TSTP Solution File: SWV372+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV372+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 21:50:53 EDT 2023
% Result : Theorem 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV372+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.34 % Computer : n025.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Aug 29 03:07:10 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.56 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.PrZiorrzLy/cvc5---1.0.5_329.p...
% 0.20/0.56 ------- get file name : TPTP file name is SWV372+1
% 0.20/0.56 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_329.smt2...
% 0.20/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.56 % SZS status Theorem for SWV372+1
% 0.20/0.56 % SZS output start Proof for SWV372+1
% 0.20/0.56 (
% 0.20/0.56 (let ((_let_1 (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (=> (tptp.phi (tptp.findmin_cpq_eff _let_1)) (tptp.contains_pq (tptp.i _let_1) (tptp.findmin_cpq_res _let_1)))))))) (let ((_let_2 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (=> (not (tptp.ok _let_1)) (not (tptp.phi _let_1))))))) (let ((_let_3 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (= (tptp.contains_cpq _let_1 X) (tptp.contains_pq (tptp.i _let_1) X)))))) (let ((_let_4 (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)))))) (let ((_let_5 (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))))))) (let ((_let_6 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.findmin_cpq_eff (tptp.triple U tptp.create_slb V)) (tptp.triple U tptp.create_slb tptp.bad))))) (let ((_let_7 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.ok (tptp.triple U V tptp.bad)) false)))) (let ((_let_8 (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_9 (forall ((U $$unsorted)) (= (tptp.update_slb tptp.create_slb U) tptp.create_slb)))) (let ((_let_10 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (tptp.findmin_cpq_res _let_10))) (let ((_let_12 (tptp.contains_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11))) (let ((_let_13 (tptp.findmin_pqp_res SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (= _let_11 _let_13))) (let ((_let_15 (tptp.contains_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13))) (let ((_let_16 (tptp.contains_cpq _let_10 _let_11))) (let ((_let_17 (= _let_16 _let_12))) (let ((_let_18 (not _let_12))) (let ((_let_19 (_let_8))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 (tptp.contains_pq (tptp.i _let_10) _let_11))) (let ((_let_22 (= _let_21 _let_16))) (let ((_let_23 (not _let_16))) (let ((_let_24 (_let_3))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (tptp.findmin_cpq_eff _let_10))) (let ((_let_27 (tptp.phi _let_26))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_21))) (let ((_let_30 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (or (not (tptp.phi (tptp.findmin_cpq_eff _let_1))) (tptp.contains_pq (tptp.i _let_1) (tptp.findmin_cpq_res _let_1))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (or))) (let ((_let_34 (not _let_30))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_32) :args (_let_34))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_33)) _let_32 :args (_let_31 true _let_30)))) (let ((_let_36 (= tptp.create_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_37 (or _let_36 _let_14))) (let ((_let_38 (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted)) (or (= tptp.create_slb V) (= (tptp.findmin_cpq_res (tptp.triple U V W)) (tptp.findmin_pqp_res U)))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (= (tptp.findmin_cpq_eff (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.create_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.create_slb tptp.bad)))) (let ((_let_41 (= tptp.create_slb (tptp.update_slb tptp.create_slb _let_13)))) (let ((_let_42 (tptp.update_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13))) (let ((_let_43 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_42 tptp.bad))) (let ((_let_44 (= _let_26 _let_43))) (let ((_let_45 (not _let_36))) (let ((_let_46 (_let_6))) (let ((_let_47 (ASSUME :args _let_46))) (let ((_let_48 (forall ((U $$unsorted)) (= tptp.create_slb (tptp.update_slb tptp.create_slb U))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (tptp.phi _let_43))) (let ((_let_51 (not _let_44))) (let ((_let_52 (not _let_50))) (let ((_let_53 (tptp.ok _let_43))) (let ((_let_54 (or _let_53 _let_52))) (let ((_let_55 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (or (tptp.ok _let_1) (not (tptp.phi _let_1))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (forall ((U $$unsorted) (V $$unsorted)) (not (tptp.ok (tptp.triple U V tptp.bad)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (ASSUME :args (_let_52)))) (let ((_let_60 (ASSUME :args (_let_44)))) (let ((_let_61 (ASSUME :args (_let_27)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_59 _let_60 _let_61) :args (_let_27 _let_44 _let_52)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_61)) (CONG (SYMM (SYMM _let_60)) :args (APPLY_UF tptp.phi)) (FALSE_INTRO _let_59))) :args (_let_52 _let_44 _let_27)) :args ((not (and _let_27 _let_44 _let_52)) SB_LITERAL))) (CONG (REFL :args (_let_28)) (REFL :args (_let_51)) (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_50))) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG (REFL :args (_let_29)) (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_33)) :args ((or _let_27 _let_29))) _let_35 :args (_let_27 true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_52 (not _let_54)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_42 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.triple U V tptp.bad)))) :args (_let_57))) _let_58 :args ((not _let_53) false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_42 tptp.bad QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.triple U V W)))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_52 true _let_53 false _let_54)) :args (_let_51 false _let_27 true _let_50)))) (let ((_let_63 (and _let_36 _let_41 _let_40))) (let ((_let_64 (_let_36 _let_41 _let_40))) (let ((_let_65 (APPLY_UF tptp.triple))) (let ((_let_66 (ASSUME :args (_let_36)))) (let ((_let_67 (SYMM _let_66))) (let ((_let_68 (ASSUME :args (_let_41)))) (let ((_let_69 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_70 (ASSUME :args (_let_40)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_63)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_68 _let_70) (SCOPE (TRANS (CONG (CONG _let_69 _let_67 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args _let_65) :args (APPLY_UF tptp.findmin_cpq_eff)) (SYMM (SYMM _let_70)) (CONG _let_69 (TRANS (SYMM (SYMM _let_68)) (CONG (SYMM _let_67) (REFL :args (_let_13)) :args (APPLY_UF tptp.update_slb))) (REFL :args (tptp.bad)) :args _let_65)) :args _let_64)) :args _let_64)) :args (true _let_63)) :args ((or _let_44 _let_45 (not _let_41) (not _let_40)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.update_slb tptp.create_slb U) tptp.create_slb))))) :args (_let_48))) _let_49 :args (_let_41 false _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.triple U tptp.create_slb V)))) :args _let_46)) _let_47 :args (_let_40 false _let_6)) :args (_let_45 true _let_44 false _let_41 false _let_40)))) (let ((_let_72 (or _let_36 _let_15 _let_44))) (let ((_let_73 (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.findmin_pqp_res U))) (or (= tptp.create_slb V) (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))))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (ASSUME :args (_let_18)))) (let ((_let_76 (ASSUME :args (_let_14)))) (let ((_let_77 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_75 _let_76 _let_77) :args (_let_15 _let_14 _let_18)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_77)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (SYMM _let_76) :args (APPLY_UF tptp.contains_slb)) (FALSE_INTRO _let_75))) :args (_let_18 _let_14 _let_15)) :args ((not (and _let_15 _let_14 _let_18)) SB_LITERAL))) (CONG (REFL :args ((not _let_15))) (REFL :args ((not _let_14))) (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_12))) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_36 _let_15 _let_44 (not _let_72)))) _let_71 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.triple U V W)))) :args (_let_73))) _let_74 :args (_let_72 false _let_73)) :args (_let_15 true _let_36 true _let_44 false _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_14 (not _let_37)))) _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.triple U V W)))) :args (_let_38))) _let_39 :args (_let_37 false _let_38)) :args (_let_14 true _let_36 false _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_17)) :args ((or _let_16 _let_18 (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_22)) :args ((or _let_21 _let_23 (not _let_22)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 1)) _let_35 :args ((not _let_21) true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_11 QUANTIFIERS_INST_E_MATCHING ((tptp.contains_pq (tptp.i (tptp.triple U V W)) X)))) :args _let_24))) _let_25 :args (_let_22 false _let_3)) :args (_let_23 true _let_21 false _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_11 QUANTIFIERS_INST_E_MATCHING ((tptp.contains_cpq (tptp.triple U V W) X)))) :args _let_19)) _let_20 :args (_let_17 false _let_8)) :args (_let_18 true _let_16 false _let_17)) :args (false false _let_15 false _let_14 true _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))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.contains_pq (tptp.insert_pq U V) W) (or (tptp.contains_pq U W) (= V W)))) (forall ((U $$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))) (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)))) (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 $$unsorted)) (=> (and (not (= V W)) (tptp.contains_slb U W)) (= (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V X)) W) (tptp.lookup_slb U W)))) _let_9 (forall ((U $$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_8 _let_7 (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 $$unsorted)) (=> (and (tptp.contains_slb V X) (tptp.strictly_less_than X (tptp.lookup_slb V X))) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) tptp.bad)))) _let_6 _let_5 (forall ((U $$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 $$unsorted)) (= (tptp.findmin_cpq_res (tptp.triple U tptp.create_slb V)) tptp.bottom)) _let_4 (forall ((U $$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 $$unsorted)) (= (tptp.i (tptp.triple U tptp.create_slb V)) tptp.create_pq)) (forall ((U $$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))) (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_3 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (=> (not (tptp.contains_cpq _let_1 (tptp.findmin_cpq_res _let_1))) (not (tptp.ok (tptp.findmin_cpq_eff _let_1)))))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.57 )
% 0.20/0.57 % SZS output end Proof for SWV372+1
% 0.20/0.57 % cvc5---1.0.5 exiting
% 0.20/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------