%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRA012+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n004.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 00:00:34 EDT 2023

% Result   : Theorem 98.32s 98.60s
% Output   : Proof 98.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRA012+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n004.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun Aug 27 03:40:07 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 98.32/98.60  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.hnDDDPmFfk/cvc5---1.0.5_16742.p...
% 98.32/98.60  ------- get file name : TPTP file name is GRA012+1
% 98.32/98.60  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16742.smt2...
% 98.32/98.60  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 98.32/98.60  --- Run --no-e-matching --full-saturate-quant at 5...
% 98.32/98.60  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 98.32/98.60  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 98.32/98.60  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 98.32/98.60  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 98.32/98.60  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 98.32/98.60  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 98.32/98.60  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 98.32/98.60  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 98.32/98.60  --- Run --relevant-triggers --full-saturate-quant at 5...
% 98.32/98.60  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 98.32/98.60  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 98.32/98.60  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 98.32/98.60  --- Run --no-cbqi --full-saturate-quant at 10...
% 98.32/98.60  --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 98.32/98.60  % SZS status Theorem for GRA012+1
% 98.32/98.60  % SZS output start Proof for GRA012+1
% 98.32/98.60  (
% 98.32/98.60  (let ((_let_1 (not (=> tptp.complete (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.shortest_path V1 V2 P) (= (tptp.number_of_in tptp.triangles P) (tptp.minus (tptp.length_of P) tptp.n1)))))))) (let ((_let_2 (forall ((P $$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 $$unsorted)) (tptp.triangle E1 E2 E3))))) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.number_of_in tptp.triangles P)))))) (let ((_let_3 (forall ((V1 $$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_4 (forall ((E1 $$unsorted) (E2 $$unsorted) (E3 $$unsorted)) (= (tptp.triangle E1 E2 E3) (and (tptp.edge E1) (tptp.edge E2) (tptp.edge E3) (tptp.sequential E1 E2) (tptp.sequential E2 E3) (tptp.sequential E3 E1)))))) (let ((_let_5 (forall ((V1 $$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 $$unsorted)) (and (= (tptp.tail_of E3) (tptp.tail_of E1)) (= (tptp.head_of E3) (tptp.head_of E2))))) (not (tptp.precedes E2 E1 P))))))) (let ((_let_6 (forall ((V1 $$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 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))) (tptp.precedes E1 E2 P))))))) (let ((_let_8 (forall ((E1 $$unsorted) (E2 $$unsorted)) (= (tptp.sequential E1 E2) (and (tptp.edge E1) (tptp.edge E2) (not (= E1 E2)) (= (tptp.head_of E1) (tptp.tail_of E2))))))) (let ((_let_9 (=> tptp.complete (forall ((V1 $$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_10 (forall ((E $$unsorted)) (=> (tptp.edge E) (and (tptp.vertex (tptp.head_of E)) (tptp.vertex (tptp.tail_of E))))))) (let ((_let_11 (forall ((E $$unsorted)) (=> (tptp.edge E) (not (= (tptp.head_of E) (tptp.tail_of E))))))) (let ((_let_12 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43))) (let ((_let_13 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43))) (let ((_let_14 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_15 (= _let_14 _let_13))) (let ((_let_16 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43))) (let ((_let_17 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_18 (= _let_17 _let_16))) (let ((_let_19 (not _let_15))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43))) (let ((_let_21 (not _let_18))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43))) (let ((_let_23 (not _let_12))) (let ((_let_24 (or _let_23 _let_22 _let_21 _let_20 _let_19))) (let ((_let_25 (and _let_15 _let_18))) (let ((_let_26 (= _let_14 _let_16))) (let ((_let_27 (= _let_17 _let_13))) (let ((_let_28 (and _let_27 _let_26))) (let ((_let_29 (= _let_28 _let_25))) (let ((_let_30 (or _let_23 _let_29))) (let ((_let_31 (forall ((E $$unsorted)) (let ((_let_1 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_2 (tptp.tail_of E))) (let ((_let_3 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_4 (tptp.head_of E))) (or (not (tptp.edge E)) (= (and (= _let_4 _let_1) (= _let_2 _let_3)) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (not _let_31))) (let ((_let_34 (= _let_17 _let_14))) (let ((_let_35 (tptp.vertex _let_14))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.vertex _let_17))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36 _let_34 _let_33))) (let ((_let_40 (forall ((V1 $$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_41 (TRUST_SUBS_EQ (ASSUME :args (_let_8)) :args ((= tptp.sequential (lambda ((BOUND_VARIABLE_1302 $$unsorted) (BOUND_VARIABLE_1303 $$unsorted)) (and (tptp.edge BOUND_VARIABLE_1302) (tptp.edge BOUND_VARIABLE_1303) (not (= BOUND_VARIABLE_1302 BOUND_VARIABLE_1303)) (= (tptp.head_of BOUND_VARIABLE_1302) (tptp.tail_of BOUND_VARIABLE_1303))))))))) (let ((_let_42 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.shortest_path (lambda ((BOUND_VARIABLE_1419 $$unsorted) (BOUND_VARIABLE_1420 $$unsorted) (BOUND_VARIABLE_1421 $$unsorted)) (and (tptp.path BOUND_VARIABLE_1419 BOUND_VARIABLE_1420 BOUND_VARIABLE_1421) (not (= BOUND_VARIABLE_1419 BOUND_VARIABLE_1420)) (forall ((P $$unsorted)) (or (not (tptp.path BOUND_VARIABLE_1419 BOUND_VARIABLE_1420 P)) (tptp.less_or_equal (tptp.length_of BOUND_VARIABLE_1421) (tptp.length_of P))))))))))) (let ((_let_43 (AND_INTRO _let_42 _let_41))) (let ((_let_44 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO _let_43 :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.triangle (lambda ((BOUND_VARIABLE_1493 $$unsorted) (BOUND_VARIABLE_1494 $$unsorted) (BOUND_VARIABLE_1495 $$unsorted)) (and (tptp.edge BOUND_VARIABLE_1493) (tptp.edge BOUND_VARIABLE_1494) (tptp.edge BOUND_VARIABLE_1495) (not (= BOUND_VARIABLE_1493 BOUND_VARIABLE_1494)) (= (tptp.head_of BOUND_VARIABLE_1493) (tptp.tail_of BOUND_VARIABLE_1494)) (not (= BOUND_VARIABLE_1494 BOUND_VARIABLE_1495)) (= (tptp.head_of BOUND_VARIABLE_1494) (tptp.tail_of BOUND_VARIABLE_1495)) (not (= BOUND_VARIABLE_1493 BOUND_VARIABLE_1495)) (= (tptp.head_of BOUND_VARIABLE_1495) (tptp.tail_of BOUND_VARIABLE_1493))))))))) (let ((_let_45 (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_46 (ASSUME :args (_let_1)))) (let ((_let_47 (AND_INTRO (MACRO_SR_PRED_TRANSFORM (NOT_IMPLIES_ELIM1 (EQ_RESOLVE _let_46 _let_45)) :args ((= tptp.complete true))) _let_44 _let_42 _let_41))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_47 :args ((=> tptp.complete _let_40) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_49 (not _let_34))) (let ((_let_50 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_51 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_52 _let_50 _let_49))) (let ((_let_56 (and _let_55 (or _let_54 _let_52 _let_50 _let_49 (not (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_57 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_58 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_61 (not _let_60))) (let ((_let_62 (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_63 _let_61 _let_59 _let_56 _let_57))) (let ((_let_65 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1139 $$unsorted) (BOUND_VARIABLE_1137 $$unsorted) (BOUND_VARIABLE_1135 $$unsorted)) (let ((_let_1 (tptp.head_of BOUND_VARIABLE_1135))) (let ((_let_2 (not (tptp.edge BOUND_VARIABLE_1135)))) (or (not (tptp.path V1 V2 P)) (not (tptp.on_path BOUND_VARIABLE_1135 P)) (not (tptp.on_path BOUND_VARIABLE_1137 P)) (and (or _let_2 (not (tptp.edge BOUND_VARIABLE_1137)) (= BOUND_VARIABLE_1135 BOUND_VARIABLE_1137) (not (= _let_1 (tptp.tail_of BOUND_VARIABLE_1137)))) (or _let_2 (not (tptp.edge BOUND_VARIABLE_1139)) (= BOUND_VARIABLE_1135 BOUND_VARIABLE_1139) (not (= _let_1 (tptp.tail_of BOUND_VARIABLE_1139))) (not (tptp.precedes BOUND_VARIABLE_1139 BOUND_VARIABLE_1137 P)))) (tptp.precedes BOUND_VARIABLE_1135 BOUND_VARIABLE_1137 P))))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_41 :args ((forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1139 $$unsorted) (BOUND_VARIABLE_1137 $$unsorted) (BOUND_VARIABLE_1135 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.on_path BOUND_VARIABLE_1135 P)) (not (tptp.on_path BOUND_VARIABLE_1137 P)) (and (not (tptp.sequential BOUND_VARIABLE_1135 BOUND_VARIABLE_1137)) (or (not (tptp.sequential BOUND_VARIABLE_1135 BOUND_VARIABLE_1139)) (not (tptp.precedes BOUND_VARIABLE_1139 BOUND_VARIABLE_1137 P)))) (tptp.precedes BOUND_VARIABLE_1135 BOUND_VARIABLE_1137 P))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_67 (_let_65))) (let ((_let_68 (not _let_57))) (let ((_let_69 (and (or (not (= _let_14 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (not (= _let_17 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) _let_68))) (let ((_let_70 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_71 (not _let_70))) (let ((_let_72 (forall ((P $$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_73 (not _let_72))) (let ((_let_74 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_75 (or _let_63 _let_74 _let_73 _let_71 _let_69))) (let ((_let_76 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_1239 $$unsorted)) (or (not (tptp.path V1 V2 P)) (= V1 V2) (not (forall ((P $$unsorted)) (or (not (tptp.path V1 V2 P)) (tptp.less_or_equal (tptp.length_of P) (tptp.length_of P))))) (not (tptp.precedes E1 E2 P)) (and (or (not (= (tptp.tail_of E1) (tptp.tail_of BOUND_VARIABLE_1239))) (not (= (tptp.head_of E2) (tptp.head_of BOUND_VARIABLE_1239)))) (not (tptp.precedes E2 E1 P))))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_43 :args ((forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_1239 $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (not (tptp.precedes E1 E2 P)) (and (or (not (= (tptp.tail_of E1) (tptp.tail_of BOUND_VARIABLE_1239))) (not (= (tptp.head_of E2) (tptp.head_of BOUND_VARIABLE_1239)))) (not (tptp.precedes E2 E1 P))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_78 (_let_76))) (let ((_let_79 (tptp.precedes E2 E1 P))) (let ((_let_80 (not (= (tptp.path V1 V2 P) false)))) (let ((_let_81 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_82 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_83 (= _let_81 _let_82))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_52 _let_54 _let_50 _let_84))) (let ((_let_86 (and _let_85 (or _let_52 (not (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) (not (= (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) _let_81)) (not (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_87 (or _let_63 _let_59 _let_61 _let_86 _let_70))) (let ((_let_88 (not _let_86))) (let ((_let_89 (not _let_85))) (let ((_let_90 (forall ((E3 $$unsorted)) (or (not (tptp.edge E3)) (= E3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (not (= (tptp.tail_of E3) (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (= E3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) (not (= (tptp.head_of E3) (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))))) (let ((_let_91 (not _let_90))) (let ((_let_92 (not _let_50))) (let ((_let_93 (and _let_51 _let_53 _let_92 _let_83 _let_91))) (let ((_let_94 (or _let_59 _let_61 _let_52 _let_54 _let_50 _let_84 _let_93))) (let ((_let_95 (forall ((E1 $$unsorted) (E2 $$unsorted)) (let ((_let_1 (= (tptp.head_of E1) (tptp.tail_of E2)))) (let ((_let_2 (= E1 E2))) (let ((_let_3 (tptp.edge E2))) (let ((_let_4 (tptp.edge E1))) (or (not (tptp.on_path E1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.on_path E2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not _let_4) (not _let_3) _let_2 (not _let_1) (and _let_4 _let_3 (not _let_2) _let_1 (not (forall ((E3 $$unsorted)) (or (not (tptp.edge E3)) (= E2 E3) (not (= (tptp.head_of E2) (tptp.tail_of E3))) (= E1 E3) (not (= (tptp.head_of E3) (tptp.tail_of E1))))))))))))))) (let ((_let_96 (not _let_94))) (let ((_let_97 (tptp.number_of_in tptp.sequential_pairs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_98 (tptp.number_of_in tptp.triangles SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_99 (= _let_98 _let_97))) (let ((_let_100 (not _let_95))) (let ((_let_101 (or _let_63 _let_100 _let_99))) (let ((_let_102 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (forall ((E1 $$unsorted) (E2 $$unsorted)) (let ((_let_1 (= (tptp.head_of E1) (tptp.tail_of E2)))) (let ((_let_2 (= E1 E2))) (let ((_let_3 (tptp.edge E2))) (let 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false _let_154)) :args (_let_152 false _let_153)) :args (_let_150 true _let_29 true _let_25 true _let_28 true _let_15 true _let_34 true _let_26 false _let_152)) :args (_let_149 true _let_27)) _let_148 :args (_let_25 true _let_28 true _let_29)))) (let ((_let_162 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_25 1)) :args ((or _let_18 _let_158))) _let_161 :args (_let_18 false _let_25)))) (let ((_let_163 (_let_93))) (let ((_let_164 (_let_90))) (let ((_let_165 (= _let_82 _let_17))) (let ((_let_166 (not _let_22))) (let ((_let_167 (not _let_165))) (let ((_let_168 (or _let_54 _let_167))) (let ((_let_169 (forall ((E $$unsorted)) (or (not (tptp.edge E)) (not (= (tptp.head_of E) (tptp.tail_of E))))))) (let ((_let_170 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_171 (and _let_18 _let_22))) (let ((_let_172 (_let_18 _let_22))) (let ((_let_173 (ASSUME :args (_let_18)))) (let ((_let_174 (SYMM _let_173))) (let ((_let_175 (APPLY_UF tptp.tail_of))) (let ((_let_176 (ASSUME :args (_let_22)))) (let ((_let_177 (not _let_20))) (let ((_let_178 (and _let_26 _let_18))) (let ((_let_179 (_let_26 _let_18))) (let ((_let_180 (ASSUME :args (_let_26)))) (let ((_let_181 (_let_20))) (let ((_let_182 (ASSUME :args _let_181))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_19 _let_21 _let_22 _let_20 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_182 (SCOPE (CONG (SYMM (SYMM _let_182)) :args _let_175) :args _let_181)) :args _let_181)) :args ((or _let_26 _let_177))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_178)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_180 _let_173) (SCOPE (TRANS (SYMM _let_174) (SYMM (SYMM (SYMM _let_180)))) :args _let_179)) :args _let_179)) :args (true _let_178)) :args ((or _let_34 _let_151 _let_21))) _let_137 _let_162 :args (_let_151 true _let_34 false _let_18)) :args (_let_177 true _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_171)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_173 _let_176) (SCOPE (TRANS (CONG (SYMM (SYMM _let_176)) :args _let_175) _let_174) :args _let_172)) :args _let_172)) :args (true _let_171)) :args ((or _let_165 _let_21 _let_166))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_168)) :args ((or _let_54 _let_167 (not _let_168)))) _let_130 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_170 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.edge E) false))))) :args (_let_169)))) _let_170 :args (_let_168 false _let_169)) :args (_let_167 false _let_53 false _let_168)) _let_162 :args (_let_166 true _let_165 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_164) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43 QUANTIFIERS_INST_CBQI_PROP)) :args _let_164))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_163) (CONG (REFL :args _let_163) (REFL :args (_let_52)) (REFL :args (_let_54)) (MACRO_SR_PRED_INTRO :args ((= (not _let_92) _let_50))) (REFL :args (_let_84)) (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_90))) :args _let_113)) :args ((or _let_52 _let_54 _let_50 _let_84 _let_90 _let_93))) _let_131 _let_130 _let_129 _let_128 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_94 6)) _let_126 :args ((not _let_93) true _let_94)) :args (_let_90 false _let_51 false _let_53 true _let_50 false _let_83 true _let_93)) :args (_let_24 false _let_90)) _let_162 (MACRO_RESOLUTION_TRUST _let_159 _let_161 :args (_let_15 false _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG (REFL :args (_let_30)) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_12))) :args _let_113)) :args ((or _let_12 _let_30))) _let_147 :args (_let_12 true _let_30)) :args (false true _let_20 true _let_22 false _let_24 false _let_18 false _let_15 false _let_12)) :args (_let_11 _let_10 _let_9 (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_8 _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 _let_5 _let_4 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (= (tptp.length_of P) (tptp.number_of_in tptp.edges P)))) _let_3 _let_2 (forall ((Things $$unsorted) (InThese $$unsorted)) (tptp.less_or_equal (tptp.number_of_in Things InThese) (tptp.number_of_in Things tptp.graph))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 98.32/98.60  )
% 98.32/98.60  % SZS output end Proof for GRA012+1
% 98.32/98.61  % cvc5---1.0.5 exiting
% 98.32/98.61  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------