TSTP Solution File: SWV381+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV381+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 21:50:55 EDT 2023
% Result : Theorem 0.19s 0.56s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n025.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 : Tue Aug 29 03:53:40 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.56 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.piIncWNYy8/cvc5---1.0.5_18884.p...
% 0.19/0.56 ------- get file name : TPTP file name is SWV381+1
% 0.19/0.56 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18884.smt2...
% 0.19/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.56 % SZS status Theorem for SWV381+1
% 0.19/0.56 % SZS output start Proof for SWV381+1
% 0.19/0.56 (
% 0.19/0.56 (let ((_let_1 (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (=> (tptp.phi (tptp.findmin_cpq_eff _let_1)) (tptp.issmallestelement_pq (tptp.i _let_1) (tptp.findmin_cpq_res _let_1)))))))) (let ((_let_2 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (exists ((X $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (and (tptp.contains_cpq _let_1 X) (tptp.strictly_less_than X (tptp.findmin_cpq_res _let_1))))) (not (tptp.phi (tptp.findmin_cpq_eff (tptp.triple U V W)))))))) (let ((_let_3 (forall ((U $$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 $$unsorted)) (= (tptp.issmallestelement_pq U V) (forall ((W $$unsorted)) (=> (tptp.contains_pq U W) (tptp.less_than V W))))))) (let ((_let_5 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.strictly_less_than U V) (and (tptp.less_than U V) (not (tptp.less_than V U))))))) (let ((_let_6 (forall ((U $$unsorted) (V $$unsorted)) (or (tptp.less_than U V) (tptp.less_than V U))))) (let ((_let_7 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (BOUND_VARIABLE_1522 $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (or (not (tptp.phi (tptp.findmin_cpq_eff _let_1))) (not (tptp.contains_cpq _let_1 BOUND_VARIABLE_1522)) (not (tptp.strictly_less_than BOUND_VARIABLE_1522 (tptp.findmin_cpq_res _let_1)))))))) (let ((_let_8 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (tptp.findmin_cpq_res _let_8))) (let ((_let_10 (tptp.strictly_less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.contains_cpq _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.phi (tptp.findmin_cpq_eff _let_8)))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13 _let_11))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (tptp.i _let_8))) (let ((_let_20 (tptp.contains_pq _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_21 (= _let_20 _let_12))) (let ((_let_22 (_let_3))) (let ((_let_23 (ASSUME :args _let_22))) (let ((_let_24 (tptp.less_than _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_25 (not _let_20))) (let ((_let_26 (or _let_25 _let_24))) (let ((_let_27 (forall ((W $$unsorted)) (let ((_let_1 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (or (not (tptp.contains_pq (tptp.i _let_1) W)) (tptp.less_than (tptp.findmin_cpq_res _let_1) W)))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (tptp.issmallestelement_pq _let_19 _let_9))) (let ((_let_30 (= _let_29 _let_27))) (let ((_let_31 (not _let_27))) (let ((_let_32 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.issmallestelement_pq U V) (forall ((W $$unsorted)) (or (not (tptp.contains_pq U W)) (tptp.less_than V W))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (or _let_15 _let_29))) (let ((_let_35 (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.issmallestelement_pq (tptp.i _let_1) (tptp.findmin_cpq_res _let_1))))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or))) (let ((_let_39 (not _let_35))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_37) :args (_let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) (REFL :args (_let_36)) :args _let_38)) _let_37 :args (_let_36 true _let_35)))) (let ((_let_41 (_let_31))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_41)) :args _let_41)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_27))) (REFL :args (_let_28)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_30)) :args ((or _let_29 _let_31 (not _let_30)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 1)) _let_40 :args ((not _let_29) true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (_let_19 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.issmallestelement_pq U V)))) :args (_let_32))) _let_33 :args (_let_30 false _let_32)) :args (_let_31 true _let_29 false _let_30)) :args (_let_28 true _let_27)))) (let ((_let_43 (not _let_24))) (let ((_let_44 (tptp.less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9))) (let ((_let_45 (and _let_44 _let_43))) (let ((_let_46 (= _let_10 _let_45))) (let ((_let_47 (_let_5))) (let ((_let_48 (ASSUME :args _let_47))) (let ((_let_49 (or _let_24 _let_44))) (let ((_let_50 (_let_6))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 1)) _let_42 :args (_let_43 true _let_26)))) (let ((_let_53 (not _let_44))) (let ((_let_54 (_let_45))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.contains_cpq (tptp.triple U V W) BOUND_VARIABLE_1522) false))))) :args (_let_7))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_11 _let_13 _let_18))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_38)) :args ((or _let_14 _let_34))) _let_40 :args (_let_14 true _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_46)) :args ((or _let_10 (not _let_45) (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_54) (CONG (REFL :args _let_54) (REFL :args (_let_53)) (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_24))) :args _let_38)) :args ((or _let_24 _let_53 _let_45))) _let_52 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_24 _let_44 (not _let_49)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.less_than U V) true))))) :args _let_50)) _let_51 :args (_let_49 false _let_6)) :args (_let_44 true _let_24 false _let_49)) :args (_let_45 true _let_24 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.less_than V U)))) :args _let_47)) _let_48 :args (_let_46 false _let_5)) :args (_let_10 false _let_45 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_21)) :args ((or _let_25 _let_12 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_20))) :args _let_38)) :args ((or _let_20 _let_26))) _let_42 :args (_let_20 true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((tptp.contains_pq (tptp.i (tptp.triple U V W)) X)))) :args _let_22))) _let_23 :args (_let_21 false _let_3)) :args (_let_12 false _let_20 false _let_21)) :args (_let_18 false _let_14 false _let_10 false _let_12)) _let_17 :args (false true _let_16 false _let_7)) :args ((forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (and (tptp.less_than U V) (tptp.less_than V W)) (tptp.less_than U W))) _let_6 (forall ((U $$unsorted)) (tptp.less_than U U)) _let_5 (forall ((U $$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)))) _let_4 (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 $$unsorted)) (=> (and (not (= V W)) (tptp.contains_slb U W)) (= (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V X)) W) (tptp.lookup_slb U W)))) (forall ((U $$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 $$unsorted)) (=> (tptp.strictly_less_than X Y) (= (tptp.check_cpq (tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)) false))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.contains_cpq (tptp.triple U V W) X) (tptp.contains_slb V X))) (forall ((U $$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)) (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 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.57 )
% 0.19/0.57 % SZS output end Proof for SWV381+1
% 0.19/0.57 % cvc5---1.0.5 exiting
% 0.19/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------