%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV391+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 21:50:58 EDT 2023

% Result   : Theorem 0.39s 0.57s
% Output   : Proof 0.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : SWV391+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.11  % Command    : do_cvc5 %s %d
% 0.11/0.30  % Computer : n023.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Tue Aug 29 08:31:55 EDT 2023
% 0.11/0.30  % CPUTime    : 
% 0.15/0.44  %----Proving TF0_NAR, FOF, or CNF
% 0.39/0.57  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.PopWcO4hUc/cvc5---1.0.5_21767.p...
% 0.39/0.57  ------- get file name : TPTP file name is SWV391+1
% 0.39/0.57  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21767.smt2...
% 0.39/0.57  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.39/0.57  % SZS status Theorem for SWV391+1
% 0.39/0.57  % SZS output start Proof for SWV391+1
% 0.39/0.57  (
% 0.39/0.57  (let ((_let_1 (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (let ((_let_2 (tptp.remove_cpq _let_1 X))) (=> (and (tptp.check_cpq _let_2) (tptp.ok _let_2)) (tptp.check_cpq _let_1)))))))) (let ((_let_2 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (tptp.ok (tptp.remove_cpq (tptp.triple U V W) X)) (tptp.contains_slb V X))))) (let ((_let_3 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.remove_cpq (tptp.triple U V W) X))) (=> (and (tptp.check_cpq _let_1) (tptp.ok _let_1)) (forall ((Y $$unsorted)) (=> (tptp.pair_in_list V X Y) (tptp.less_than Y X)))))))) (let ((_let_4 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (tptp.pair_in_list U V W) (forall ((X $$unsorted)) (=> (tptp.contains_slb U X) (or (tptp.pair_in_list (tptp.remove_slb U X) V W) (= V X)))))))) (let ((_let_5 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.check_cpq (tptp.triple U V W)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.pair_in_list V X Y) (tptp.less_than Y X))))))) (let ((_let_6 (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_7 (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_8 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.ok (tptp.triple U V tptp.bad)) false)))) (let ((_let_9 (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_10 (forall ((U $$unsorted) (V $$unsorted)) (or (tptp.less_than U V) (tptp.less_than V U))))) (let ((_let_11 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_12 (tptp.remove_cpq _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.check_cpq _let_12))) (let ((_let_14 (tptp.ok _let_12))) (let ((_let_15 (tptp.less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (tptp.pair_in_list SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_17 (not _let_16))) (let ((_let_18 (not _let_14))) (let ((_let_19 (not _let_13))) (let ((_let_20 (or _let_19 _let_18 _let_17 _let_15))) (let ((_let_21 (tptp.check_cpq _let_11))) (let ((_let_22 (or _let_19 _let_18 _let_21))) (let ((_let_23 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (let ((_let_2 (tptp.remove_cpq _let_1 X))) (or (not (tptp.check_cpq _let_2)) (not (tptp.ok _let_2)) (tptp.check_cpq _let_1))))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (or))) (let ((_let_27 (not _let_23))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_25) :args (_let_27))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_23))) (REFL :args (_let_24)) :args _let_26)) _let_25 :args (_let_24 true _let_23)))) (let ((_let_29 (REFL :args (_let_22)))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_13))) :args _let_26)) :args ((or _let_13 _let_22))) _let_28 :args (_let_13 true _let_22)))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 1)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_14))) :args _let_26)) :args ((or _let_14 _let_22))) _let_28 :args (_let_14 true _let_22)))) (let ((_let_32 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (BOUND_VARIABLE_1289 $$unsorted)) (let ((_let_1 (tptp.remove_cpq (tptp.triple U V W) X))) (or (not (tptp.check_cpq _let_1)) (not (tptp.ok _let_1)) (not (tptp.pair_in_list V X BOUND_VARIABLE_1289)) (tptp.less_than BOUND_VARIABLE_1289 X)))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_35 (tptp.less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_36 (not _let_15))) (let ((_let_37 (tptp.remove_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_38 (tptp.pair_in_list _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_39 (tptp.contains_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.pair_in_list SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_40 _let_38 _let_34))) (let ((_let_44 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (BOUND_VARIABLE_1264 $$unsorted)) (or (not (tptp.pair_in_list U V W)) (not (tptp.contains_slb U BOUND_VARIABLE_1264)) (tptp.pair_in_list (tptp.remove_slb U BOUND_VARIABLE_1264) V W) (= V BOUND_VARIABLE_1264))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (not _let_38))) (let ((_let_47 (or _let_46 _let_35))) (let ((_let_48 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.pair_in_list (tptp.remove_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) X Y)) (tptp.less_than Y X))))) (let ((_let_49 (tptp.remove_pqp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_50 (tptp.triple _let_49 _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_51 (tptp.check_cpq _let_50))) (let ((_let_52 (= _let_51 _let_48))) (let ((_let_53 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.check_cpq (tptp.triple U V W)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.pair_in_list V X Y)) (tptp.less_than Y X))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 ((tptp.triple U V W)))) (let ((_let_57 (= _let_12 _let_50))) (let ((_let_58 (tptp.lookup_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_59 (tptp.less_than _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_40 _let_60 _let_57))) (let ((_let_62 (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_63 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (tptp.less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_58))) (let ((_let_65 (or _let_59 _let_64))) (let ((_let_66 (and _let_64 _let_60))) (let ((_let_67 (_let_10))) (let ((_let_68 (ASSUME :args _let_67))) (let ((_let_69 (tptp.strictly_less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_58))) (let ((_let_70 (= _let_69 _let_66))) (let ((_let_71 (not _let_66))) (let ((_let_72 (_let_9))) (let ((_let_73 (ASSUME :args _let_72))) (let ((_let_74 (tptp.triple _let_49 _let_37 tptp.bad))) (let ((_let_75 (= _let_12 _let_74))) (let ((_let_76 (not _let_69))) (let ((_let_77 (or _let_40 _let_76 _let_75))) (let ((_let_78 (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_79 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (tptp.ok _let_74))) (let ((_let_81 (not _let_75))) (let ((_let_82 (forall ((U $$unsorted) (V $$unsorted)) (not (tptp.ok (tptp.triple U V tptp.bad)))))) (let ((_let_83 (not _let_80))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (or _let_18 _let_39))) (let ((_let_86 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.ok (tptp.remove_cpq (tptp.triple U V W) X))) (tptp.contains_slb V X))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_18 _let_39 (not _let_85)))) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :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.remove_cpq (tptp.triple U V W) X)))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_39 false _let_14 false _let_85)))) (let ((_let_89 (not _let_64))) (let ((_let_90 (_let_66))) (let ((_let_91 (not _let_51))) (let ((_let_92 (_let_48))) (let ((_let_93 (or _let_42 _let_35))) (let ((_let_94 (not _let_35))) (let ((_let_95 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.pair_in_list SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (tptp.less_than Y X))))) (let ((_let_96 (not _let_93))) (let ((_let_97 (= _let_21 _let_95))) (let ((_let_98 (not _let_95))) (let ((_let_99 (_let_98))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_99)) :args _let_99)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_98) _let_95))) (REFL :args (_let_96)) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_97)) :args ((or _let_21 _let_98 (not _let_97)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 2)) _let_28 :args ((not _let_21) true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_97 false _let_53)) :args (_let_98 true _let_21 false _let_97)) :args (_let_96 true _let_95)))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_93 1)) _let_100 :args (_let_94 true _let_93)))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_93 0)) (CONG (REFL :args (_let_93)) (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_26)) :args ((or _let_41 _let_93))) _let_100 :args (_let_41 true _let_93)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_40 _let_42 _let_38 _let_34 (not _let_43)))) _let_88 _let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_35 _let_46 (not _let_47)))) _let_101 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_92) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.pair_in_list _let_37 X Y) false))))) :args _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_52)) :args ((or _let_48 _let_91 (not _let_52)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_91)))) (CONG (SYMM (ASSUME :args (_let_57))) :args (APPLY_UF tptp.check_cpq)) (TRUE_INTRO (ASSUME :args (_let_13))))) :args (_let_13 _let_57 _let_91))) (CONG (REFL :args (_let_19)) (REFL :args ((not _let_57))) (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_51))) :args _let_26)) _let_30 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_40 _let_60 _let_57 (not _let_61)))) _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_90) (CONG (REFL :args _let_90) (REFL :args (_let_89)) (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_26)) :args ((or _let_59 _let_66 _let_89))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_70)) :args ((or _let_69 _let_71 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_40 _let_76 _let_75 (not _let_77)))) _let_88 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_83)))) (CONG (SYMM (ASSUME :args (_let_75))) :args (APPLY_UF tptp.ok)) (TRUE_INTRO (ASSUME :args (_let_14))))) :args (_let_14 _let_75 _let_83))) (CONG (REFL :args (_let_18)) (REFL :args (_let_81)) (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_80))) :args _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (_let_49 _let_37 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.triple U V tptp.bad)))) :args (_let_82))) _let_84 :args (_let_83 false _let_82)) _let_31 :args (_let_81 true _let_80 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :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.remove_cpq (tptp.triple U V W) X)))) :args (_let_78))) _let_79 :args (_let_77 false _let_78)) :args (_let_76 false _let_39 true _let_75 false _let_77)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_58 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.strictly_less_than U V)))) :args _let_72)) _let_73 :args (_let_70 false _let_9)) :args (_let_71 true _let_69 false _let_70)) (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_59 _let_64 (not _let_65)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.less_than U V) true))))) :args _let_67)) _let_68 :args (_let_65 false _let_10)) :args (_let_59 true _let_66 false _let_64 false _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :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.remove_cpq (tptp.triple U V W) X)))) :args (_let_62))) _let_63 :args (_let_61 false _let_62)) :args (_let_57 false _let_39 false _let_59 false _let_61)) :args (_let_51 false _let_13 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_49 _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_52 false _let_53)) :args (_let_48 false _let_51 false _let_52)) :args (_let_47 false _let_48)) :args (_let_46 true _let_35 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.pair_in_list (tptp.remove_slb U BOUND_VARIABLE_1264) V W) true))))) :args (_let_44)))) _let_45 :args (_let_43 false _let_44)) :args (_let_34 false _let_39 false _let_41 true _let_38 false _let_43)))) (let ((_let_104 (and _let_94 _let_34))) (let ((_let_105 (_let_94 _let_34))) (let ((_let_106 (ASSUME :args (_let_94)))) (let ((_let_107 (ASSUME :args (_let_34)))) (let ((_let_108 (SYMM (SYMM _let_107)))) (let ((_let_109 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_110 (and _let_41 _let_34))) (let ((_let_111 (_let_41 _let_34))) (let ((_let_112 (ASSUME :args (_let_41)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_18 _let_17 _let_15 (not _let_20)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_110)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_112 _let_107) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_108 _let_109 :args (APPLY_UF tptp.pair_in_list)) (TRUE_INTRO _let_112))) :args _let_111)) :args _let_111)) :args (true _let_110)) _let_102 _let_103 :args (_let_16 false _let_41 false _let_34)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_104)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_106 _let_107) (SCOPE (FALSE_ELIM (TRANS (CONG _let_109 _let_108 :args (APPLY_UF tptp.less_than)) (FALSE_INTRO _let_106))) :args _let_105)) :args _let_105)) :args (true _let_104)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_35))) (REFL :args ((not _let_34))) (REFL :args (_let_36)) :args _let_26)) _let_101 _let_103 :args (_let_36 true _let_35 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((tptp.remove_cpq (tptp.triple U V W) X) (not (= (tptp.pair_in_list V X BOUND_VARIABLE_1289) false))))) :args (_let_32))) _let_33 :args (_let_20 false _let_32)) _let_31 _let_30 :args (false false _let_16 true _let_15 false _let_20 false _let_14 false _let_13)) :args ((forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (and (tptp.less_than U V) (tptp.less_than V W)) (tptp.less_than U W))) _let_10 (forall ((U $$unsorted)) (tptp.less_than U U)) _let_9 (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 $$unsorted)) (not (tptp.contains_slb tptp.create_slb U))) (forall ((U $$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))) _let_8 (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 $$unsorted)) (=> (not (tptp.contains_slb V X)) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple U V tptp.bad)))) _let_7 _let_6 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.findmin_cpq_eff (tptp.triple U tptp.create_slb V)) (tptp.triple U tptp.create_slb tptp.bad))) (forall ((U $$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_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.39/0.57  )
% 0.39/0.57  % SZS output end Proof for SWV391+1
% 0.39/0.57  % cvc5---1.0.5 exiting
% 0.39/0.58  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------