%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV394+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n003.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 0.22s 0.58s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SWV394+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n003.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 06:55:55 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.58  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Tz7mh8dXSM/cvc5---1.0.5_3079.p...
% 0.22/0.58  ------- get file name : TPTP file name is SWV394+1
% 0.22/0.58  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3079.smt2...
% 0.22/0.58  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.58  % SZS status Theorem for SWV394+1
% 0.22/0.58  % SZS output start Proof for SWV394+1
% 0.22/0.58  (
% 0.22/0.58  (let ((_let_1 (not (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 $$unsorted)) (=> (tptp.pair_in_list V X Y) (tptp.less_than Y X))))))))) (let ((_let_2 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.pair_in_list V X Y) (tptp.strictly_less_than X Y) (tptp.ok (tptp.remove_cpq (tptp.triple U V W) X))) (tptp.pair_in_list (tptp.remove_slb V X) X Y))))) (let ((_let_3 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.check_cpq (tptp.triple U V W)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.pair_in_list V X Y) (tptp.less_than Y X))))))) (let ((_let_4 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (tptp.contains_slb V X) (tptp.strictly_less_than X (tptp.lookup_slb V X))) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) tptp.bad)))))) (let ((_let_5 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (tptp.contains_slb V X) (tptp.less_than (tptp.lookup_slb V X) X)) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) W)))))) (let ((_let_6 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (not (tptp.contains_slb V X)) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple U V tptp.bad)))))) (let ((_let_7 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.ok (tptp.triple U V tptp.bad)) false)))) (let ((_let_8 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.strictly_less_than U V) (and (tptp.less_than U V) (not (tptp.less_than V U))))))) (let ((_let_9 (forall ((U $$unsorted) (V $$unsorted)) (or (tptp.less_than U V) (tptp.less_than V U))))) (let ((_let_10 (tptp.remove_cpq (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (tptp.ok _let_10))) (let ((_let_12 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.bad))) (let ((_let_13 (tptp.ok _let_12))) (let ((_let_14 (= _let_10 _let_12))) (let ((_let_15 (tptp.less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (tptp.pair_in_list SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (not _let_16))) (let ((_let_18 (not _let_11))) (let ((_let_19 (tptp.check_cpq _let_10))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_17 _let_15))) (let ((_let_22 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (BOUND_VARIABLE_1251 $$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_1251)) (tptp.less_than BOUND_VARIABLE_1251 X)))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (or))) (let ((_let_26 (not _let_22))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_24) :args (_let_26))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_22))) (REFL :args (_let_23)) :args _let_25)) _let_24 :args (_let_23 true _let_22)))) (let ((_let_28 (REFL :args (_let_21)))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 1)) (CONG _let_28 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_11))) :args _let_25)) :args ((or _let_11 _let_21))) _let_27 :args (_let_11 true _let_21)))) (let ((_let_30 (forall ((U $$unsorted) (V $$unsorted)) (not (tptp.ok (tptp.triple U V tptp.bad)))))) (let ((_let_31 (not _let_13))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (_let_30))) (let ((_let_34 ((tptp.triple U V tptp.bad)))) (let ((_let_35 (tptp.contains_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_36 (or _let_35 _let_14))) (let ((_let_37 (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_38 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (tptp.remove_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_40 (tptp.remove_pqp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_41 (tptp.triple _let_40 _let_39 tptp.bad))) (let ((_let_42 (= _let_10 _let_41))) (let ((_let_43 (tptp.lookup_slb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_44 (tptp.strictly_less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_43))) (let ((_let_45 (not _let_44))) (let ((_let_46 (not _let_35))) (let ((_let_47 (or _let_46 _let_45 _let_42))) (let ((_let_48 (tptp.triple _let_40 _let_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_49 (= _let_10 _let_48))) (let ((_let_50 (tptp.less_than _let_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_46 _let_51 _let_49))) (let ((_let_53 (tptp.less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_43))) (let ((_let_54 (and _let_53 _let_51))) (let ((_let_55 (= _let_44 _let_54))) (let ((_let_56 (or _let_50 _let_53))) (let ((_let_57 (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_58 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (tptp.ok _let_41))) (let ((_let_60 (not _let_42))) (let ((_let_61 (not _let_59))) (let ((_let_62 (REFL :args (_let_18)))) (let ((_let_63 (TRUE_INTRO (ASSUME :args (_let_11))))) (let ((_let_64 (APPLY_UF tptp.ok))) (let ((_let_65 (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_66 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (tptp.check_cpq _let_48))) (let ((_let_68 (not _let_49))) (let ((_let_69 (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_70 (= _let_67 _let_69))) (let ((_let_71 (not _let_67))) (let ((_let_72 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.check_cpq (tptp.triple U V W)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.pair_in_list V X Y)) (tptp.less_than Y X))))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (tptp.pair_in_list _let_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_75 _let_15))) (let ((_let_77 (not _let_76))) (let ((_let_78 (tptp.strictly_less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_17 _let_79 _let_18 _let_74))) (let ((_let_81 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.pair_in_list V X Y)) (not (tptp.strictly_less_than X Y)) (not (tptp.ok (tptp.remove_cpq (tptp.triple U V W) X))) (tptp.pair_in_list (tptp.remove_slb V X) X Y))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (not _let_15))) (let ((_let_84 (tptp.less_than SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_85 (and _let_84 _let_83))) (let ((_let_86 (= _let_78 _let_85))) (let ((_let_87 (_let_8))) (let ((_let_88 (ASSUME :args _let_87))) (let ((_let_89 (or _let_15 _let_84))) (let ((_let_90 (_let_9))) (let ((_let_91 (ASSUME :args _let_90))) (let ((_let_92 ((not (= (tptp.less_than U V) true))))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 3)) _let_27 :args (_let_83 true _let_21)))) (let ((_let_94 (not _let_84))) (let ((_let_95 (_let_85))) (let ((_let_96 (_let_69))) (let ((_let_97 (not _let_53))) (let ((_let_98 (_let_54))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_31)))) (CONG (SYMM (ASSUME :args (_let_14))) :args _let_64) _let_63)) :args (_let_11 _let_14 _let_31))) (CONG _let_62 (REFL :args ((not _let_14))) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_13))) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_14 (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_98) (CONG (REFL :args _let_98) (REFL :args (_let_97)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_25)) :args ((or _let_50 _let_54 _let_97))) (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_50 _let_53 (not _let_56)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_92)) :args _let_90)) _let_91 :args (_let_56 false _let_9)) (REORDERING (CNF_EQUIV_POS2 :args (_let_55)) :args ((or _let_44 (not _let_54) (not _let_55)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.strictly_less_than U V)))) :args _let_87)) _let_88 :args (_let_55 false _let_8)) (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_46 _let_51 _let_49 (not _let_52)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_71)))) (CONG (SYMM (ASSUME :args (_let_49))) :args (APPLY_UF tptp.check_cpq)) (TRUE_INTRO (ASSUME :args (_let_19))))) :args (_let_19 _let_49 _let_71))) (CONG (REFL :args (_let_20)) (REFL :args (_let_68)) (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_67))) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG _let_28 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_25)) :args ((or _let_19 _let_21))) _let_27 :args (_let_19 true _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_70)) :args ((or _let_69 _let_71 (not _let_70)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_96) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.pair_in_list _let_39 X Y) false))))) :args _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_15 _let_75 _let_77))) _let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_18 _let_17 _let_79 _let_74 (not _let_80)))) _let_29 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 2)) (CONG _let_28 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_25)) :args ((or _let_16 _let_21))) _let_27 :args (_let_16 true _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_86)) :args ((or _let_78 (not _let_85) (not _let_86)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_95) (CONG (REFL :args _let_95) (REFL :args (_let_94)) (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_15))) :args _let_25)) :args ((or _let_15 _let_94 _let_85))) _let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_15 _let_84 (not _let_89)))) _let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_92)) :args _let_90)) _let_91 :args (_let_89 false _let_9)) :args (_let_84 true _let_15 false _let_89)) :args (_let_85 true _let_15 false _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.less_than V U)))) :args _let_87)) _let_88 :args (_let_86 false _let_8)) :args (_let_78 false _let_85 false _let_86)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :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_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.strictly_less_than X Y) false)) (tptp.triple U V W)))) :args (_let_81))) _let_82 :args (_let_80 false _let_81)) :args (_let_74 false _let_11 false _let_16 false _let_78 false _let_80)) :args (_let_77 true _let_15 false _let_74)) :args ((not _let_69) true _let_76)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_40 _let_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.triple U V W)))) :args (_let_72))) _let_73 :args (_let_70 false _let_72)) :args (_let_71 true _let_69 false _let_70)) :args (_let_68 false _let_19 true _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :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_65))) _let_66 :args (_let_52 false _let_65)) (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_45 _let_42 (not _let_47)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_61)))) (CONG (SYMM (ASSUME :args (_let_42))) :args _let_64) _let_63)) :args (_let_11 _let_42 _let_61))) (CONG _let_62 (REFL :args (_let_60)) (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_59))) :args _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_40 _let_39 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_33)) _let_32 :args (_let_61 false _let_30)) _let_29 :args (_let_60 true _let_59 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :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_57))) _let_58 :args (_let_47 false _let_57)) :args (_let_46 false _let_53 false _let_56 true _let_54 false _let_55 true _let_50 true _let_49 false _let_52 true _let_44 true _let_42 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :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_37))) _let_38 :args (_let_36 false _let_37)) :args (_let_14 true _let_35 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_33)) _let_32 :args (_let_31 false _let_30)) _let_29 :args (false false _let_14 true _let_13 false _let_11)) :args ((forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (and (tptp.less_than U V) (tptp.less_than V W)) (tptp.less_than U W))) _let_9 (forall ((U $$unsorted)) (tptp.less_than U U)) _let_8 (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_7 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (not (tptp.ok (tptp.triple U V W))) (= W tptp.bad))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.insert_cpq (tptp.triple U V W) X) (tptp.triple (tptp.insert_pqp U X) (tptp.insert_slb V (tptp.pair X tptp.bottom)) W))) _let_6 _let_5 _let_4 (forall ((U $$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_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.59  )
% 0.22/0.59  % SZS output end Proof for SWV394+1
% 0.22/0.59  % cvc5---1.0.5 exiting
% 0.22/0.59  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------