7 false _let_17)))) (let ((_let_43 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_44 (and _let_8 _let_43 (= (not (forall ((E3 $$unsorted)) (or (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 E3)) (not (tptp.precedes E3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_45 (or _let_13 _let_29 _let_44))) (let ((_let_46 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1199 $$unsorted) (BOUND_VARIABLE_1197 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.precedes BOUND_VARIABLE_1197 BOUND_VARIABLE_1199 P)) (and (tptp.on_path BOUND_VARIABLE_1197 P) (tptp.on_path BOUND_VARIABLE_1199 P) (= (not (forall ((E3 $$unsorted)) (or (not (tptp.sequential BOUND_VARIABLE_1197 E3)) (not (tptp.precedes E3 BOUND_VARIABLE_1199 P))))) (not (tptp.sequential BOUND_VARIABLE_1197 BOUND_VARIABLE_1199)))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 1)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_35)) :args ((or _let_28 _let_31))) _let_37 :args (_let_28 true _let_31)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_29 _let_13 _let_44 (not _let_45)))) _let_48 _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.path V1 V2 P) false)) (not (= (tptp.precedes BOUND_VARIABLE_1197 BOUND_VARIABLE_1199 P) false))))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_44 false _let_28 false _let_7 false _let_45)))) (let ((_let_50 (not _let_44))) (let ((_let_51 (not _let_11))) (let ((_let_52 (not _let_10))) (let ((_let_53 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_54 (and _let_24 (tptp.in_path _let_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in_path (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_55 (not _let_43))) (let ((_let_56 (or _let_13 _let_55 _let_54))) (let ((_let_57 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (E $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.on_path E P)) (and (tptp.edge E) (tptp.in_path (tptp.head_of E) P) (tptp.in_path (tptp.tail_of E) P)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (_let_57))) (let ((_let_60 ((not (= (tptp.path V1 V2 P) false)) (not (= (tptp.on_path E P) false))))) (let ((_let_61 (and _let_26 _let_25 (not (forall ((E $$unsorted)) (or (not (tptp.edge E)) (not (= (tptp.tail_of E) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (= (and (= (tptp.head_of E) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (= (tptp.path_cons E tptp.empty) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((TP $$unsorted)) (or (not (tptp.path (tptp.head_of E) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 TP)) (not (= (tptp.path_cons E TP) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))))))))) (let ((_let_62 (or _let_13 _let_61))) (let ((_let_63 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (tptp.path V1 V2 P)) (and (tptp.vertex V1) (tptp.vertex V2) (not (forall ((E $$unsorted)) (or (not (tptp.edge E)) (not (= V1 (tptp.tail_of E))) (= (and (= V2 (tptp.head_of E)) (= P (tptp.path_cons E tptp.empty))) (not (forall ((TP $$unsorted)) (or (not (tptp.path (tptp.head_of E) V2 TP)) (not (= P (tptp.path_cons E TP))))))))))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_13 _let_61 (not _let_62)))) _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.path V1 V2 P) false))))) :args (_let_63)))) _let_64 :args (_let_62 false _let_63)) :args (_let_61 false _let_7 false _let_62)))) (let ((_let_66 (not _let_61))) (let ((_let_67 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_68 (not _let_67))) (let ((_let_69 (and (or (not (= (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) _let_9)) (not (= (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) _let_53))) _let_68))) (let ((_let_70 (or _let_30 _let_29 _let_69))) (let ((_let_71 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_1248 $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (not (tptp.precedes E1 E2 P)) (and (or (not (= (tptp.tail_of E1) (tptp.tail_of BOUND_VARIABLE_1248))) (not (= (tptp.head_of E2) (tptp.head_of BOUND_VARIABLE_1248)))) (not (tptp.precedes E2 E1 P))))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (SYMM (ASSUME :args (_let_22))))) (let ((_let_74 (not _let_24))) (let ((_let_75 (not _let_25))) (let ((_let_76 (not _let_26))) (let ((_let_77 (_let_27))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_13 _let_12 _let_11 (not _let_14)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_60)) :args _let_59)) _let_58 :args (_let_14 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_11 0)) :args ((or _let_10 _let_51))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_77) (CONG (REFL :args _let_77) (REFL :args (_let_76)) (REFL :args (_let_75)) (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) (REFL :args (_let_52)) (REFL :args (_let_74)) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) (REFL :args (_let_13)) :args _let_35)) :args ((or _let_15 _let_22 _let_27 _let_76 _let_75 _let_52 _let_74 _let_13))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_17 1)) :args ((or _let_16 _let_41))) _let_40 :args (_let_16 false _let_17)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_68)))) (CONG _let_73 (SYMM _let_73) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args (APPLY_UF tptp.precedes)) (TRUE_INTRO (ASSUME :args (_let_28))))) :args (_let_28 _let_22 _let_68))) (CONG (REFL :args (_let_29)) (REFL :args (_let_23)) (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_35)) _let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_69 1)) :args ((or _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_30 _let_29 _let_69 (not _let_70)))) _let_39 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.shortest_path V1 V2 P) false)) (not (= (tptp.precedes E1 E2 P) false)) (tptp.tail_of BOUND_VARIABLE_1248)))) :args (_let_71)))) _let_72 :args (_let_70 false _let_71)) :args (_let_69 false _let_18 false _let_28 false _let_70)) :args (_let_68 false _let_69)) :args (_let_23 false _let_28 true _let_67)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 2)) _let_37 :args ((not _let_27) true _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_61 0)) :args ((or _let_26 _let_66))) _let_65 :args (_let_26 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_61 1)) :args ((or _let_25 _let_66))) _let_65 :args (_let_25 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_54 0)) :args ((or _let_24 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_13 _let_55 _let_54 (not _let_56)))) _let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 1)) :args ((or _let_43 _let_50))) _let_49 :args (_let_43 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_60)) :args _let_59)) _let_58 :args (_let_56 false _let_57)) :args (_let_54 false _let_7 false _let_43 false _let_56)) :args (_let_24 false _let_54)) _let_42 :args (_let_52 true _let_15 true _let_22 true _let_27 false _let_26 false _let_25 false _let_24 false _let_7)) :args (_let_51 true _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 0)) :args ((or _let_8 _let_50))) _let_49 :args (_let_8 false _let_44)) _let_42 :args (false false _let_14 true _let_11 false _let_8 false _let_7)) :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))) _let_6 _let_5 (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 $$unsorted)) (= (tptp.sequential E1 E2) (and (tptp.edge E1) (tptp.edge E2) (not (= E1 E2)) (= (tptp.head_of E1) (tptp.tail_of E2))))) (forall ((P $$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 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))) (tptp.precedes E1 E2 P))))) _let_4 _let_3 _let_2 (forall ((E1 $$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 $$unsorted)) (=> (tptp.path V1 V2 P) (= (tptp.length_of P) (tptp.number_of_in tptp.edges P)))) (forall ((V1 $$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)))) (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)))) (forall ((Things $$unsorted) (InThese $$unsorted)) (tptp.less_or_equal (tptp.number_of_in Things InThese) (tptp.number_of_in Things tptp.graph))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.57  )
% 0.20/0.57  % SZS output end Proof for GRA003+1
% 0.20/0.57  % cvc5---1.0.5 exiting
% 0.20/0.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------