TSTP Solution File: SWV396+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV396+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 21:50:59 EDT 2023
% Result : Theorem 0.33s 0.66s
% Output : Proof 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV396+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n009.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 07:45:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.33/0.66 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Zq3vvGx84S/cvc5---1.0.5_32211.p...
% 0.33/0.66 ------- get file name : TPTP file name is SWV396+1
% 0.33/0.66 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32211.smt2...
% 0.33/0.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.33/0.66 % SZS status Theorem for SWV396+1
% 0.33/0.66 % SZS output start Proof for SWV396+1
% 0.33/0.66 (
% 0.33/0.66 (let ((_let_1 (not (forall ((U $$unsorted)) (=> (forall ((V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.pair_in_list U X Y) (tptp.strictly_less_than X Y) (tptp.ok (tptp.remove_cpq (tptp.triple V U W) X))) (tptp.pair_in_list (tptp.remove_slb U X) X Y))) (forall ((Z $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted) (X5 $$unsorted)) (let ((_let_1 (tptp.insert_slb U (tptp.pair X4 X5)))) (=> (and (tptp.pair_in_list _let_1 X2 X3) (tptp.strictly_less_than X2 X3) (tptp.ok (tptp.remove_cpq (tptp.triple Z _let_1 X1) X2))) (tptp.pair_in_list (tptp.remove_slb _let_1 X2) X2 X3))))))))) (let ((_let_2 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (tptp.contains_slb V X) (tptp.strictly_less_than X (tptp.lookup_slb V X))) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) tptp.bad)))))) (let ((_let_3 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (tptp.contains_slb V X) (tptp.less_than (tptp.lookup_slb V X) X)) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) W)))))) (let ((_let_4 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (not (tptp.contains_slb V X)) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple U V tptp.bad)))))) (let ((_let_5 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (not (tptp.ok (tptp.triple U V W))) (= W tptp.bad))))) (let ((_let_6 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.ok (tptp.triple U V tptp.bad)) false)))) (let ((_let_7 (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 ((_let_8 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V W)) V) W)))) (let ((_let_9 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.pair V X))) (=> (and (not (= V W)) (tptp.contains_slb U W)) (= (tptp.remove_slb (tptp.insert_slb U _let_1) W) (tptp.insert_slb (tptp.remove_slb U W) _let_1))))))) (let ((_let_10 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.remove_slb (tptp.insert_slb U (tptp.pair V W)) V) U)))) (let ((_let_11 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.pair_in_list (tptp.insert_slb U (tptp.pair V X)) W Y) (or (tptp.pair_in_list U W Y) (and (= V W) (= X Y))))))) (let ((_let_12 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.contains_slb (tptp.insert_slb U (tptp.pair V X)) W) (or (tptp.contains_slb U W) (= V W)))))) (let ((_let_13 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.strictly_less_than U V) (and (tptp.less_than U V) (not (tptp.less_than V U))))))) (let ((_let_14 (forall ((U $$unsorted) (V $$unsorted)) (or (tptp.less_than U V) (tptp.less_than V U))))) (let ((_let_15 (tptp.pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (tptp.insert_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_15))) (let ((_let_17 (tptp.lookup_slb _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_18 (tptp.less_than _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_17))) (let ((_let_21 (and _let_20 _let_19))) (let ((_let_22 (tptp.strictly_less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_17))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (not _let_21))) (let ((_let_25 (_let_13))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (tptp.remove_slb _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_28 (tptp.remove_pqp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_29 (tptp.triple _let_28 _let_27 tptp.bad))) (let ((_let_30 (tptp.remove_cpq (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_31 (= _let_30 _let_29))) (let ((_let_32 (not _let_22))) (let ((_let_33 (tptp.contains_slb _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_31))) (let ((_let_36 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.contains_slb V X)) (not (tptp.strictly_less_than X (tptp.lookup_slb V X))) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) tptp.bad)))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.remove_cpq (tptp.triple U V W) X)))) :args (_let_36))) _let_37 :args (_let_35 false _let_36)))) (let ((_let_39 (tptp.ok _let_30))) (let ((_let_40 (tptp.ok _let_29))) (let ((_let_41 (not _let_31))) (let ((_let_42 (tptp.pair_in_list _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_43 (not _let_39))) (let ((_let_44 (tptp.strictly_less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.pair_in_list _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_47 (not _let_46))) (let ((_let_48 (forall ((V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.pair_in_list SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)) (not (tptp.strictly_less_than X Y)) (not (tptp.ok (tptp.remove_cpq (tptp.triple V SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 W) X))) (tptp.pair_in_list (tptp.remove_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X) X Y))))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47 _let_45 _let_43 _let_42))) (let ((_let_51 (forall ((U $$unsorted) (BOUND_VARIABLE_1244 $$unsorted) (BOUND_VARIABLE_1242 $$unsorted) (BOUND_VARIABLE_1240 $$unsorted) (BOUND_VARIABLE_1238 $$unsorted) (BOUND_VARIABLE_1236 $$unsorted) (BOUND_VARIABLE_1234 $$unsorted)) (let ((_let_1 (tptp.insert_slb U (tptp.pair BOUND_VARIABLE_1242 BOUND_VARIABLE_1244)))) (or (not (forall ((V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.pair_in_list U X Y)) (not (tptp.strictly_less_than X Y)) (not (tptp.ok (tptp.remove_cpq (tptp.triple V U W) X))) (tptp.pair_in_list (tptp.remove_slb U X) X Y)))) (not (tptp.pair_in_list _let_1 BOUND_VARIABLE_1238 BOUND_VARIABLE_1240)) (not (tptp.strictly_less_than BOUND_VARIABLE_1238 BOUND_VARIABLE_1240)) (not (tptp.ok (tptp.remove_cpq (tptp.triple BOUND_VARIABLE_1234 _let_1 BOUND_VARIABLE_1236) BOUND_VARIABLE_1238))) (tptp.pair_in_list (tptp.remove_slb _let_1 BOUND_VARIABLE_1238) BOUND_VARIABLE_1238 BOUND_VARIABLE_1240)))))) (let ((_let_52 (not _let_50))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (or))) (let ((_let_55 (not _let_51))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_53) :args (_let_55))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_51))) (REFL :args (_let_52)) :args _let_54)) _let_53 :args (_let_52 true _let_51)))) (let ((_let_57 (REFL :args (_let_50)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 3)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_39))) :args _let_54)) :args ((or _let_39 _let_50))) _let_56 :args (_let_39 true _let_50)))) (let ((_let_59 (forall ((U $$unsorted) (V $$unsorted)) (not (tptp.ok (tptp.triple U V tptp.bad)))))) (let ((_let_60 (not _let_40))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_59))) (let ((_let_63 ((tptp.triple U V tptp.bad)))) (let ((_let_64 (REFL :args (_let_43)))) (let ((_let_65 (TRUE_INTRO (ASSUME :args (_let_39))))) (let ((_let_66 (APPLY_UF tptp.ok))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_60)))) (CONG (SYMM (ASSUME :args (_let_31))) :args _let_66) _let_65)) :args (_let_39 _let_31 _let_60))) (CONG _let_64 (REFL :args (_let_41)) (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_40))) :args _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (_let_28 _let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_60 false _let_59)) _let_58 :args (_let_41 true _let_40 false _let_39)))) (let ((_let_68 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_16 tptp.bad))) (let ((_let_69 (= _let_30 _let_68))) (let ((_let_70 (or _let_33 _let_69))) (let ((_let_71 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (tptp.contains_slb V X) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple U V tptp.bad)))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (tptp.ok _let_68))) (let ((_let_74 (not _let_69))) (let ((_let_75 (not _let_73))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_33 _let_69 (not _let_70)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_75)))) (CONG (SYMM (ASSUME :args (_let_69))) :args _let_66) _let_65)) :args (_let_39 _let_69 _let_75))) (CONG _let_64 (REFL :args (_let_74)) (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_73))) :args _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_75 false _let_59)) _let_58 :args (_let_74 true _let_73 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.remove_cpq (tptp.triple U V W) X)))) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_33 true _let_69 false _let_70)))) (let ((_let_77 (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_32 _let_31 (not _let_35)))))) (let ((_let_78 (= _let_30 (tptp.triple _let_28 _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_79 (or _let_34 _let_19 _let_78))) (let ((_let_80 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_81 (tptp.remove_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_82 (tptp.triple _let_28 _let_81 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_83 (tptp.remove_cpq (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_84 (= _let_83 _let_82))) (let ((_let_85 (tptp.insert_slb _let_81 _let_15))) (let ((_let_86 (= _let_27 _let_85))) (let ((_let_87 (= tptp.bad SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_88 (tptp.ok _let_83))) (let ((_let_89 (tptp.ok _let_82))) (let ((_let_90 (or _let_89 _let_87))) (let ((_let_91 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.contains_slb V X)) (not (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)))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (_let_91))) (let ((_let_94 ((tptp.remove_cpq (tptp.triple U V W) X)))) (let ((_let_95 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.remove_slb _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_96 (tptp.pair_in_list SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_97 (not _let_80))) (let ((_let_98 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= U (tptp.remove_slb (tptp.insert_slb U (tptp.pair V W)) V))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_101 (and _let_80 _let_100))) (let ((_let_102 (or _let_96 _let_101))) (let ((_let_103 (= _let_46 _let_102))) (let ((_let_104 (_let_11))) (let ((_let_105 (ASSUME :args _let_104))) (let ((_let_106 ((tptp.pair_in_list (tptp.insert_slb U (tptp.pair V X)) W Y)))) (let ((_let_107 (tptp.contains_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_108 (or _let_107 _let_80))) (let ((_let_109 (= _let_33 _let_108))) (let ((_let_110 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.lookup_slb _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_111 (not _let_101))) (let ((_let_112 (_let_12))) (let ((_let_113 (ASSUME :args _let_112))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.contains_slb (tptp.insert_slb U (tptp.pair V X)) W)))) :args _let_112)) _let_113 :args (_let_109 false _let_12)))) (let ((_let_115 (not _let_109))) (let ((_let_116 (not _let_108))) (let ((_let_117 (_let_109))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 2)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_54)) :args ((or _let_44 _let_50))) _let_56 :args (_let_44 true _let_50)))) (let ((_let_119 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= W (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V W)) V))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (and _let_44 _let_80 _let_100 _let_110))) (let ((_let_122 (_let_44 _let_80 _let_100 _let_110))) (let ((_let_123 (ASSUME :args (_let_44)))) (let ((_let_124 (APPLY_UF tptp.strictly_less_than))) (let ((_let_125 (ASSUME :args (_let_100)))) (let ((_let_126 (ASSUME :args (_let_80)))) (let ((_let_127 (SYMM _let_126))) (let ((_let_128 (SYMM _let_127))) (let ((_let_129 (ASSUME :args (_let_110)))) (let ((_let_130 (REFL :args (_let_16)))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_96 _let_101 (not _let_102)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_121)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_123 _let_126 _let_125 _let_129) (SCOPE (TRUE_ELIM (TRANS (CONG _let_127 (TRANS (CONG _let_130 _let_127 :args (APPLY_UF tptp.lookup_slb)) (SYMM _let_129)) :args _let_124) (CONG _let_128 (SYMM (SYMM _let_125)) :args _let_124) (TRUE_INTRO _let_123))) :args _let_122)) :args _let_122)) :args (true _let_121)) :args ((or _let_45 _let_22 _let_97 (not _let_100) (not _let_110)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.insert_slb U (tptp.pair V W))))) :args (_let_119))) _let_120 :args (_let_110 false _let_119)) _let_118 _let_77 _let_67 _let_38 (REORDERING (CNF_EQUIV_POS2 :args _let_117) :args ((or _let_33 _let_116 _let_115))) _let_114 (REORDERING (CNF_OR_NEG :args (_let_108 1)) :args ((or _let_97 _let_108))) (REORDERING (CNF_AND_POS :args (_let_101 1)) :args ((or _let_100 _let_111))) (REORDERING (CNF_AND_POS :args (_let_101 0)) :args ((or _let_80 _let_111))) :args (_let_111 false _let_110 false _let_44 true _let_22 true _let_31 false _let_35 false _let_33 false _let_109 false _let_108 false _let_100 false _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_103)) :args ((or _let_47 _let_102 (not _let_103)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 1)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_54)) :args ((or _let_46 _let_50))) _let_56 :args (_let_46 true _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_106)) :args _let_104)) _let_105 :args (_let_103 false _let_11)) :args (_let_102 false _let_46 false _let_103)) :args (_let_96 true _let_101 false _let_102)))) (let ((_let_132 (not _let_42))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_50 4)) _let_56 :args (_let_132 true _let_50)))) (let ((_let_134 (not _let_96))) (let ((_let_135 (MACRO_SR_PRED_INTRO :args ((= (not _let_132) _let_42))))) (let ((_let_136 (ASSUME :args (_let_132)))) (let ((_let_137 (FALSE_INTRO _let_136))) (let ((_let_138 (APPLY_UF tptp.pair_in_list))) (let ((_let_139 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_140 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_141 (ASSUME :args (_let_95)))) (let ((_let_142 (ASSUME :args (_let_96)))) (let ((_let_143 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_126 _let_141 _let_142 _let_136) :args (_let_132 _let_96 _let_80 _let_95)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_142)) (CONG (TRANS (SYMM (SYMM _let_141)) (CONG _let_130 _let_128 :args (APPLY_UF tptp.remove_slb))) _let_140 _let_139 :args _let_138) _let_137)) :args (_let_80 _let_95 _let_96 _let_132)) :args ((not (and _let_132 _let_96 _let_80 _let_95)) SB_LITERAL))) (CONG _let_135 (REFL :args (_let_134)) (REFL :args (_let_97)) (REFL :args ((not _let_95))) :args _let_54)) _let_133 _let_131 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.insert_slb U (tptp.pair V W))))) :args (_let_98))) _let_99 :args (_let_95 false _let_98)) :args (_let_97 true _let_42 false _let_96 false _let_95)))) (let ((_let_144 (tptp.lookup_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_145 (= _let_17 _let_144))) (let ((_let_146 (not _let_107))) (let ((_let_147 (or _let_80 _let_146 _let_145))) (let ((_let_148 (tptp.less_than _let_144 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_149 (not _let_148))) (let ((_let_150 (or _let_146 _let_149 _let_84))) (let ((_let_151 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_117) :args ((or _let_34 _let_108 _let_115))) _let_76 _let_114 :args (_let_108 false _let_33 false _let_109)))) (let ((_let_152 (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_80 _let_107 _let_116))))) (let ((_let_153 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (= V W) (not (tptp.contains_slb U W)) (= (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V X)) W) (tptp.lookup_slb U W)))))) (let ((_let_154 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_155 (and _let_18 _let_145))) (let ((_let_156 (_let_18 _let_145))) (let ((_let_157 (ASSUME :args (_let_18)))) (let ((_let_158 (ASSUME :args (_let_145)))) (let ((_let_159 (or _let_80 _let_146 _let_86))) (let ((_let_160 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.pair V X))) (or (= V W) (not (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))))))) (let ((_let_161 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_162 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_159)) :args ((or _let_80 _let_146 _let_86 (not _let_159)))) _let_143 (MACRO_RESOLUTION_TRUST _let_152 _let_143 _let_151 :args (_let_107 true _let_80 false _let_108)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_161 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.remove_slb (tptp.insert_slb U (tptp.pair V X)) W)))) :args (_let_160))) _let_161 :args (_let_159 false _let_160)) :args (_let_86 true _let_80 false _let_107 false _let_159)))) (let ((_let_163 (not _let_86))) (let ((_let_164 (and _let_86 _let_87 _let_78))) (let ((_let_165 (_let_86 _let_87 _let_78))) (let ((_let_166 (APPLY_UF tptp.triple))) (let ((_let_167 (ASSUME :args (_let_86)))) (let ((_let_168 (SYMM _let_167))) (let ((_let_169 (REFL :args (_let_28)))) (let ((_let_170 (ASSUME :args (_let_87)))) (let ((_let_171 (ASSUME :args (_let_78)))) (let ((_let_172 (tptp.pair_in_list _let_81 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_173 (not _let_88))) (let ((_let_174 (or _let_134 _let_45 _let_173 _let_172))) (let ((_let_175 (_let_48))) (let ((_let_176 (or _let_172 _let_101))) (let ((_let_177 (tptp.pair_in_list _let_85 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_178 (= _let_177 _let_176))) (let ((_let_179 (not _let_176))) (let ((_let_180 (not _let_177))) (let ((_let_181 (and _let_132 _let_86))) (let ((_let_182 (_let_132 _let_86))) (let ((_let_183 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (tptp.ok (tptp.triple U V W)) (= tptp.bad W))))) (let ((_let_184 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_185 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_87 _let_89 (not _let_90)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_184 :args (_let_28 _let_81 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.triple U V W)))) :args (_let_183))) _let_184 :args (_let_90 false _let_183)) (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (ASSUME :args (_let_89)))) (CONG (SYMM (ASSUME :args (_let_84))) :args _let_66) (FALSE_INTRO (ASSUME :args (_let_173))))) :args (_let_173 _let_84 _let_89))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_173) _let_88))) (REFL :args ((not _let_84))) (REFL :args ((not _let_89))) :args _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_174)) :args ((or _let_45 _let_134 _let_172 _let_173 (not _let_174)))) _let_118 _let_131 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_176 0)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_178)) :args ((or _let_177 _let_179 (not _let_178)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_181)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_136 _let_167) (SCOPE (FALSE_ELIM (TRANS (CONG _let_168 _let_140 _let_139 :args _let_138) _let_137)) :args _let_182)) :args _let_182)) :args (true _let_181)) (CONG _let_135 (REFL :args (_let_163)) (REFL :args (_let_180)) :args _let_54)) _let_133 _let_162 :args (_let_180 true _let_42 false _let_86)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (_let_81 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_106)) :args _let_104)) _let_105 :args (_let_178 false _let_11)) :args (_let_179 true _let_177 false _let_178)) :args ((not _let_172) true _let_176)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_175) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.pair_in_list SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y) false)) (tptp.triple V SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 W)))) :args _let_175)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 0)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_54)) :args ((or _let_48 _let_50))) _let_56 :args (_let_48 true _let_50)) :args (_let_174 false _let_48)) :args (_let_173 false _let_44 false _let_96 true _let_172 false _let_174)) (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_164)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_167 _let_170 _let_171) (SCOPE (TRANS (SYMM (SYMM _let_171)) (CONG _let_169 _let_167 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) :args _let_166) (CONG _let_169 (REFL :args (_let_85)) (SYMM _let_170) :args _let_166) (CONG _let_169 _let_168 (REFL :args (tptp.bad)) :args _let_166)) :args _let_165)) :args _let_165)) :args (true _let_164)) :args ((or _let_31 _let_163 (not _let_87) (not _let_78)))) _let_162 _let_67 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_155)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_157 _let_158) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_158) _let_140 :args (APPLY_UF tptp.less_than)) (TRUE_INTRO _let_157))) :args _let_156)) :args _let_156)) :args (true _let_155)) (REORDERING (CNF_OR_POS :args (_let_150)) :args ((or _let_146 _let_149 _let_84 (not _let_150)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_94)) :args _let_93)) _let_92 :args (_let_150 false _let_91)) (REORDERING (CNF_OR_POS :args (_let_147)) :args ((or _let_80 _let_146 _let_145 (not _let_147)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_154 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.lookup_slb (tptp.insert_slb U (tptp.pair V X)) W)))) :args (_let_153))) _let_154 :args (_let_147 false _let_153)) _let_152 _let_151 :args ((or _let_80 _let_19 _let_84) true _let_148 false _let_150 false _let_145 false _let_147 false _let_107 false _let_108)) _let_143 (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_34 _let_19 _let_78 (not _let_79)))) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_94)) :args _let_93)) _let_92 :args (_let_79 false _let_91)) :args (_let_19 false _let_90 true _let_89 true _let_88 true _let_87 false _let_86 true _let_31 false _let_84 true _let_80 false _let_78 false _let_33 false _let_79)))) (let ((_let_186 (or _let_18 _let_20))) (let ((_let_187 (_let_14))) (let ((_let_188 (ASSUME :args _let_187))) (let ((_let_189 (not _let_20))) (let ((_let_190 (_let_21))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_190) (CONG (REFL :args _let_190) (REFL :args (_let_189)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_54)) :args ((or _let_18 _let_21 _let_189))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_186)) :args ((or _let_18 _let_20 (not _let_186)))) _let_185 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_188 :args (_let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.less_than U V) true))))) :args _let_187)) _let_188 :args (_let_186 false _let_14)) :args (_let_20 true _let_18 false _let_186)) _let_185 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_23)) :args ((or _let_22 _let_24 (not _let_23)))) (MACRO_RESOLUTION_TRUST _let_77 _let_76 _let_67 _let_38 :args (_let_32 false _let_33 true _let_31 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.strictly_less_than U V)))) :args _let_25)) _let_26 :args (_let_23 false _let_13)) :args (_let_24 true _let_22 false _let_23)) :args (false false _let_20 true _let_18 true _let_21)) :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_14 (forall ((U $$unsorted)) (tptp.less_than U U)) _let_13 (forall ((U $$unsorted)) (tptp.less_than tptp.bottom U)) (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_12 (forall ((U $$unsorted) (V $$unsorted)) (not (tptp.pair_in_list tptp.create_slb U V))) _let_11 _let_10 _let_9 _let_8 _let_7 (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))) _let_6 _let_5 (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_4 _let_3 _let_2 (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_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.33/0.66 )
% 0.33/0.66 % SZS output end Proof for SWV396+1
% 0.33/0.66 % cvc5---1.0.5 exiting
% 0.33/0.67 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------