TSTP Solution File: SWV415+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV415+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 21:51:04 EDT 2023
% Result : Theorem 0.61s 0.83s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV415+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : do_cvc5 %s %d
% 0.11/0.31 % Computer : n015.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.16/0.31 % WCLimit : 300
% 0.16/0.31 % DateTime : Tue Aug 29 06:29:10 EDT 2023
% 0.16/0.32 % CPUTime :
% 0.16/0.43 %----Proving TF0_NAR, FOF, or CNF
% 0.61/0.83 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.bu7RCUU400/cvc5---1.0.5_10106.p...
% 0.61/0.83 ------- get file name : TPTP file name is SWV415+2
% 0.61/0.83 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10106.smt2...
% 0.61/0.83 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.61/0.83 % SZS status Theorem for SWV415+2
% 0.61/0.83 % SZS output start Proof for SWV415+2
% 0.61/0.83 (
% 0.61/0.83 (let ((_let_1 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (= (tptp.i (tptp.insert_cpq _let_1 X)) (tptp.insert_pq (tptp.i _let_1) X)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X10 $$unsorted) (X11 $$unsorted) (X12 $$unsorted) (X13 $$unsorted) (X14 $$unsorted)) (= (tptp.i (tptp.triple X10 X12 X13)) (tptp.i (tptp.triple X11 X12 X14)))))) (let ((_let_4 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.i (tptp.triple U tptp.create_slb W)) (tptp.i (tptp.triple V tptp.create_slb X)))))) (let ((_let_5 (=> (and _let_4 (forall ((Y $$unsorted)) (=> (forall ((Z $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (= (tptp.i (tptp.triple Z Y X2)) (tptp.i (tptp.triple X1 Y X3)))) (forall ((X4 $$unsorted) (X5 $$unsorted) (X6 $$unsorted) (X7 $$unsorted) (X8 $$unsorted) (X9 $$unsorted)) (let ((_let_1 (tptp.insert_slb Y (tptp.pair X8 X9)))) (= (tptp.i (tptp.triple X4 _let_1 X6)) (tptp.i (tptp.triple X5 _let_1 X7)))))))) _let_3))) (let ((_let_6 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.i (tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)) (tptp.insert_pq (tptp.i (tptp.triple U V W)) X))))) (let ((_let_7 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.i (tptp.triple U tptp.create_slb V)) tptp.create_pq)))) (let ((_let_8 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.insert_cpq (tptp.triple U V W) X) (tptp.triple (tptp.insert_pqp U X) (tptp.insert_slb V (tptp.pair X tptp.bottom)) W))))) (let ((_let_9 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (tptp.i _let_9))) (let ((_let_11 (tptp.insert_cpq _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (= (tptp.i _let_11) (tptp.insert_pq _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_13 (tptp.insert_pqp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (tptp.triple _let_13 (tptp.insert_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.bottom)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (= _let_11 _let_14))) (let ((_let_16 (tptp.i (tptp.triple _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_17 (= (tptp.i _let_14) (tptp.insert_pq _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_18 (= _let_10 _let_16))) (let ((_let_19 (not _let_12))) (let ((_let_20 (_let_2))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (or))) (let ((_let_23 (_let_8))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 (_let_6))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 ((tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)))) (let ((_let_28 (forall ((Y $$unsorted) (BOUND_VARIABLE_1550 $$unsorted) (BOUND_VARIABLE_1548 $$unsorted) (BOUND_VARIABLE_1546 $$unsorted) (BOUND_VARIABLE_1544 $$unsorted) (BOUND_VARIABLE_1542 $$unsorted) (BOUND_VARIABLE_1540 $$unsorted)) (let ((_let_1 (tptp.insert_slb Y (tptp.pair BOUND_VARIABLE_1548 BOUND_VARIABLE_1550)))) (or (not (forall ((Z $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (= (tptp.i (tptp.triple Z Y X2)) (tptp.i (tptp.triple X1 Y X3))))) (= (tptp.i (tptp.triple BOUND_VARIABLE_1540 _let_1 BOUND_VARIABLE_1544)) (tptp.i (tptp.triple BOUND_VARIABLE_1542 _let_1 BOUND_VARIABLE_1546)))))))) (let ((_let_29 (and _let_4 _let_28))) (let ((_let_30 (tptp.insert_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 (tptp.pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))) (let ((_let_31 (tptp.i (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))) (let ((_let_32 (tptp.i (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)))) (let ((_let_33 (= _let_32 _let_31))) (let ((_let_34 (forall ((Z $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (= (tptp.i (tptp.triple Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 X2)) (tptp.i (tptp.triple X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 X3)))))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33))) (let ((_let_37 (tptp.i (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)))) (let ((_let_38 (tptp.i (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))) (let ((_let_39 (= _let_38 _let_37))) (let ((_let_40 (= _let_31 (tptp.insert_pq _let_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))) (let ((_let_41 (= _let_32 (tptp.insert_pq _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))) (let ((_let_42 (_let_34))) (let ((_let_43 (and _let_40 _let_41 _let_39))) (let ((_let_44 (ASSUME :args (_let_40)))) (let ((_let_45 (APPLY_UF tptp.insert_pq))) (let ((_let_46 (ASSUME :args (_let_39)))) (let ((_let_47 (ASSUME :args (_let_41)))) (let ((_let_48 (not _let_28))) (let ((_let_49 (_let_48))) (let ((_let_50 (tptp.i (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.create_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_51 (tptp.i (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.create_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_52 (= _let_51 _let_50))) (let ((_let_53 (= tptp.create_pq _let_50))) (let ((_let_54 (= tptp.create_pq _let_51))) (let ((_let_55 (forall ((U $$unsorted) (V $$unsorted)) (= tptp.create_pq (tptp.i (tptp.triple U tptp.create_slb V)))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (_let_55))) (let ((_let_58 ((tptp.triple U tptp.create_slb V)))) (let ((_let_59 (and _let_54 _let_53))) (let ((_let_60 (ASSUME :args (_let_53)))) (let ((_let_61 (ASSUME :args (_let_54)))) (let ((_let_62 (not _let_4))) (let ((_let_63 (_let_62))) (let ((_let_64 (_let_3))) (let ((_let_65 (and _let_15 _let_17 _let_18))) (let ((_let_66 (ASSUME :args (_let_18)))) (let ((_let_67 (ASSUME :args (_let_17)))) (let ((_let_68 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_65)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_67 _let_68) (SCOPE (TRANS (CONG (SYMM (SYMM _let_68)) :args (APPLY_UF tptp.i)) (SYMM (SYMM _let_67)) (CONG (SYMM _let_66) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args _let_45)) :args (_let_18 _let_17 _let_15))) :args (_let_15 _let_17 _let_18))) :args (true _let_65)) :args ((or _let_12 (not _let_15) (not _let_17) (not _let_18)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_64) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.triple X10 X12 X13) (tptp.triple X11 X12 X14)))) :args _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_3 (not _let_29)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_29)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_63)) :args _let_63)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_4))) (REFL :args ((not _let_52))) :args _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_59)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_60 _let_61) (SCOPE (TRANS (SYMM _let_61) (SYMM (SYMM _let_60))) :args (_let_53 _let_54))) :args (_let_54 _let_53))) :args (true _let_59)) :args ((or _let_52 (not _let_54) (not _let_53)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_58)) :args _let_57)) _let_56 :args (_let_54 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_58)) :args _let_57)) _let_56 :args (_let_53 false _let_55)) :args (_let_52 false _let_54 false _let_53)) :args (_let_4 false _let_52)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_49)) :args _let_49)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_28))) (REFL :args ((not _let_36))) :args _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_43)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_44 _let_46 _let_47) (SCOPE (TRANS (SYMM (SYMM _let_47)) (CONG (SYMM _let_46) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)) :args _let_45) (SYMM _let_44)) :args (_let_40 _let_39 _let_41))) :args (_let_40 _let_41 _let_39))) :args (true _let_43)) :args ((or _let_33 (not _let_40) (not _let_41) (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_41 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_40 false _let_6)) (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING ((tptp.triple Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 X2) (tptp.triple X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 X3)))) :args _let_42))) (CNF_OR_NEG :args (_let_36 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG (REFL :args (_let_36)) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_22)) :args ((or _let_34 _let_36))) :args (_let_36 false _let_41 false _let_40 false _let_39 true _let_33 false _let_34)) :args (_let_28 false _let_36)) :args (_let_29 false _let_4 false _let_28)) :args (_let_3 false _let_29)) :args (_let_18 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (_let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.bottom QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_17 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.insert_cpq (tptp.triple U V W) X)))) :args _let_23)) _let_24 :args (_let_15 false _let_8)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_21) :args _let_20)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_19)) :args _let_22)) _let_21 :args (_let_19 true _let_1)) :args (false false _let_18 false _let_17 false _let_15 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 $$unsorted)) (=> (and (not (= V W)) (tptp.contains_slb U W)) (= (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V X)) W) (tptp.lookup_slb U W)))) (forall ((U $$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))) _let_8 (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))) _let_7 _let_6 (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_5 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.61/0.84 )
% 0.61/0.84 % SZS output end Proof for SWV415+2
% 0.61/0.84 % cvc5---1.0.5 exiting
% 0.61/0.84 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------