%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRA009+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n008.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 00:00:33 EDT 2023

% Result   : Theorem 25.73s 26.24s
% Output   : Proof 25.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRA009+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun Aug 27 03:15:02 EDT 2023
% 0.14/0.34  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 25.73/26.24  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.CI1GCihQzH/cvc5---1.0.5_15292.p...
% 25.73/26.24  ------- get file name : TPTP file name is GRA009+2
% 25.73/26.24  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15292.smt2...
% 25.73/26.24  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.73/26.24  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.73/26.24  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.73/26.24  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.73/26.24  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.73/26.24  % SZS status Theorem for GRA009+2
% 25.73/26.24  % SZS output start Proof for GRA009+2
% 25.73/26.24  (
% 25.73/26.24  (let ((_let_1 (not (=> tptp.complete (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.shortest_path V1 V2 P) (forall ((E1 $$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)))))))))) (let ((_let_2 (forall ((E1 $$unsorted) (E2 $$unsorted) (E3 $$unsorted)) (= (tptp.triangle E1 E2 E3) (and (tptp.edge E1) (tptp.edge E2) (tptp.edge E3) (tptp.sequential E1 E2) (tptp.sequential E2 E3) (tptp.sequential E3 E1)))))) (let ((_let_3 (forall ((V1 $$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 $$unsorted)) (and (= (tptp.tail_of E3) (tptp.tail_of E1)) (= (tptp.head_of E3) (tptp.head_of E2))))) (not (tptp.precedes E2 E1 P))))))) (let ((_let_4 (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (=> (tptp.path V1 V2 P) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))))) (let ((_let_5 (forall ((P $$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 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))) (tptp.precedes E1 E2 P))))))) (let ((_let_6 (forall ((E1 $$unsorted) (E2 $$unsorted)) (= (tptp.sequential E1 E2) (and (tptp.edge E1) (tptp.edge E2) (not (= E1 E2)) (= (tptp.head_of E1) (tptp.tail_of E2))))))) (let ((_let_7 (=> tptp.complete (forall ((V1 $$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)))))))))))) (let ((_let_8 (forall ((E $$unsorted)) (=> (tptp.edge E) (and (tptp.vertex (tptp.head_of E)) (tptp.vertex (tptp.tail_of E))))))) (let ((_let_9 (forall ((E $$unsorted)) (=> (tptp.edge E) (not (= (tptp.head_of E) (tptp.tail_of E))))))) (let ((_let_10 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_11 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (= _let_11 _let_10))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_15 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_13))) (let ((_let_19 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_20 (not _let_19))) (let ((_let_21 (and _let_18 _let_20))) (let ((_let_22 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.shortest_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_21))) (let ((_let_27 (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_28 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (_let_27))) (let ((_let_30 (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_31 (not _let_30))) (let ((_let_32 (and _let_31 (or (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_33 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36 _let_34 _let_32 _let_22))) (let ((_let_40 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1148 $$unsorted) (BOUND_VARIABLE_1146 $$unsorted) (BOUND_VARIABLE_1144 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.on_path BOUND_VARIABLE_1144 P)) (not (tptp.on_path BOUND_VARIABLE_1146 P)) (and (not (tptp.sequential BOUND_VARIABLE_1144 BOUND_VARIABLE_1146)) (or (not (tptp.sequential BOUND_VARIABLE_1144 BOUND_VARIABLE_1148)) (not (tptp.precedes BOUND_VARIABLE_1148 BOUND_VARIABLE_1146 P)))) (tptp.precedes BOUND_VARIABLE_1144 BOUND_VARIABLE_1146 P))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_40))) (let ((_let_43 (not _let_32))) (let ((_let_44 (forall ((E3 $$unsorted)) (not (tptp.triangle SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 E3))))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_25 _let_36 _let_34 _let_31 _let_45))) (let ((_let_47 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1319 $$unsorted) (BOUND_VARIABLE_1317 $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (not (tptp.on_path BOUND_VARIABLE_1317 P)) (not (tptp.on_path BOUND_VARIABLE_1319 P)) (not (tptp.sequential BOUND_VARIABLE_1317 BOUND_VARIABLE_1319)) (not (forall ((E3 $$unsorted)) (not (tptp.triangle BOUND_VARIABLE_1317 BOUND_VARIABLE_1319 E3)))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_50 (ASSUME :args (_let_1)))) (let ((_let_51 (MACRO_SR_PRED_TRANSFORM (NOT_IMPLIES_ELIM1 (EQ_RESOLVE _let_50 _let_49)) :args ((= tptp.complete true))))) (let ((_let_52 (EQ_RESOLVE _let_50 (TRANS _let_49 (MACRO_SR_EQ_INTRO _let_51 :args ((not (=> tptp.complete _let_47)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_53 (or))) (let ((_let_54 (not _let_47))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_52) :args (_let_54))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_47))) (REFL :args (_let_48)) :args _let_53)) _let_52 :args (_let_48 true _let_47)))) (let ((_let_56 (REFL :args (_let_46)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 3)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_53)) :args ((or _let_30 _let_46))) _let_55 :args (_let_30 true _let_46)))) (let ((_let_58 (and _let_37 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (forall ((P $$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_59 (= _let_24 _let_58))) (let ((_let_60 (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_61 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_53)) :args ((or _let_24 _let_46))) _let_55 :args (_let_24 true _let_46)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 0)) :args ((or _let_37 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_59)) :args ((or _let_25 _let_58 (not _let_59)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :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_60))) _let_61 :args (_let_59 false _let_60)) :args (_let_58 false _let_24 false _let_59)) :args (_let_37 false _let_58)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 2)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_53)) :args ((or _let_33 _let_46))) _let_55 :args (_let_33 true _let_46)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_53)) :args ((or _let_35 _let_46))) _let_55 :args (_let_35 true _let_46)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_36 _let_34 _let_38 _let_22 _let_32 (not _let_39)))) _let_65 _let_64 _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_32 0)) :args ((or _let_31 _let_43))) _let_57 :args (_let_43 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :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_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_42)) _let_41 :args (_let_39 false _let_40)) :args (_let_22 false _let_35 false _let_33 false _let_37 true _let_32 false _let_39)))) (let ((_let_67 (and _let_12 _let_16))) (let ((_let_68 (= _let_11 _let_14))) (let ((_let_69 (= _let_15 _let_10))) (let ((_let_70 (and _let_69 _let_68))) (let ((_let_71 (= _let_67 _let_70))) (let ((_let_72 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_73 (not _let_72))) (let ((_let_74 (or _let_73 _let_71))) (let ((_let_75 (forall ((E $$unsorted)) (let ((_let_1 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_2 (tptp.tail_of E))) (let ((_let_3 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_4 (tptp.head_of E))) (or (not (tptp.edge E)) (= (and (= _let_4 _let_1) (= _let_2 _let_3)) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))) (let ((_let_76 (not _let_74))) (let ((_let_77 (not _let_75))) (let ((_let_78 (= _let_11 _let_15))) (let ((_let_79 (tptp.vertex _let_15))) (let ((_let_80 (not _let_79))) (let ((_let_81 (tptp.vertex _let_11))) (let ((_let_82 (not _let_81))) (let ((_let_83 (or _let_82 _let_80 _let_78 _let_77))) (let ((_let_84 (forall ((V1 $$unsorted) (V2 $$unsorted)) (or (not (tptp.vertex V1)) (not (tptp.vertex V2)) (= V1 V2) (not (forall ((E $$unsorted)) (let ((_let_1 (tptp.tail_of E))) (let ((_let_2 (tptp.head_of E))) (or (not (tptp.edge E)) (= (and (= V1 _let_2) (= V2 _let_1)) (and (= V2 _let_2) (= V1 _let_1)))))))))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_51 :args ((=> tptp.complete _let_84) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_86 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_89 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_90 (and _let_89 _let_88 _let_87 _let_78))) (let ((_let_91 (not _let_78))) (let ((_let_92 (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_93 (= _let_92 _let_90))) (let ((_let_94 (not _let_90))) (let ((_let_95 (_let_6))) (let ((_let_96 (ASSUME :args _let_95))) (let ((_let_97 (tptp.edge E2))) (let ((_let_98 (not _let_92))) (let ((_let_99 (and _let_98 (or (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_20)))) (let ((_let_100 (or _let_38 _let_34 _let_36 _let_99 _let_19))) (let ((_let_101 (and (or (not (= _let_15 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (not (= _let_11 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))) _let_20))) (let ((_let_102 (or _let_25 _let_23 _let_101))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_99 0)) :args ((or _let_98 (not _let_99)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_36 _let_34 _let_38 _let_19 _let_99 (not _let_100)))) _let_65 _let_64 _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 1)) :args ((or _let_20 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_25 _let_23 _let_101 (not _let_102)))) _let_62 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING ((tptp.tail_of BOUND_VARIABLE_1248) (tptp.precedes E2 E1 P) (not (= (tptp.shortest_path V1 V2 P) false))))) :args _let_29)) _let_28 :args (_let_102 false _let_27)) :args (_let_101 false _let_24 false _let_22 false _let_102)) :args (_let_20 false _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :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_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.path V1 V2 P) false)) (not (= (tptp.on_path BOUND_VARIABLE_1146 P) false)) (tptp.sequential BOUND_VARIABLE_1144 BOUND_VARIABLE_1148)))) :args _let_42)) _let_41 :args (_let_100 false _let_40)) :args (_let_99 false _let_35 false _let_33 false _let_37 true _let_19 false _let_100)) :args (_let_98 false _let_99)))) (let ((_let_104 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_105 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_106 (= _let_105 _let_104))) (let ((_let_107 (and _let_88 _let_89 _let_87 _let_106))) (let ((_let_108 (= _let_30 _let_107))) (let ((_let_109 ((tptp.sequential E1 E2)))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_108)) :args ((or _let_31 _let_107 (not _let_108)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_109)) :args _let_95))) _let_96 :args (_let_108 false _let_6)) :args (_let_107 false _let_30 false _let_108)))) (let ((_let_111 (not _let_107))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_107 1)) :args ((or _let_89 _let_111))) _let_110 :args (_let_89 false _let_107)))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_107 0)) :args ((or _let_88 _let_111))) _let_110 :args (_let_88 false _let_107)))) (let ((_let_114 (not _let_89))) (let ((_let_115 (not _let_88))) (let ((_let_116 (REFL :args (_let_115)))) (let ((_let_117 (REFL :args (_let_114)))) (let ((_let_118 (_let_90))) (let ((_let_119 (and (tptp.vertex _let_105) _let_79))) (let ((_let_120 (or _let_115 _let_119))) (let ((_let_121 (forall ((E $$unsorted)) (or (not (tptp.edge E)) (and (tptp.vertex (tptp.head_of E)) (tptp.vertex (tptp.tail_of E))))))) (let ((_let_122 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (_let_121))) (let ((_let_124 ((not (= (tptp.edge E) false))))) (let 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(MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_107 2)) :args ((or _let_87 _let_111))) _let_110 :args (_let_87 false _let_107)) _let_113 _let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_93)) :args ((or _let_92 _let_94 (not _let_93)))) _let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.edge E1) _let_97))) :args _let_95)) _let_96 :args (_let_93 false _let_6)) :args (_let_94 true _let_92 false _let_93)) :args (_let_91 true _let_86 false _let_88 false _let_89 true _let_90)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_85 :args (_let_11 _let_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.vertex V1) false)) (not (= (tptp.vertex V2) false))))) :args (_let_84)))) _let_85 :args (_let_83 false _let_84)) :args (_let_77 false _let_81 false _let_79 true _let_78 false _let_83)) :args (_let_76 true _let_75)))) (let ((_let_129 (= _let_104 _let_11))) (let ((_let_130 (= _let_105 _let_14))) (let ((_let_131 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_132 (not _let_131))) (let ((_let_133 (and _let_88 _let_72 _let_132 _let_130))) (let ((_let_134 (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_135 (= _let_134 _let_133))) (let ((_let_136 (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_137 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_138 (not _let_137))) (let ((_let_139 (and _let_89 _let_72 _let_138 _let_68))) (let ((_let_140 (= _let_136 _let_139))) (let ((_let_141 (not _let_70))) (let ((_let_142 (not _let_129))) (let ((_let_143 (or _let_114 _let_142))) (let ((_let_144 (forall ((E $$unsorted)) (or (not (tptp.edge E)) (not (= (tptp.head_of E) (tptp.tail_of E))))))) (let ((_let_145 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_let_128 :args (_let_72 true _let_74)))) (let ((_let_161 (tptp.triangle SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_162 (= _let_161 _let_155))) (let ((_let_163 (not _let_155))) (let ((_let_164 (_let_2))) (let ((_let_165 (ASSUME :args _let_164))) (let ((_let_166 (_let_44))) (let ((_let_167 (REFL :args (_let_73)))) (let ((_let_168 (_let_156))) (let ((_let_169 (APPLY_UF tptp.sequential))) (let ((_let_170 (_let_139))) (let ((_let_171 (ASSUME :args (_let_30)))) (let ((_let_172 (ASSUME :args (_let_137)))) (let ((_let_173 (ASSUME :args (_let_153)))) (let ((_let_174 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args (_let_71)) :args ((or _let_67 _let_70 _let_71))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_171 _let_172 _let_173) :args (_let_30 _let_153 _let_137)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_173)) (CONG (REFL :args 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(SYMM (TRUE_INTRO (ASSUME :args (_let_136)))) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (SYMM (ASSUME :args (_let_131))) :args _let_169) (FALSE_INTRO (ASSUME :args (_let_98))))) :args (_let_98 _let_131 _let_136))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_98) _let_92))) (REFL :args (_let_132)) (REFL :args (_let_158)) :args _let_53)) _let_103 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_168) (CONG (REFL :args _let_168) _let_167 _let_116 (MACRO_SR_PRED_INTRO :args ((= (not _let_132) _let_131))) (REFL :args (_let_159)) :args _let_53)) :args ((or _let_115 _let_73 _let_159 _let_131 _let_156))) _let_160 _let_113 (REORDERING (CNF_EQUIV_POS2 :args (_let_157)) :args ((or _let_154 (not _let_156) (not _let_157)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_109)) :args _let_95))) _let_96 :args (_let_157 false _let_6)) (REORDERING (CNF_AND_NEG :args (_let_155)) :args ((or _let_31 _let_115 _let_114 _let_73 _let_158 (not _let_154) _let_155))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_162)) :args ((or _let_161 _let_163 (not _let_162)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_166) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_166)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 4)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_53)) :args ((or _let_44 _let_46))) _let_55 :args (_let_44 true _let_46)) :args ((not _let_161) false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_165 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING ((tptp.sequential E2 E3) (tptp.sequential E3 E1)))) :args _let_164)) _let_165 :args (_let_162 false _let_2)) :args (_let_163 true _let_161 false _let_162)) _let_160 _let_112 _let_113 _let_57 :args ((or _let_159 _let_158) true _let_92 false _let_131 false _let_72 false _let_88 true _let_156 false _let_157 true _let_154 true _let_155 false _let_72 false _let_89 false _let_88 false _let_30)) (REORDERING (CNF_EQUIV_POS1 :args (_let_135)) :args ((or _let_133 _let_153 (not _let_135)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING _let_152)) :args _let_95)) _let_96 :args (_let_135 false _let_6)) (REORDERING (CNF_AND_POS :args (_let_133 3)) :args ((or _let_130 (not _let_133)))) (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_148)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_149 _let_151 _let_150) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM (SYMM _let_151)) (SYMM _let_150) :args (=)) (FALSE_INTRO _let_149))) :args (_let_142 _let_106 _let_68))) :args (_let_106 _let_142 _let_68))) :args (true _let_148)) (CONG (REFL :args ((not _let_106))) (MACRO_SR_PRED_INTRO :args ((= (not _let_142) _let_129))) _let_147 (REFL :args ((not _let_130))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_143)) :args ((or _let_114 _let_142 (not _let_143)))) _let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_145 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.edge E) false))))) :args (_let_144)))) _let_145 :args (_let_143 false _let_144)) :args (_let_142 false _let_89 false _let_143)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_107 3)) :args ((or _let_106 _let_111))) _let_110 :args (_let_106 false _let_107)) (REORDERING (CNF_AND_POS :args (_let_70 1)) :args ((or _let_68 _let_141))) (REORDERING (CNF_AND_POS :args (_let_70 0)) :args ((or _let_69 _let_141))) :args (_let_141 false _let_30 false _let_137 false _let_72 false _let_89 true _let_139 false _let_140 true _let_136 true _let_134 false _let_135 true _let_133 true _let_130 true _let_129 false _let_106 false _let_68 false _let_69)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_74 1)) _let_128 :args ((not _let_71) true _let_74)) :args (_let_67 true _let_70 true _let_71)))) (let ((_let_175 (not _let_67))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_13 _let_17 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 1)) :args ((or _let_16 _let_175))) _let_174 :args (_let_16 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 0)) :args ((or _let_12 _let_175))) _let_174 :args (_let_12 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 0)) :args ((or _let_18 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_23 _let_21 (not _let_26)))) _let_62 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_29)) _let_28 :args (_let_26 false _let_27)) :args (_let_21 false _let_24 false _let_22 false _let_26)) :args (_let_18 false _let_21)) :args (false false _let_16 false _let_12 false _let_18)) :args (_let_9 _let_8 _let_7 (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 $$unsorted)) (and (tptp.on_path E P) (or (= V (tptp.head_of E)) (= V (tptp.tail_of E)))))))) _let_6 _let_5 (forall ((P $$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 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))))))) _let_4 _let_3 _let_2 (forall ((V1 $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.73/26.24  )
% 25.73/26.24  % SZS output end Proof for GRA009+2
% 25.73/26.24  % cvc5---1.0.5 exiting
% 25.73/26.25  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------