%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 21:50:52 EDT 2023

% Result   : Theorem 0.20s 0.62s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % 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   : Tue Aug 29 05:07:35 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.62  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.dwKrHk7qzk/cvc5---1.0.5_2070.p...
% 0.20/0.62  ------- get file name : TPTP file name is SWV370+1
% 0.20/0.62  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2070.smt2...
% 0.20/0.62  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.62  % SZS status Theorem for SWV370+1
% 0.20/0.62  % SZS output start Proof for SWV370+1
% 0.20/0.62  (
% 0.20/0.62  (let ((_let_1 (not (forall ((U $$unsorted)) (=> (forall ((V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.triple V U W))) (= (tptp.contains_cpq _let_1 X) (tptp.contains_pq (tptp.i _let_1) X)))) (forall ((Y $$unsorted) (Z $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (let ((_let_1 (tptp.triple Y (tptp.insert_slb U (tptp.pair X1 X2)) Z))) (= (tptp.contains_cpq _let_1 X3) (tptp.contains_pq (tptp.i _let_1) X3))))))))) (let ((_let_2 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.i (tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)) (tptp.insert_pq (tptp.i (tptp.triple U V W)) X))))) (let ((_let_3 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.contains_cpq (tptp.triple U V W) X) (tptp.contains_slb V X))))) (let ((_let_4 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.contains_slb (tptp.insert_slb U (tptp.pair V X)) W) (or (tptp.contains_slb U W) (= V W)))))) (let ((_let_5 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.contains_pq (tptp.insert_pq U V) W) (or (tptp.contains_pq U W) (= V W)))))) (let ((_let_6 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_7 (tptp.i _let_6))) (let ((_let_8 (tptp.insert_pq _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (tptp.insert_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_10 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_11 (tptp.i _let_10))) (let ((_let_12 (= _let_11 _let_8))) (let ((_let_13 (tptp.contains_pq _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_14 (tptp.contains_pq _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (_let_2))) (let ((_let_16 (ASSUME :args _let_15))) (let ((_let_17 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)))) :args _let_15)) _let_16 :args (_let_12 false _let_2)))) (let ((_let_18 (tptp.contains_cpq _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (= _let_18 _let_13))) (let ((_let_20 (tptp.contains_slb _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (= _let_18 _let_20))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (tptp.contains_pq _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_24 (or _let_23 _let_22))) (let ((_let_25 (= _let_14 _let_24))) (let ((_let_26 (tptp.contains_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_27 (or _let_26 _let_22))) (let ((_let_28 (= _let_20 _let_27))) (let ((_let_29 (forall ((V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.triple V SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 W))) (= (tptp.contains_cpq _let_1 X) (tptp.contains_pq (tptp.i _let_1) X)))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_19))) (let ((_let_32 (forall ((U $$unsorted) (BOUND_VARIABLE_1509 $$unsorted) (BOUND_VARIABLE_1507 $$unsorted) (BOUND_VARIABLE_1505 $$unsorted) (BOUND_VARIABLE_1503 $$unsorted) (BOUND_VARIABLE_1501 $$unsorted)) (let ((_let_1 (tptp.triple BOUND_VARIABLE_1501 (tptp.insert_slb U (tptp.pair BOUND_VARIABLE_1505 BOUND_VARIABLE_1507)) BOUND_VARIABLE_1503))) (or (not (forall ((V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.triple V U W))) (= (tptp.contains_cpq _let_1 X) (tptp.contains_pq (tptp.i _let_1) X))))) (= (tptp.contains_cpq _let_1 BOUND_VARIABLE_1509) (tptp.contains_pq (tptp.i _let_1) BOUND_VARIABLE_1509))))))) (let ((_let_33 (not _let_31))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (or))) (let ((_let_36 (not _let_32))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_34) :args (_let_36))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_32))) (REFL :args (_let_33)) :args _let_35)) _let_34 :args (_let_33 true _let_32)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 1)) _let_37 :args ((not _let_19) true _let_31)))) (let ((_let_39 (_let_19))) (let ((_let_40 (not _let_14))) (let ((_let_41 (and _let_12 _let_14))) (let ((_let_42 (ASSUME :args (_let_14)))) (let ((_let_43 (APPLY_UF tptp.contains_pq))) (let ((_let_44 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_45 (ASSUME :args (_let_12)))) (let ((_let_46 (SYMM _let_45))) (let ((_let_47 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_41)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_42 _let_45) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_46) _let_44 :args _let_43) (TRUE_INTRO _let_42))) :args (_let_14 _let_12))) :args (_let_12 _let_14))) :args (true _let_41)) :args ((or _let_13 (not _let_12) _let_40))))) (let ((_let_48 (_let_3))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 ((tptp.contains_cpq (tptp.triple U V W) X)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_50)) :args _let_48)) _let_49 :args (_let_21 false _let_3)))) (let ((_let_52 (not _let_21))) (let ((_let_53 (not _let_18))) (let ((_let_54 (_let_21))) (let ((_let_55 (_let_5))) (let ((_let_56 (ASSUME :args _let_55))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.contains_pq (tptp.insert_pq U V) W)))) :args _let_55))) _let_56 :args (_let_25 false _let_5)))) (let ((_let_58 (not _let_25))) (let ((_let_59 (not _let_24))) (let ((_let_60 (_let_25))) (let ((_let_61 (REORDERING (CNF_EQUIV_POS2 :args _let_60) :args ((or _let_14 _let_59 _let_58))))) (let ((_let_62 (_let_4))) (let ((_let_63 (ASSUME :args _let_62))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_63 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.contains_slb (tptp.insert_slb U (tptp.pair V X)) W)))) :args _let_62))) _let_63 :args (_let_28 false _let_4)))) (let ((_let_65 (not _let_28))) (let ((_let_66 (not _let_20))) (let ((_let_67 (_let_28))) (let ((_let_68 (tptp.contains_cpq _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_69 (= _let_26 _let_68))) (let ((_let_70 (not _let_26))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_50)) :args _let_48))) _let_49 :args (_let_69 false _let_3)))) (let ((_let_72 (= _let_23 _let_68))) (let ((_let_73 (not _let_68))) (let ((_let_74 (_let_29))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_74) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.contains_pq (tptp.i (tptp.triple V SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 W)) X)))) :args _let_74))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG (REFL :args (_let_31)) (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_35)) :args ((or _let_29 _let_31))) _let_37 :args (_let_29 true _let_31)) :args (_let_72 false _let_29)))) (let ((_let_76 (not _let_23))) (let ((_let_77 (not _let_72))) (let ((_let_78 (_let_72))) (let ((_let_79 (not _let_69))) (let ((_let_80 (_let_69))) (let ((_let_81 (not _let_27))) (let ((_let_82 (REORDERING (CNF_EQUIV_POS2 :args _let_67) :args ((or _let_20 _let_81 _let_65))))) (let ((_let_83 (REORDERING (CNF_EQUIV_POS2 :args _let_54) :args ((or _let_18 _let_66 _let_52))))) (let ((_let_84 (CNF_EQUIV_NEG2 :args _let_39))) (let ((_let_85 (MACRO_RESOLUTION_TRUST _let_47 _let_17 _let_84 _let_38 _let_83 _let_51 _let_82 _let_64 (CNF_OR_NEG :args (_let_27 0)) (REORDERING (CNF_EQUIV_POS2 :args _let_80) :args ((or _let_26 _let_73 _let_79))) _let_71 _let_61 _let_57 (REORDERING (CNF_EQUIV_POS1 :args _let_78) :args ((or _let_76 _let_68 _let_77))) _let_75 (CNF_OR_NEG :args (_let_24 0)) :args (_let_76 false _let_12 true _let_13 true _let_19 false _let_18 false _let_21 false _let_20 false _let_28 false _let_27 false _let_26 false _let_69 false _let_14 false _let_25 false _let_68 false _let_72 false _let_24)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_22 _let_26 _let_81))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_80) :args ((or _let_70 _let_68 _let_79))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_78) :args ((or _let_23 _let_73 _let_77))) _let_85 _let_75 :args (_let_73 true _let_23 false _let_72)) _let_71 :args (_let_70 true _let_68 false _let_69)) (CNF_OR_NEG :args (_let_24 1)) (REORDERING (CNF_EQUIV_POS1 :args _let_67) :args ((or _let_66 _let_27 _let_65))) _let_64 _let_61 _let_57 (REORDERING (CNF_EQUIV_POS1 :args _let_54) :args ((or _let_53 _let_20 _let_52))) _let_51 _let_47 _let_17 (REORDERING (CNF_EQUIV_NEG1 :args _let_39) :args ((or _let_18 _let_13 _let_19))) _let_38 :args (_let_13 true _let_26 true _let_22 false _let_27 false _let_28 true _let_24 false _let_25 false _let_20 false _let_21 true _let_14 false _let_12 false _let_18 true _let_19)))) (let ((_let_87 (and _let_13 _let_12))) (let ((_let_88 (_let_13 _let_12))) (let ((_let_89 (ASSUME :args (_let_13)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_87)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_89 _let_45) (SCOPE (TRUE_ELIM (TRANS (CONG _let_46 _let_44 :args _let_43) (TRUE_INTRO _let_89))) :args _let_88)) :args _let_88)) :args (true _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_60) :args ((or _let_24 _let_40 _let_58))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_22 _let_59))) _let_85 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 1)) (MACRO_RESOLUTION_TRUST _let_82 (MACRO_RESOLUTION_TRUST _let_83 (MACRO_RESOLUTION_TRUST _let_84 _let_38 _let_86 :args (_let_53 true _let_19 false _let_13)) _let_51 :args (_let_66 true _let_18 false _let_21)) _let_64 :args (_let_81 true _let_20 false _let_28)) :args ((not _let_22) true _let_27)) :args (_let_59 true _let_23 true _let_22)) _let_57 :args (_let_40 true _let_24 false _let_25)) _let_86 _let_17 :args (false true _let_14 false _let_13 false _let_12)) :args ((forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (and (tptp.less_than U V) (tptp.less_than V W)) (tptp.less_than U W))) (forall ((U $$unsorted) (V $$unsorted)) (or (tptp.less_than U V) (tptp.less_than V U))) (forall ((U $$unsorted)) (tptp.less_than U U)) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.strictly_less_than U V) (and (tptp.less_than U V) (not (tptp.less_than V U))))) (forall ((U $$unsorted)) (tptp.less_than tptp.bottom U)) (not (tptp.isnonempty_pq tptp.create_pq)) (forall ((U $$unsorted) (V $$unsorted)) (tptp.isnonempty_pq (tptp.insert_pq U V))) (forall ((U $$unsorted)) (not (tptp.contains_pq tptp.create_pq U))) _let_5 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.issmallestelement_pq U V) (forall ((W $$unsorted)) (=> (tptp.contains_pq U W) (tptp.less_than V W))))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.remove_pq (tptp.insert_pq U V) V) U)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (and (tptp.contains_pq U W) (not (= V W))) (= (tptp.remove_pq (tptp.insert_pq U V) W) (tptp.insert_pq (tptp.remove_pq U W) V)))) (forall ((U $$unsorted) (V $$unsorted)) (=> (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)) (= (tptp.findmin_pq_eff U V) U))) (forall ((U $$unsorted) (V $$unsorted)) (=> (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)) (= (tptp.findmin_pq_res U V) V))) (forall ((U $$unsorted) (V $$unsorted)) (=> (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)) (= (tptp.removemin_pq_eff U V) (tptp.remove_pq U V)))) (forall ((U $$unsorted) (V $$unsorted)) (=> (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)) (= (tptp.removemin_pq_res U V) V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.insert_pq (tptp.insert_pq U V) W) (tptp.insert_pq (tptp.insert_pq U W) V))) (not (tptp.isnonempty_slb tptp.create_slb)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (tptp.isnonempty_slb (tptp.insert_slb U (tptp.pair V W)))) (forall ((U $$unsorted)) (not (tptp.contains_slb tptp.create_slb U))) _let_4 (forall ((U $$unsorted) (V $$unsorted)) (not (tptp.pair_in_list tptp.create_slb U V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.pair_in_list (tptp.insert_slb U (tptp.pair V X)) W Y) (or (tptp.pair_in_list U W Y) (and (= V W) (= X Y))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.remove_slb (tptp.insert_slb U (tptp.pair V W)) V) U)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.pair V X))) (=> (and (not (= V W)) (tptp.contains_slb U W)) (= (tptp.remove_slb (tptp.insert_slb U _let_1) W) (tptp.insert_slb (tptp.remove_slb U W) _let_1))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V W)) V) W)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (not (= V W)) (tptp.contains_slb U W)) (= (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V X)) W) (tptp.lookup_slb U W)))) (forall ((U $$unsorted)) (= (tptp.update_slb tptp.create_slb U) tptp.create_slb)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (tptp.strictly_less_than X W) (= (tptp.update_slb (tptp.insert_slb U (tptp.pair V X)) W) (tptp.insert_slb (tptp.update_slb U W) (tptp.pair V W))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.pair V X))) (=> (tptp.less_than W X) (= (tptp.update_slb (tptp.insert_slb U _let_1) W) (tptp.insert_slb (tptp.update_slb U W) _let_1))))) (forall ((U $$unsorted)) (tptp.succ_cpq U U)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (tptp.succ_cpq U V) (tptp.succ_cpq U (tptp.insert_cpq V W)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (tptp.succ_cpq U V) (tptp.succ_cpq U (tptp.remove_cpq V W)))) (forall ((U $$unsorted) (V $$unsorted)) (=> (tptp.succ_cpq U V) (tptp.succ_cpq U (tptp.findmin_cpq_eff V)))) (forall ((U $$unsorted) (V $$unsorted)) (=> (tptp.succ_cpq U V) (tptp.succ_cpq U (tptp.removemin_cpq_eff V)))) (forall ((U $$unsorted) (V $$unsorted)) (tptp.check_cpq (tptp.triple U tptp.create_slb V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.less_than Y X) (= (tptp.check_cpq (tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)) (tptp.check_cpq (tptp.triple U V W))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.strictly_less_than X Y) (= (tptp.check_cpq (tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)) false))) _let_3 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.ok (tptp.triple U V tptp.bad)) false)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (not (tptp.ok (tptp.triple U V W))) (= W tptp.bad))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.insert_cpq (tptp.triple U V W) X) (tptp.triple (tptp.insert_pqp U X) (tptp.insert_slb V (tptp.pair X tptp.bottom)) W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (not (tptp.contains_slb V X)) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple U V tptp.bad)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (tptp.contains_slb V X) (tptp.less_than (tptp.lookup_slb V X) X)) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) W)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (tptp.contains_slb V X) (tptp.strictly_less_than X (tptp.lookup_slb V X))) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) tptp.bad)))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.findmin_cpq_eff (tptp.triple U tptp.create_slb V)) (tptp.triple U tptp.create_slb tptp.bad))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.findmin_pqp_res U))) (=> (and (not (= V tptp.create_slb)) (not (tptp.contains_slb V _let_1))) (= (tptp.findmin_cpq_eff (tptp.triple U V W)) (tptp.triple U (tptp.update_slb V _let_1) tptp.bad))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.findmin_pqp_res U))) (=> (and (not (= V tptp.create_slb)) (tptp.contains_slb V _let_1) (tptp.strictly_less_than _let_1 (tptp.lookup_slb V _let_1))) (= (tptp.findmin_cpq_eff (tptp.triple U V W)) (tptp.triple U (tptp.update_slb V _let_1) tptp.bad))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.findmin_pqp_res U))) (=> (and (not (= V tptp.create_slb)) (tptp.contains_slb V _let_1) (tptp.less_than (tptp.lookup_slb V _let_1) _let_1)) (= (tptp.findmin_cpq_eff (tptp.triple U V W)) (tptp.triple U (tptp.update_slb V _let_1) W))))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.findmin_cpq_res (tptp.triple U tptp.create_slb V)) tptp.bottom)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (not (= V tptp.create_slb)) (= (tptp.findmin_cpq_res (tptp.triple U V W)) (tptp.findmin_pqp_res U)))) (forall ((U $$unsorted)) (= (tptp.removemin_cpq_eff U) (tptp.remove_cpq (tptp.findmin_cpq_eff U) (tptp.findmin_cpq_res U)))) (forall ((U $$unsorted)) (= (tptp.removemin_cpq_res U) (tptp.findmin_cpq_res U))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.i (tptp.triple U tptp.create_slb V)) tptp.create_pq)) _let_2 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.pi_sharp_remove U V) (tptp.contains_pq U V))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.pi_remove U V) (tptp.pi_sharp_remove (tptp.i U) V))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.pi_sharp_find_min U V) (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)))) (forall ((U $$unsorted)) (= (tptp.pi_find_min U) (exists ((V $$unsorted)) (tptp.pi_sharp_find_min (tptp.i U) V)))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.pi_sharp_removemin U V) (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)))) (forall ((U $$unsorted)) (= (tptp.pi_removemin U) (exists ((V $$unsorted)) (tptp.pi_sharp_find_min (tptp.i U) V)))) (forall ((U $$unsorted)) (= (tptp.phi U) (exists ((V $$unsorted)) (and (tptp.succ_cpq U V) (tptp.ok V) (tptp.check_cpq V))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.63  )
% 0.20/0.63  % SZS output end Proof for SWV370+1
% 0.20/0.63  % cvc5---1.0.5 exiting
% 0.20/0.63  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------