%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRA002+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 00:00:29 EDT 2023

% Result   : Theorem 64.62s 64.85s
% Output   : Proof 64.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRA002+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun Aug 27 03:25:54 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.51  %----Proving TF0_NAR, FOF, or CNF
% 64.62/64.85  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.X090V64sOp/cvc5---1.0.5_15968.p...
% 64.62/64.85  ------- get file name : TPTP file name is GRA002+1
% 64.62/64.85  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15968.smt2...
% 64.62/64.85  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 64.62/64.85  --- Run --no-e-matching --full-saturate-quant at 5...
% 64.62/64.85  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 64.62/64.85  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 64.62/64.85  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 64.62/64.85  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 64.62/64.85  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 64.62/64.85  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 64.62/64.85  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 64.62/64.85  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 64.62/64.85  --- Run --relevant-triggers --full-saturate-quant at 5...
% 64.62/64.85  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 64.62/64.85  % SZS status Theorem for GRA002+1
% 64.62/64.85  % SZS output start Proof for GRA002+1
% 64.62/64.85  (
% 64.62/64.85  (let ((_let_1 (not (=> tptp.complete (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.shortest_path V1 V2 P) (tptp.less_or_equal (tptp.minus (tptp.length_of P) tptp.n1) (tptp.number_of_in tptp.triangles tptp.graph)))))))) (let ((_let_2 (forall ((Things $$unsorted) (InThese $$unsorted)) (tptp.less_or_equal (tptp.number_of_in Things InThese) (tptp.number_of_in Things tptp.graph))))) (let ((_let_3 (forall ((P $$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 $$unsorted)) (tptp.triangle E1 E2 E3))))) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.number_of_in tptp.triangles P)))))) (let ((_let_4 (forall ((V1 $$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_5 (forall ((E1 $$unsorted) (E2 $$unsorted) (E3 $$unsorted)) (= (tptp.triangle E1 E2 E3) (and (tptp.edge E1) (tptp.edge E2) (tptp.edge E3) (tptp.sequential E1 E2) (tptp.sequential E2 E3) (tptp.sequential E3 E1)))))) (let ((_let_6 (forall ((V1 $$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 $$unsorted)) (and (= (tptp.tail_of E3) (tptp.tail_of E1)) (= (tptp.head_of E3) (tptp.head_of E2))))) (not (tptp.precedes E2 E1 P))))))) (let ((_let_7 (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (=> (tptp.path V1 V2 P) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))))) (let ((_let_8 (forall ((P $$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 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))))))))) (let ((_let_9 (forall ((P $$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 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))) (tptp.precedes E1 E2 P))))))) (let ((_let_10 (forall ((E1 $$unsorted) (E2 $$unsorted)) (= (tptp.sequential E1 E2) (and (tptp.edge E1) (tptp.edge E2) (not (= E1 E2)) (= (tptp.head_of E1) (tptp.tail_of E2))))))) (let ((_let_11 (forall ((V1 $$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 ((_let_12 (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_13 (=> tptp.complete (forall ((V1 $$unsorted) (V2 $$unsorted)) (=> (and (tptp.vertex V1) (tptp.vertex V2) (not (= V1 V2))) (exists ((E $$unsorted)) (let ((_let_1 (tptp.tail_of E))) (let ((_let_2 (tptp.head_of E))) (and (tptp.edge E) (xor (and (= V1 _let_2) (= V2 _let_1)) (and (= V2 _let_2) (= V1 _let_1)))))))))))) (let ((_let_14 (forall ((E $$unsorted)) (=> (tptp.edge E) (and (tptp.vertex (tptp.head_of E)) (tptp.vertex (tptp.tail_of E))))))) (let ((_let_15 (forall ((E $$unsorted)) (=> (tptp.edge E) (not (= (tptp.head_of E) (tptp.tail_of E))))))) (let ((_let_16 (io_tptp.tail_of_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73))) (let ((_let_17 (io_tptp.tail_of_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_18 (= _let_17 _let_16))) (let ((_let_19 (not _let_18))) (let ((_let_20 (io_tptp.head_of_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73))) (let ((_let_21 (= _let_17 _let_20))) (let ((_let_22 (not _let_21))) (let ((_let_23 (and _let_22 _let_19))) (let ((_let_24 (not (io_tptp.on_path_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28)))) (let ((_let_25 (or _let_24 _let_23))) (let ((_let_26 (forall ((E $$unsorted)) (let ((_let_1 (io_tptp.tail_of_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (or (not (io_tptp.on_path_8 E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28)) (and (not (= (io_tptp.head_of_2 E) _let_1)) (not (= (io_tptp.tail_of_3 E) _let_1)))))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (not _let_26))) (let ((_let_29 (io_tptp.vertex_4 _let_17))) (let ((_let_30 (and _let_29 _let_28))) (let ((_let_31 (io_tptp.in_path_9 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_32 (not _let_31))) (let ((_let_33 (io_tptp.path_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_30))) (let ((_let_36 (forall ((b_V1 it_4_$$unsorted) (b_V2 it_4_$$unsorted) (b_P it_15_$$unsorted) (b_V it_4_$$unsorted)) (or (not (io_tptp.path_5 b_V1 b_V2 b_P)) (not (io_tptp.in_path_9 b_V b_P)) (and (io_tptp.vertex_4 b_V) (not (forall ((E $$unsorted)) (or (not (io_tptp.on_path_8 E b_P)) (and (not (= b_V (io_tptp.head_of_2 E))) (not (= b_V (io_tptp.tail_of_3 E)))))))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (V $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.in_path V P)) (and (tptp.vertex V) (not (forall ((E $$unsorted)) (or (not (tptp.on_path E P)) (and (not (= V (tptp.head_of E))) (not (= V (tptp.tail_of E)))))))))) _let_36))))))) (let ((_let_38 (io_tptp.head_of_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_39 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_40 (and _let_39 (io_tptp.in_path_9 _let_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28) _let_31))) (let ((_let_41 (io_tptp.on_path_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_34 _let_42 _let_40))) (let ((_let_44 (forall ((b_V1 it_4_$$unsorted) (b_V2 it_4_$$unsorted) (b_P it_15_$$unsorted) (E $$unsorted)) (or (not (io_tptp.path_5 b_V1 b_V2 b_P)) (not (io_tptp.on_path_8 E b_P)) (and (tptp.edge E) (io_tptp.in_path_9 (io_tptp.head_of_2 E) b_P) (io_tptp.in_path_9 (io_tptp.tail_of_3 E) b_P)))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (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_44))))))) (let ((_let_46 (forall ((E3 $$unsorted)) (not (tptp.triangle SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 E3))))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_49 (not _let_48))) (let ((_let_50 (io_tptp.on_path_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_42 _let_49 _let_47))) (let ((_let_53 (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (io_tptp.on_path_8 E1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28)) (not (io_tptp.on_path_8 E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28)) (not (tptp.sequential E1 E2)) (not (forall ((E3 $$unsorted)) (not (tptp.triangle E1 E2 E3)))))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (io_tptp.number_of_in_15 i_tptp.sequential_pairs_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_56 (io_tptp.number_of_in_15 i_tptp.triangles_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_57 (= _let_56 _let_55))) (let ((_let_58 (not _let_53))) (let ((_let_59 (or _let_34 _let_58 _let_57))) (let ((_let_60 (forall ((b_P it_15_$$unsorted) (b_V1 it_4_$$unsorted) (b_V2 it_4_$$unsorted)) (or (not (io_tptp.path_5 b_V1 b_V2 b_P)) (not (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (io_tptp.on_path_8 E1 b_P)) (not (io_tptp.on_path_8 E2 b_P)) (not (tptp.sequential E1 E2)) (not (forall ((E3 $$unsorted)) (not (tptp.triangle E1 E2 E3))))))) (= (io_tptp.number_of_in_15 i_tptp.sequential_pairs_16 b_P) (io_tptp.number_of_in_15 i_tptp.triangles_19 b_P)))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (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_60))))))) (let ((_let_62 (io_tptp.number_of_in_15 i_tptp.triangles_19 i_tptp.graph_20))) (let ((_let_63 (io_tptp.minus_18 (io_tptp.length_of_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28) i_tptp.n1_17))) (let ((_let_64 (io_tptp.less_or_equal_13 _let_63 _let_62))) (let ((_let_65 (= _let_63 _let_55))) (let ((_let_66 (io_tptp.less_or_equal_13 _let_56 _let_62))) (let ((_let_67 (not _let_57))) (let ((_let_68 (io_tptp.shortest_path_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_64))) (let ((_let_71 (not _let_64))) (let ((_let_72 (forall ((b_P it_15_$$unsorted) (b_V1 it_4_$$unsorted) (b_V2 it_4_$$unsorted)) (or (not (io_tptp.shortest_path_11 b_V1 b_V2 b_P)) (io_tptp.less_or_equal_13 (io_tptp.minus_18 (io_tptp.length_of_12 b_P) i_tptp.n1_17) (io_tptp.number_of_in_15 i_tptp.triangles_19 i_tptp.graph_20)))))) (let ((_let_73 (not _let_70))) (let ((_let_74 (not (=> tptp.complete _let_72)))) (let ((_let_75 (PREPROCESS :args ((= (not (=> tptp.complete (forall ((P $$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_74))))) (let ((_let_76 (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_77 (ASSUME :args (_let_1)))) (let ((_let_78 (MACRO_SR_PRED_TRANSFORM (NOT_IMPLIES_ELIM1 (EQ_RESOLVE _let_77 (TRANS _let_76 _let_75))) :args ((= tptp.complete true))))) (let ((_let_79 (EQ_RESOLVE _let_77 (TRANS _let_76 _let_75 (MACRO_SR_EQ_INTRO _let_78 :args (_let_74 SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_80 (or))) (let ((_let_81 (not _let_72))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_79) :args (_let_81))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_72))) (REFL :args (_let_73)) :args _let_80)) _let_79 :args (_let_73 true _let_72)))) (let ((_let_83 (or _let_34 _let_65))) (let ((_let_84 (forall ((b_V1 it_4_$$unsorted) (b_V2 it_4_$$unsorted) (b_P it_15_$$unsorted)) (or (not (io_tptp.path_5 b_V1 b_V2 b_P)) (= (io_tptp.number_of_in_15 i_tptp.sequential_pairs_16 b_P) (io_tptp.minus_18 (io_tptp.length_of_12 b_P) i_tptp.n1_17)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V1 $$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_84))))))) (let ((_let_86 (and _let_33 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30)) (forall ((b_P it_15_$$unsorted)) (or (not (io_tptp.path_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 b_P)) (io_tptp.less_or_equal_13 (io_tptp.length_of_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28) (io_tptp.length_of_12 b_P))))))) (let ((_let_87 (= _let_68 _let_86))) (let ((_let_88 (forall ((b_V1 it_4_$$unsorted) (b_V2 it_4_$$unsorted) (b_SP it_15_$$unsorted)) (= (io_tptp.shortest_path_11 b_V1 b_V2 b_SP) (and (io_tptp.path_5 b_V1 b_V2 b_SP) (not (= b_V1 b_V2)) (forall ((b_P it_15_$$unsorted)) (or (not (io_tptp.path_5 b_V1 b_V2 b_P)) (io_tptp.less_or_equal_13 (io_tptp.length_of_12 b_SP) (io_tptp.length_of_12 b_P))))))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (or (not (tptp.path V1 V2 P)) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))) _let_88))))))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 0)) (CONG (REFL :args (_let_70)) (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_80)) :args ((or _let_68 _let_70))) _let_82 :args (_let_68 true _let_70)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_86 0)) :args ((or _let_33 (not _let_86)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_87)) :args ((or _let_69 _let_86 (not _let_87)))) _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_86 false _let_68 false _let_87)) :args (_let_33 false _let_86)))) (let ((_let_92 (forall ((b_Things it_90_$$unsorted) (b_InThese it_15_$$unsorted)) (io_tptp.less_or_equal_13 (io_tptp.number_of_in_15 b_Things b_InThese) (io_tptp.number_of_in_15 b_Things i_tptp.graph_20))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_2)) 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it_4_$$unsorted) (b_V2 it_4_$$unsorted) (E1 $$unsorted) (E2 $$unsorted) (b_P it_15_$$unsorted) (BOUND_VARIABLE_1239 $$unsorted)) (or (not (io_tptp.shortest_path_11 b_V1 b_V2 b_P)) (not (io_tptp.precedes_10 E1 E2 b_P)) (and (or (not (= (io_tptp.tail_of_3 E1) (io_tptp.tail_of_3 BOUND_VARIABLE_1239))) (not (= (io_tptp.head_of_2 E2) (io_tptp.head_of_2 BOUND_VARIABLE_1239)))) (not (io_tptp.precedes_10 E2 E1 b_P))))))) (let ((_let_146 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_1239 $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (not (tptp.precedes E1 E2 P)) (and (or (not (= (tptp.tail_of E1) (tptp.tail_of BOUND_VARIABLE_1239))) (not (= (tptp.head_of E2) (tptp.head_of BOUND_VARIABLE_1239)))) (not (tptp.precedes E2 E1 P))))) _let_145))))))) (let ((_let_147 (io_tptp.precedes_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_148 (not _let_147))) (let ((_let_149 (or _let_49 _let_148))) (let ((_let_150 (and _let_49 _let_149))) (let ((_let_151 (or _let_34 _let_51 _let_42 _let_150 _let_142))) (let ((_let_152 (forall ((b_P it_15_$$unsorted) (b_V1 it_4_$$unsorted) (b_V2 it_4_$$unsorted) (BOUND_VARIABLE_1139 $$unsorted) (BOUND_VARIABLE_1137 $$unsorted) (BOUND_VARIABLE_1135 $$unsorted)) (or (not (io_tptp.path_5 b_V1 b_V2 b_P)) (not (io_tptp.on_path_8 BOUND_VARIABLE_1135 b_P)) (not (io_tptp.on_path_8 BOUND_VARIABLE_1137 b_P)) (and (not (tptp.sequential BOUND_VARIABLE_1135 BOUND_VARIABLE_1137)) (or (not (tptp.sequential BOUND_VARIABLE_1135 BOUND_VARIABLE_1139)) (not (io_tptp.precedes_10 BOUND_VARIABLE_1139 BOUND_VARIABLE_1137 b_P)))) (io_tptp.precedes_10 BOUND_VARIABLE_1135 BOUND_VARIABLE_1137 b_P))))) (let ((_let_153 (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_9 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QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.edge E) false))))) :args (_let_246)))) _let_247 :args (_let_245 false _let_246)) :args (_let_244 false _let_39 false _let_245)))) (let ((_let_249 (REFL :args (_let_105)))) (let ((_let_250 (MACRO_SR_PRED_INTRO :args ((= (not _let_244) _let_104))))) (let ((_let_251 (= _let_38 _let_20))) (let ((_let_252 (ASSUME :args (_let_21)))) (let ((_let_253 (SYMM _let_252))) (let ((_let_254 (ASSUME :args (_let_244)))) (let ((_let_255 (SYMM (FALSE_INTRO _let_254)))) (let ((_let_256 (ASSUME :args (_let_101)))) (let ((_let_257 (CONG (SYMM _let_256) :args _let_234))) (let ((_let_258 (= _let_38 _let_16))) (let ((_let_259 (ASSUME :args (_let_18)))) (let ((_let_260 (SYMM _let_259))) (let ((_let_261 (_let_23))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_261) (CONG (REFL :args _let_261) (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_80)) :args ((or _let_21 _let_18 _let_23))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_259 _let_256 _let_236) (SCOPE (TRANS _let_237 _let_257 (SYMM _let_260)) :args (_let_18 _let_101 _let_103))) _let_259 _let_254) :args (_let_244 _let_18 _let_103 _let_101)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_255 (TRUE_INTRO (SYMM (TRANS (SYMM (SYMM (ASSUME :args (_let_258)))) _let_260))))) :args (_let_258 _let_18 _let_244)) :args ((not (and _let_244 _let_18 _let_103 _let_101)) SB_LITERAL))) (CONG _let_250 (REFL :args (_let_19)) _let_241 _let_249 :args _let_80)) _let_248 _let_231 _let_243 :args (_let_19 true _let_104 false _let_103 false _let_101)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_252 _let_256 _let_236) (SCOPE (TRANS _let_237 _let_257 (SYMM _let_253)) :args (_let_21 _let_101 _let_103))) _let_252 _let_254) :args (_let_244 _let_21 _let_103 _let_101)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_255 (TRUE_INTRO (SYMM (TRANS (SYMM (SYMM (ASSUME :args (_let_251)))) _let_253))))) :args (_let_251 _let_21 _let_244)) :args ((not (and _let_244 _let_21 _let_103 _let_101)) SB_LITERAL))) (CONG _let_250 (REFL :args (_let_22)) _let_241 _let_249 :args _let_80)) _let_248 _let_231 _let_243 :args (_let_22 true _let_104 false _let_103 false _let_101)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 1)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_100)) :args _let_100) (REWRITE :args ((=> _let_28 (not (or _let_24 (and (not (= _let_20 _let_17)) (not (= _let_16 _let_17)))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_26))) (REFL :args (_let_27)) :args _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 1)) :args ((or _let_28 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_32 _let_30 (not _let_35)))) _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_40 2)) :args ((or _let_31 _let_99))) _let_98 :args (_let_31 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 _let_17 QUANTIFIERS_INST_E_MATCHING ((not (= (io_tptp.path_5 b_V1 b_V2 b_P) false)) (not (= (io_tptp.in_path_9 b_V b_P) false))))) :args (_let_36)))) _let_37 :args (_let_35 false _let_36)) :args (_let_30 false _let_33 false _let_31 false _let_35)) :args (_let_28 false _let_30)) :args (_let_27 true _let_26)) :args ((not _let_23) true _let_25)) :args (false true _let_18 true _let_21 true _let_23)) :args (_let_15 _let_14 _let_13 (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 $$unsorted)) (and (tptp.path (tptp.head_of E) V2 TP) (= P (tptp.path_cons E TP)))))))))) _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (= (tptp.length_of P) (tptp.number_of_in tptp.edges P)))) _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 64.62/64.85  )
% 64.62/64.85  % SZS output end Proof for GRA002+1
% 64.62/64.85  % cvc5---1.0.5 exiting
% 64.62/64.86  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------