%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 00:00:30 EDT 2023

% Result   : Theorem 0.19s 0.54s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n026.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
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun Aug 27 04:01:19 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.19/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.54  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.rrQYFmR3WG/cvc5---1.0.5_17984.p...
% 0.19/0.54  ------- get file name : TPTP file name is GRA002+4
% 0.19/0.54  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17984.smt2...
% 0.19/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.54  % SZS status Theorem for GRA002+4
% 0.19/0.54  % SZS output start Proof for GRA002+4
% 0.19/0.54  (
% 0.19/0.54  (let ((_let_1 (not (=> tptp.complete (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.shortest_path V1 V2 P) (tptp.less_or_equal (tptp.minus (tptp.length_of P) tptp.n1) (tptp.number_of_in tptp.triangles tptp.graph)))))))) (let ((_let_2 (=> tptp.complete (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.shortest_path V1 V2 P) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.number_of_in tptp.triangles P))))))) (let ((_let_3 (forall ((Things $$unsorted) (InThese $$unsorted)) (tptp.less_or_equal (tptp.number_of_in Things InThese) (tptp.number_of_in Things tptp.graph))))) (let ((_let_4 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.minus (tptp.length_of P) tptp.n1)))))) (let ((_let_5 (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (=> (tptp.path V1 V2 P) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))))) (let ((_let_6 (tptp.number_of_in tptp.triangles tptp.graph))) (let ((_let_7 (tptp.minus (tptp.length_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) tptp.n1))) (let ((_let_8 (tptp.less_or_equal _let_7 _let_6))) (let ((_let_9 (tptp.number_of_in tptp.triangles SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (tptp.number_of_in tptp.sequential_pairs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.less_or_equal _let_9 _let_6))) (let ((_let_13 (= _let_7 _let_10))) (let ((_let_14 (tptp.shortest_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_8))) (let ((_let_17 (not _let_8))) (let ((_let_18 (forall ((P $$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 ((_let_19 (not _let_16))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (or))) (let ((_let_22 (not _let_18))) (let ((_let_23 (_let_22))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_23)) :args _let_23)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_18))) (REFL :args (_let_19)) :args _let_21)) (NOT_IMPLIES_ELIM2 _let_20) :args (_let_19 true _let_18)))) (let ((_let_25 (or _let_15 _let_11))) (let ((_let_26 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.number_of_in tptp.triangles P)))))) (let ((_let_27 (_let_26))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 0)) (CONG (REFL :args (_let_16)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_21)) :args ((or _let_14 _let_16))) _let_24 :args (_let_14 true _let_16)))) (let ((_let_29 (_let_3))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_13))) (let ((_let_34 (forall ((V1 $$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 ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (and _let_31 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (forall ((P $$unsorted)) (or (not (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 P)) (tptp.less_or_equal (tptp.length_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.length_of P))))))) (let ((_let_37 (= _let_14 _let_36))) (let ((_let_38 (forall ((V1 $$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_39 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (ASSUME :args (_let_12)))) (let ((_let_41 (ASSUME :args (_let_11)))) (let ((_let_42 (ASSUME :args (_let_13)))) (let ((_let_43 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_40 _let_41 _let_42 _let_43) :args (_let_17 _let_11 _let_13 _let_12)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_43)) (CONG (TRANS (SYMM (SYMM _let_42)) (SYMM (SYMM _let_41))) (REFL :args (_let_6)) :args (APPLY_UF tptp.less_or_equal)) (TRUE_INTRO _let_40))) :args (_let_12 _let_11 _let_13 _let_17)) :args ((not (and _let_17 _let_11 _let_13 _let_12)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_8))) (REFL :args ((not _let_11))) (REFL :args ((not _let_13))) (REFL :args ((not _let_12))) :args _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_13 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 0)) :args ((or _let_31 (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or _let_15 _let_36 (not _let_37)))) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :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_38))) _let_39 :args (_let_37 false _let_38)) :args (_let_36 false _let_14 false _let_37)) :args (_let_31 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.path V1 V2 P) false))))) :args (_let_34)))) _let_35 :args (_let_33 false _let_34)) :args (_let_13 false _let_31 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.triangles SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.number_of_in Things InThese)))) :args _let_29)) _let_30 :args (_let_12 false _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_15 _let_11 (not _let_25)))) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_27) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.shortest_path V1 V2 P) false))))) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_26 (not tptp.complete)))) (NOT_IMPLIES_ELIM1 _let_20) :args (_let_26 false tptp.complete)) :args (_let_25 false _let_26)) :args (_let_11 false _let_14 false _let_25)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_16 1)) _let_24 :args (_let_17 true _let_16)) :args (false false _let_13 false _let_12 false _let_11 true _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)))))))))) (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 $$unsorted)) (and (tptp.on_path E P) (or (= V (tptp.head_of E)) (= V (tptp.tail_of E)))))))) (forall ((E1 $$unsorted) (E2 $$unsorted)) (= (tptp.sequential E1 E2) (and (tptp.edge E1) (tptp.edge E2) (not (= E1 E2)) (= (tptp.head_of E1) (tptp.tail_of E2))))) (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.path V1 V2 P) (forall ((E1 $$unsorted) (E2 $$unsorted)) (=> (and (tptp.on_path E1 P) (tptp.on_path E2 P) (or (tptp.sequential E1 E2) (exists ((E3 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))) (tptp.precedes E1 E2 P))))) (forall ((P $$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 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))))))) _let_5 (forall ((V1 $$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 $$unsorted)) (and (= (tptp.tail_of E3) (tptp.tail_of E1)) (= (tptp.head_of E3) (tptp.head_of E2))))) (not (tptp.precedes E2 E1 P))))) (forall ((E1 $$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 $$unsorted)) (=> (tptp.path V1 V2 P) (= (tptp.length_of P) (tptp.number_of_in tptp.edges P)))) _let_4 (forall ((P $$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_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.54  )
% 0.19/0.54  % SZS output end Proof for GRA002+4
% 0.19/0.54  % cvc5---1.0.5 exiting
% 0.19/0.54  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------