%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.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 00:00:31 EDT 2023

% Result   : Theorem 0.18s 0.68s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.13/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n017.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 03:21:56 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.18/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.18/0.68  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.FeJMvxfjxt/cvc5---1.0.5_18780.p...
% 0.18/0.68  ------- get file name : TPTP file name is GRA004+1
% 0.18/0.68  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18780.smt2...
% 0.18/0.68  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.18/0.68  % SZS status Theorem for GRA004+1
% 0.18/0.68  % SZS output start Proof for GRA004+1
% 0.18/0.68  (
% 0.18/0.68  (let ((_let_1 (not (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.head_of E2))) (=> (and (tptp.shortest_path V1 V2 P) (tptp.precedes E1 E2 P)) (and (not (exists ((E3 $$unsorted)) (and (= (tptp.tail_of E3) (tptp.tail_of E1)) (= (tptp.head_of E3) (tptp.head_of E2))))) (not (= _let_1 (tptp.tail_of E1))) (not (= _let_1 (tptp.head_of E1)))))))))) (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 ((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 (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_8 (tptp.shortest_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_10 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (= _let_13 _let_12))) (let ((_let_15 (not _let_14))) (let ((_let_16 (and _let_15 _let_11))) (let ((_let_17 (not _let_9))) (let ((_let_18 (not _let_8))) (let ((_let_19 (or _let_18 _let_17 _let_16))) (let ((_let_20 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (= _let_20 _let_13))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or (not (= _let_20 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (not (= _let_13 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))))) (let ((_let_24 (and _let_23 _let_22 _let_15))) (let ((_let_25 (or _let_18 _let_17 _let_24))) (let ((_let_26 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_1328 $$unsorted)) (let ((_let_1 (tptp.head_of E2))) (let ((_let_2 (tptp.tail_of E1))) (or (not (tptp.shortest_path V1 V2 P)) (not (tptp.precedes E1 E2 P)) (and (or (not (= _let_2 (tptp.tail_of BOUND_VARIABLE_1328))) (not (= _let_1 (tptp.head_of BOUND_VARIABLE_1328)))) (not (= _let_1 _let_2)) (not (= _let_1 (tptp.head_of E1)))))))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_28) :args (_let_30)) (REWRITE :args ((=> _let_30 (not (or _let_18 _let_17 (and _let_23 (not (= _let_13 _let_20)) _let_15)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_29)) _let_28 :args (_let_27 true _let_26)))) (let ((_let_32 (REFL :args (_let_25)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_8))) :args _let_29)) :args ((or _let_8 _let_25))) _let_31 :args (_let_8 true _let_25)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_9))) :args _let_29)) :args ((or _let_9 _let_25))) _let_31 :args (_let_9 true _let_25)))) (let ((_let_35 (not _let_16))) (let ((_let_36 (and _let_23 _let_11))) (let ((_let_37 (or _let_18 _let_17 _let_36))) (let ((_let_38 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_1255 $$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_1255))) (not (= (tptp.head_of E2) (tptp.head_of BOUND_VARIABLE_1255)))) (not (tptp.precedes E2 E1 P))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 (not (= (tptp.precedes E1 E2 P) false)))) (let ((_let_42 (not (= (tptp.shortest_path V1 V2 P) false)))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_18 _let_17 _let_36 (not _let_37)))) _let_33 _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :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_7 QUANTIFIERS_INST_E_MATCHING (_let_42 _let_41 (tptp.tail_of BOUND_VARIABLE_1255)))) :args _let_40)) _let_39 :args (_let_37 false _let_38)) :args (_let_36 false _let_8 false _let_9 false _let_37)))) (let ((_let_44 (not _let_36))) (let ((_let_45 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_48 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_49 (and _let_48 _let_47 _let_46 _let_21))) (let ((_let_50 (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_51 (= _let_50 _let_49))) (let ((_let_52 (not _let_49))) (let ((_let_53 (_let_6))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 (not _let_50))) (let ((_let_56 (and _let_55 (or (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_11)))) (let ((_let_57 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_60 (not _let_59))) (let ((_let_61 (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_62 (not _let_61))) (let ((_let_63 (or _let_62 _let_60 _let_58 _let_56 _let_10))) (let ((_let_64 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1155 $$unsorted) (BOUND_VARIABLE_1153 $$unsorted) (BOUND_VARIABLE_1151 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.on_path BOUND_VARIABLE_1151 P)) (not (tptp.on_path BOUND_VARIABLE_1153 P)) (and (not (tptp.sequential BOUND_VARIABLE_1151 BOUND_VARIABLE_1153)) (or (not (tptp.sequential BOUND_VARIABLE_1151 BOUND_VARIABLE_1155)) (not (tptp.precedes BOUND_VARIABLE_1155 BOUND_VARIABLE_1153 P)))) (tptp.precedes BOUND_VARIABLE_1151 BOUND_VARIABLE_1153 P))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (and _let_57 _let_59 (= (not (forall ((E3 $$unsorted)) (or (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 E3)) (not (tptp.precedes E3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_67 (or _let_62 _let_17 _let_66))) (let ((_let_68 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1206 $$unsorted) (BOUND_VARIABLE_1204 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.precedes BOUND_VARIABLE_1204 BOUND_VARIABLE_1206 P)) (and (tptp.on_path BOUND_VARIABLE_1204 P) (tptp.on_path BOUND_VARIABLE_1206 P) (= (not (forall ((E3 $$unsorted)) (or (not (tptp.sequential BOUND_VARIABLE_1204 E3)) (not (tptp.precedes E3 BOUND_VARIABLE_1206 P))))) (not (tptp.sequential BOUND_VARIABLE_1204 BOUND_VARIABLE_1206)))))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (and _let_61 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (forall ((P $$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_71 (= _let_8 _let_70))) (let ((_let_72 (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_73 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_70 0)) :args ((or _let_61 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_71)) :args ((or _let_18 _let_70 (not _let_71)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :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_72))) _let_73 :args (_let_71 false _let_72)) :args (_let_70 false _let_8 false _let_71)) :args (_let_61 false _let_70)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_17 _let_62 _let_66 (not _let_67)))) _let_34 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :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_1204 BOUND_VARIABLE_1206 P) false))))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_66 false _let_9 false _let_61 false _let_67)))) (let ((_let_76 (not _let_66))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 1)) :args ((or _let_59 _let_76))) _let_75 :args (_let_59 false _let_66)))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 0)) :args ((or _let_57 _let_76))) _let_75 :args (_let_57 false _let_66)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 1)) :args ((or _let_11 _let_44))) _let_43 :args (_let_11 false _let_36)))) (let ((_let_80 (ASSUME :args (_let_9)))) (let ((_let_81 (ASSUME :args (_let_45)))) (let ((_let_82 (SYMM _let_81))) (let ((_let_83 (ASSUME :args (_let_11)))) (let ((_let_84 (and _let_48 (tptp.in_path _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in_path (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_85 (or _let_62 _let_60 _let_84))) (let ((_let_86 (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_87 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (_let_86))) (let ((_let_89 ((not (= (tptp.path V1 V2 P) false)) (not (= (tptp.on_path E P) false))))) (let ((_let_90 (and _let_47 (tptp.in_path _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in_path _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_91 (or _let_62 _let_58 _let_90))) (let ((_let_92 (not _let_48))) (let ((_let_93 (not _let_47))) (let ((_let_94 (_let_49))) (let ((_let_95 (not _let_23))) (let ((_let_96 (_let_24))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_17 _let_16 (not _let_19)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_39 :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_4 QUANTIFIERS_INST_E_MATCHING ((tptp.head_of BOUND_VARIABLE_1255) _let_42 _let_41))) :args _let_40))) _let_39 :args (_let_19 false _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 0)) :args ((or _let_15 _let_35))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_96) (CONG (REFL :args _let_96) (REFL :args (_let_95)) (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_29)) :args ((or _let_14 _let_21 _let_24 _let_95))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_94) (CONG (REFL :args _let_94) (REFL :args (_let_92)) (REFL :args (_let_93)) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) (REFL :args (_let_22)) :args _let_29)) :args ((or _let_22 _let_93 _let_92 _let_45 _let_49))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 0)) :args ((or _let_47 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_62 _let_58 _let_90 (not _let_91)))) _let_74 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :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_89)) :args _let_88)) _let_87 :args (_let_91 false _let_86)) :args (_let_90 false _let_61 false _let_57 false _let_91)) :args (_let_47 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_84 0)) :args ((or _let_48 (not _let_84)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_62 _let_60 _let_84 (not _let_85)))) _let_74 _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :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_89)) :args _let_88)) _let_87 :args (_let_85 false _let_86)) :args (_let_84 false _let_61 false _let_59 false _let_85)) :args (_let_48 false _let_84)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_80 _let_81 _let_83) :args (_let_9 _let_11 _let_45)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_83)) (CONG _let_82 (SYMM _let_82) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args (APPLY_UF tptp.precedes)) (TRUE_INTRO _let_80))) :args (_let_9 _let_45 _let_11)) :args ((not (and _let_9 _let_11 _let_45)) SB_LITERAL))) (CONG (REFL :args (_let_17)) (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) (REFL :args (_let_46)) :args _let_29)) _let_79 _let_34 :args (_let_46 true _let_10 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_51)) :args ((or _let_50 _let_52 (not _let_51)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_56 0)) :args ((or _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_10 _let_62 _let_58 _let_60 _let_56 (not _let_63)))) _let_79 _let_74 _let_78 _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :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 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.precedes BOUND_VARIABLE_1151 BOUND_VARIABLE_1153 P) true)) (tptp.precedes BOUND_VARIABLE_1155 BOUND_VARIABLE_1153 P) (not (= (tptp.path V1 V2 P) false))))) :args (_let_64))) _let_65 :args (_let_63 false _let_64)) :args (_let_56 true _let_10 false _let_61 false _let_57 false _let_59 false _let_63)) :args (_let_55 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.edge E1) (tptp.tail_of E2)))) :args _let_53))) _let_54 :args (_let_51 false _let_6)) :args (_let_52 true _let_50 false _let_51)) :args (_let_22 false _let_47 false _let_48 true _let_45 true _let_49)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 2)) _let_31 :args ((not _let_24) true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 0)) :args ((or _let_23 _let_44))) _let_43 :args (_let_23 false _let_36)) :args (_let_14 true _let_21 true _let_24 false _let_23)) :args (_let_35 false _let_14)) _let_34 _let_33 :args (false false _let_19 true _let_16 false _let_9 false _let_8)) :args ((forall ((E $$unsorted)) (=> (tptp.edge E) (not (= (tptp.head_of E) (tptp.tail_of E))))) (forall ((E $$unsorted)) (=> (tptp.edge E) (and (tptp.vertex (tptp.head_of E)) (tptp.vertex (tptp.tail_of E))))) (=> tptp.complete (forall ((V1 $$unsorted) (V2 $$unsorted)) (=> (and (tptp.vertex V1) (tptp.vertex V2) (not (= V1 V2))) (exists ((E $$unsorted)) (let ((_let_1 (tptp.tail_of E))) (let ((_let_2 (tptp.head_of E))) (and (tptp.edge E) (xor (and (= V1 _let_2) (= V2 _let_1)) (and (= V2 _let_2) (= V1 _let_1)))))))))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (and (tptp.vertex V1) (tptp.vertex V2) (exists ((E $$unsorted)) (and (tptp.edge E) (= V1 (tptp.tail_of E)) (or (and (= V2 (tptp.head_of E)) (= P (tptp.path_cons E tptp.empty))) (exists ((TP $$unsorted)) (and (tptp.path (tptp.head_of E) V2 TP) (= P (tptp.path_cons E TP)))))))) (tptp.path V1 V2 P))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (and (tptp.vertex V1) (tptp.vertex V2) (exists ((E $$unsorted)) (and (tptp.edge E) (= V1 (tptp.tail_of E)) (xor (and (= V2 (tptp.head_of E)) (= P (tptp.path_cons E tptp.empty))) (exists ((TP $$unsorted)) (and (tptp.path (tptp.head_of E) V2 TP) (= P (tptp.path_cons E TP)))))))))) _let_7 (forall ((V1 $$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 _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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.18/0.68  )
% 0.18/0.68  % SZS output end Proof for GRA004+1
% 0.18/0.68  % cvc5---1.0.5 exiting
% 0.18/0.69  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------