%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC421+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n008.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 20:25:30 EDT 2023

% Result   : Theorem 41.22s 41.45s
% Output   : Proof 41.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SWC421+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.36  % Computer : n008.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Mon Aug 28 14:34:32 EDT 2023
% 0.16/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 41.22/41.45  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.XVibc0eV6m/cvc5---1.0.5_15615.p...
% 41.22/41.45  ------- get file name : TPTP file name is SWC421+1
% 41.22/41.45  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15615.smt2...
% 41.22/41.45  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 41.22/41.45  --- Run --no-e-matching --full-saturate-quant at 5...
% 41.22/41.45  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 41.22/41.45  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 41.22/41.45  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 41.22/41.45  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 41.22/41.45  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 41.22/41.45  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 41.22/41.45  % SZS status Theorem for SWC421+1
% 41.22/41.45  % SZS output start Proof for SWC421+1
% 41.22/41.45  (
% 41.22/41.45  (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (exists ((Y $$unsorted)) (and (tptp.ssItem Y) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (and (tptp.ssList X1) (= (tptp.app (tptp.app Z _let_1) X1) V) (= (tptp.app (tptp.app X1 _let_1) Z) U)))))))) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (tptp.neq X tptp.nil) (or (not (tptp.neq W tptp.nil)) (exists ((X2 $$unsorted)) (and (tptp.ssList X2) (not (= X X2)) (exists ((X3 $$unsorted)) (and (tptp.ssList X3) (exists ((X4 $$unsorted)) (and (tptp.ssList X4) (= (tptp.tl W) X3) (= (tptp.app X3 X4) X2) (exists ((X5 $$unsorted)) (and (tptp.ssItem X5) (= (tptp.cons X5 tptp.nil) X4) (= (tptp.hd W) X5) (tptp.neq tptp.nil W))) (tptp.neq tptp.nil W))))))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_9 (tptp.ssList tptp.nil))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_12 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (tptp.ssItem _let_12))) (let ((_let_14 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (tptp.ssList _let_14))) (let ((_let_16 (tptp.cons _let_12 tptp.nil))) (let ((_let_17 (tptp.app tptp.nil _let_16))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app _let_17 _let_14)))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.app _let_14 _let_16))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app _let_20 tptp.nil)))) (let ((_let_22 (not _let_21))) (let ((_let_23 (not _let_9))) (let ((_let_24 (not _let_15))) (let ((_let_25 (not _let_13))) (let ((_let_26 (or _let_25 _let_24 _let_23 _let_22 _let_19))) (let ((_let_27 (ASSUME :args (_let_9)))) (let ((_let_28 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_29 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28 _let_13))) (let ((_let_32 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_35 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_36 (tptp.neq tptp.nil tptp.nil))) (let ((_let_37 (not _let_28))) (let ((_let_38 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.ssList _let_20))) (let ((_let_41 (tptp.ssList _let_16))) (let ((_let_42 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_43 (and _let_42 _let_13 _let_41 _let_15 _let_40 _let_39))) (let ((_let_44 (not _let_35))) (let ((_let_45 (or _let_44 _let_43))) (let ((_let_46 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_47 (and _let_46 _let_45))) (let ((_let_48 (not _let_45))) (let ((_let_49 (and _let_37 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_50 (forall ((Y $$unsorted) (BOUND_VARIABLE_5298 $$unsorted) (BOUND_VARIABLE_5296 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5296)) (not (tptp.ssList BOUND_VARIABLE_5298)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5296 _let_1) BOUND_VARIABLE_5298) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5298 _let_1) BOUND_VARIABLE_5296) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_51 (not _let_50))) (let ((_let_52 (not _let_46))) (let ((_let_53 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_30 _let_54 _let_52 _let_51 _let_49 _let_47))) (let ((_let_56 (forall ((U $$unsorted) (BOUND_VARIABLE_5498 $$unsorted)) (let ((_let_1 (tptp.hd U))) (let ((_let_2 (tptp.cons _let_1 tptp.nil))) (let ((_let_3 (tptp.tl U))) (let ((_let_4 (tptp.app _let_3 _let_2))) (let ((_let_5 (tptp.neq BOUND_VARIABLE_5498 tptp.nil))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5498)) (not _let_5) (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5298 $$unsorted) (BOUND_VARIABLE_5296 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5296)) (not (tptp.ssList BOUND_VARIABLE_5298)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5296 _let_1) BOUND_VARIABLE_5298) BOUND_VARIABLE_5498)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_5298 _let_1) BOUND_VARIABLE_5296))))))) (and (not (= tptp.nil U)) (= tptp.nil BOUND_VARIABLE_5498)) (and _let_5 (or (not (tptp.neq U tptp.nil)) (and (tptp.neq tptp.nil U) (tptp.ssItem _let_1) (tptp.ssList _let_2) (tptp.ssList _let_3) (tptp.ssList _let_4) (not (= _let_4 BOUND_VARIABLE_5498)))))))))))))) (let ((_let_57 (not _let_55))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (or))) (let ((_let_60 (not _let_56))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_58) :args (_let_60)) (REWRITE :args ((=> _let_60 (not (or _let_30 _let_54 _let_52 (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5298 $$unsorted) (BOUND_VARIABLE_5296 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5296)) (not (tptp.ssList BOUND_VARIABLE_5298)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5296 _let_1) BOUND_VARIABLE_5298) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app (tptp.app BOUND_VARIABLE_5298 _let_1) BOUND_VARIABLE_5296))))))) _let_49 (and _let_46 (or _let_44 (and _let_42 _let_13 _let_41 _let_15 _let_40 (not (= _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_56))) (REFL :args (_let_57)) :args _let_59)) _let_58 :args (_let_57 true _let_56)))) (let ((_let_62 (REFL :args (_let_55)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_47)) :args ((or _let_52 _let_47 _let_48))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 2)) (CONG _let_62 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_46))) :args _let_59)) :args ((or _let_46 _let_55))) _let_61 :args (_let_46 true _let_55)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_55 5)) _let_61 :args ((not _let_47) true _let_55)) :args (_let_48 false _let_46 true _let_47)))) (let ((_let_64 (not _let_36))) (let ((_let_65 (or _let_23 _let_23 _let_64))) (let ((_let_66 (forall ((U $$unsorted) (BOUND_VARIABLE_3316 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3316)) (= (tptp.neq U BOUND_VARIABLE_3316) (not (= U BOUND_VARIABLE_3316))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (_let_66))) (let ((_let_69 (ASSUME :args (_let_64)))) (let ((_let_70 (REFL :args (tptp.nil)))) (let ((_let_71 (ASSUME :args (_let_28)))) (let ((_let_72 (ASSUME :args (_let_35)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_69 _let_71 _let_72) :args (_let_28 _let_35 _let_64)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_72)) (CONG (SYMM _let_71) _let_70 :args (APPLY_UF tptp.neq)) (FALSE_INTRO _let_69))) :args (_let_64 _let_28 _let_35)) :args ((not (and _let_28 _let_35 _let_64)) SB_LITERAL))) (CONG (REFL :args (_let_37)) (REFL :args (_let_44)) (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_36))) :args _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_65))) :args ((or _let_23 _let_64 (not _let_65)))) _let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.nil tptp.nil QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_68))) _let_67 :args (_let_65 false _let_66)) :args (_let_64 false _let_9 false _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG (REFL :args (_let_45)) (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_35))) :args _let_59)) :args ((or _let_35 _let_45))) _let_63 :args (_let_35 true _let_45)) :args (_let_37 true _let_36 false _let_35)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 0)) (CONG _let_62 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_59)) :args ((or _let_29 _let_55))) _let_61 :args (_let_29 true _let_55)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_28 _let_13 (not _let_31)))) _let_74 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args _let_34) :args (_let_32))) _let_33 :args (_let_31 false _let_32)) :args (_let_13 false _let_29 true _let_28 false _let_31)))) (let ((_let_76 (or _let_30 _let_28 _let_15))) (let ((_let_77 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssList (tptp.tl U)))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_30 _let_28 _let_15 (not _let_76)))) _let_74 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args _let_34) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_15 false _let_29 true _let_28 false _let_76)))) (let ((_let_80 (_let_50))) (let ((_let_81 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil)))) (let ((_let_82 (or _let_54 _let_81))) (let ((_let_83 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (not _let_41))) (let ((_let_86 (or _let_24 _let_85 _let_40))) (let ((_let_87 (forall ((U $$unsorted) (BOUND_VARIABLE_3597 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3597)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3597)))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (or _let_23 _let_25 _let_41))) (let ((_let_90 (forall ((U $$unsorted) (BOUND_VARIABLE_3339 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3339)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3339 U)))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_23 _let_41 _let_25 (not _let_89)))) _let_27 _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (tptp.nil _let_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_90))) _let_91 :args (_let_89 false _let_90)) :args (_let_41 false _let_9 false _let_13 false _let_89)))) (let ((_let_93 (= _let_37 _let_42))) (let ((_let_94 (or _let_23 _let_30 _let_93))) (let ((_let_95 (not _let_93))) (let ((_let_96 (not _let_40))) (let ((_let_97 (not _let_42))) (let ((_let_98 (_let_43))) (let ((_let_99 (and _let_38 _let_81))) (let ((_let_100 (_let_38 _let_81))) (let ((_let_101 (APPLY_UF tptp.app))) (let ((_let_102 (ASSUME :args (_let_38)))) (let ((_let_103 (ASSUME :args (_let_81)))) (let ((_let_104 (tptp.app tptp.nil _let_14))) (let ((_let_105 (= (tptp.app _let_16 _let_14) (tptp.cons _let_12 _let_104)))) (let ((_let_106 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.cons _let_12 _let_14)))) (let ((_let_107 (= _let_14 _let_104))) (let ((_let_108 (= _let_16 _let_17))) (let ((_let_109 (or _let_24 _let_23 _let_25 _let_105))) (let ((_let_110 (forall ((U $$unsorted) (BOUND_VARIABLE_3639 $$unsorted) (BOUND_VARIABLE_3637 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3637)) (not (tptp.ssItem BOUND_VARIABLE_3639)) (= (tptp.cons BOUND_VARIABLE_3639 (tptp.app BOUND_VARIABLE_3637 U)) (tptp.app (tptp.cons BOUND_VARIABLE_3639 BOUND_VARIABLE_3637) U)))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (or _let_30 _let_28 _let_106))) (let ((_let_113 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (or _let_24 _let_107))) (let ((_let_116 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_117 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_118 (_let_116))) (let ((_let_119 ((not (= (tptp.ssList U) false))))) (let ((_let_120 (or _let_85 _let_108))) (let ((_let_121 (and _let_108 _let_107 _let_106 _let_105))) (let ((_let_122 (ASSUME :args (_let_108)))) (let ((_let_123 (ASSUME :args (_let_105)))) (let ((_let_124 (ASSUME :args (_let_107)))) (let ((_let_125 (ASSUME :args (_let_106)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_23 _let_25 _let_24 _let_22 _let_19 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_121)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_122 _let_123 _let_124 _let_125) (SCOPE (TRANS (SYMM (SYMM _let_125)) (CONG (REFL :args (_let_12)) (SYMM (SYMM _let_124)) :args (APPLY_UF tptp.cons)) (SYMM _let_123) (CONG (SYMM (SYMM _let_122)) (REFL :args (_let_14)) :args _let_101)) :args (_let_108 _let_105 _let_107 _let_106))) :args (_let_108 _let_107 _let_106 _let_105))) :args (true 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(=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))) (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))) (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) _let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 41.22/41.46  )
% 41.22/41.46  % SZS output end Proof for SWC421+1
% 41.22/41.46  % cvc5---1.0.5 exiting
% 41.22/41.46  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------