TSTP Solution File: SWC247+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC247+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:24:14 EDT 2023
% Result : Theorem 79.68s 79.89s
% Output : Proof 79.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC247+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 17:38:40 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 79.68/79.89 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.LA1MLn2wXj/cvc5---1.0.5_29081.p...
% 79.68/79.89 ------- get file name : TPTP file name is SWC247+1
% 79.68/79.89 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29081.smt2...
% 79.68/79.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 79.68/79.89 --- Run --no-e-matching --full-saturate-quant at 5...
% 79.68/79.89 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 79.68/79.89 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 79.68/79.89 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 79.68/79.89 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 79.68/79.89 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 79.68/79.89 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 79.68/79.89 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 79.68/79.89 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 79.68/79.89 --- Run --relevant-triggers --full-saturate-quant at 5...
% 79.68/79.89 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 79.68/79.89 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 79.68/79.89 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 79.68/79.89 % SZS status Theorem for SWC247+1
% 79.68/79.89 % SZS output start Proof for SWC247+1
% 79.68/79.89 (
% 79.68/79.89 (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.frontsegP X W)) (not (tptp.totalorderedP W)) (= tptp.nil U) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.frontsegP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (exists ((Z $$unsorted)) (and (tptp.ssItem Z) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (exists ((X2 $$unsorted)) (and (tptp.ssList X2) (= (tptp.app (tptp.app X1 (tptp.cons Z tptp.nil)) X2) U) (forall ((X3 $$unsorted)) (=> (tptp.ssItem X3) (or (not (tptp.memberP X1 X3)) (not (tptp.memberP X2 X3)) (not (tptp.lt Z X3)) (tptp.leq Z X3)))))))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))))) (let ((_let_9 (tptp.ssList tptp.nil))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_11 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_12 (tptp.ssItem _let_11))) (let ((_let_13 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_268))) (let ((_let_14 (tptp.leq _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_268))) (let ((_let_15 (and (not (= _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_268)) _let_14))) (let ((_let_16 (tptp.lt _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_268))) (let ((_let_17 (= _let_16 _let_15))) (let ((_let_18 (not _let_13))) (let ((_let_19 (not _let_12))) (let ((_let_20 (or _let_19 _let_18 _let_17))) (let ((_let_21 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_12))) (let ((_let_25 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)) (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)) (not (tptp.segmentP Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.totalorderedP Y))))))) (let ((_let_28 (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_29 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_30 (not (tptp.totalorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_31 (forall ((Z $$unsorted) (BOUND_VARIABLE_5294 $$unsorted) (BOUND_VARIABLE_5292 $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5292)) (not (tptp.ssList BOUND_VARIABLE_5294)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5292 (tptp.cons Z tptp.nil)) BOUND_VARIABLE_5294) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (forall ((X3 $$unsorted)) (or (not (tptp.ssItem X3)) (not (tptp.memberP BOUND_VARIABLE_5292 X3)) (not (tptp.memberP BOUND_VARIABLE_5294 X3)) (not (tptp.lt Z X3)) (tptp.leq Z X3)))))))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_23 _let_21 _let_32 _let_30 _let_29 _let_28 _let_27))) (let ((_let_34 (forall ((U $$unsorted) (BOUND_VARIABLE_5380 $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5294 $$unsorted) (BOUND_VARIABLE_5292 $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5292)) (not (tptp.ssList BOUND_VARIABLE_5294)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_5292 (tptp.cons Z tptp.nil)) BOUND_VARIABLE_5294))) (not (forall ((X3 $$unsorted)) (or (not (tptp.ssItem X3)) (not (tptp.memberP BOUND_VARIABLE_5292 X3)) (not (tptp.memberP BOUND_VARIABLE_5294 X3)) (not (tptp.lt Z X3)) (tptp.leq Z X3))))))) (not (tptp.totalorderedP U)) (not (tptp.ssList BOUND_VARIABLE_5380)) (not (tptp.frontsegP BOUND_VARIABLE_5380 U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.frontsegP BOUND_VARIABLE_5380 Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y))))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (or))) (let ((_let_38 (not _let_34))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_36) :args (_let_38)) (REWRITE :args ((=> _let_38 (not (or _let_23 _let_21 (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5294 $$unsorted) (BOUND_VARIABLE_5292 $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5292)) (not (tptp.ssList BOUND_VARIABLE_5294)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app (tptp.app BOUND_VARIABLE_5292 (tptp.cons Z tptp.nil)) BOUND_VARIABLE_5294))) (not (forall ((X3 $$unsorted)) (or (not (tptp.ssItem X3)) (not (tptp.memberP BOUND_VARIABLE_5292 X3)) (not (tptp.memberP BOUND_VARIABLE_5294 X3)) (not (tptp.lt Z X3)) (tptp.leq Z X3))))))) _let_30 _let_29 _let_28 _let_27))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_34))) (REFL :args (_let_35)) :args _let_37)) _let_36 :args (_let_35 true _let_34)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 1)) _let_39 :args ((not _let_21) true _let_33)))) (let ((_let_41 (REFL :args (_let_33)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 0)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_37)) :args ((or _let_22 _let_33))) _let_39 :args (_let_22 true _let_33)))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_21 _let_12 (not _let_24)))) _let_42 _let_40 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_25))) _let_26 :args (_let_24 false _let_25)) :args (_let_12 false _let_22 true _let_21 false _let_24)))) (let ((_let_44 (not _let_16))) (let ((_let_45 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_46 (or _let_18 (not (tptp.memberP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_268)) (not (tptp.memberP _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_268)) _let_44 _let_14))) (let ((_let_47 (forall ((X3 $$unsorted)) (let ((_let_1 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (or (not (tptp.ssItem X3)) (not (tptp.memberP tptp.nil X3)) (not (tptp.memberP (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) X3)) (not (tptp.lt _let_1 X3)) (tptp.leq _let_1 X3)))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (not _let_47))) (let ((_let_50 (tptp.cons _let_11 tptp.nil))) (let ((_let_51 (tptp.app tptp.nil _let_50))) (let ((_let_52 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app _let_51 _let_45)))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.ssList _let_45))) (let ((_let_55 (not _let_54))) (let ((_let_56 (not _let_9))) (let ((_let_57 (or _let_19 _let_56 _let_55 _let_53 _let_49))) (let ((_let_58 (_let_31))) (let ((_let_59 (tptp.cons _let_11 _let_45))) (let ((_let_60 (= _let_59 (tptp.app _let_50 _let_45)))) (let ((_let_61 (= _let_50 _let_51))) (let ((_let_62 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_59))) (let ((_let_63 (or _let_55 _let_19 _let_60))) (let ((_let_64 (forall ((U $$unsorted) (BOUND_VARIABLE_4809 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4809)) (= (tptp.cons BOUND_VARIABLE_4809 U) (tptp.app (tptp.cons BOUND_VARIABLE_4809 tptp.nil) U)))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_67 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.tl _let_66)))) (let ((_let_68 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_66))) (let ((_let_69 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_70 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_71 (not _let_70))) (let ((_let_72 (not _let_69))) (let ((_let_73 (or _let_72 _let_71 _let_67))) (let ((_let_74 (forall ((U $$unsorted) (BOUND_VARIABLE_3557 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3557)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3557 U))))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (not _let_68))) (let ((_let_77 (or _let_72 _let_71 _let_76))) (let ((_let_78 (forall ((V $$unsorted) (BOUND_VARIABLE_3468 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3468)) (not (= (tptp.cons BOUND_VARIABLE_3468 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_79 (not _let_77))) (let ((_let_80 (not _let_78))) (let ((_let_81 (or _let_23 _let_21 _let_80))) (let ((_let_82 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((V $$unsorted) (BOUND_VARIABLE_3468 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3468)) (not (= U (tptp.cons BOUND_VARIABLE_3468 V)))))))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (_let_80))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84) (REWRITE :args ((=> _let_80 (not (or _let_72 _let_71 (not (= _let_66 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_80) _let_78))) (REFL :args (_let_79)) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_23 _let_21 _let_80 (not _let_81)))) _let_42 _let_40 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_82)))) _let_83 :args (_let_81 false _let_82)) :args (_let_80 false _let_22 true _let_21 false _let_81)) :args (_let_79 true _let_78)))) (let ((_let_86 (REFL :args (_let_77)))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 0)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_69))) :args _let_37)) :args ((or _let_69 _let_77))) _let_85 :args (_let_69 true _let_77)))) (let ((_let_88 (and _let_69 _let_68 _let_67))) (let ((_let_89 (ASSUME :args (_let_69)))) (let ((_let_90 (ASSUME :args (_let_67)))) (let ((_let_91 (ASSUME :args (_let_68)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_88)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_89 _let_90 _let_91) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (CONG (SYMM (SYMM _let_91)) :args (APPLY_UF tptp.tl)) (SYMM _let_90)) :args (APPLY_UF tptp.ssList)) (TRUE_INTRO _let_89))) :args (_let_69 _let_67 _let_68))) :args (_let_69 _let_68 _let_67))) :args (true _let_88)) _let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 2)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_68))) :args _let_37)) :args ((or _let_68 _let_77))) _let_85 :args (_let_68 true _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_72 _let_71 _let_67 (not _let_73)))) _let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 1)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_37)) :args ((or _let_70 _let_77))) _let_85 :args (_let_70 true _let_77)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_74))) _let_75 :args (_let_73 false _let_74)) :args (_let_67 false _let_69 false _let_70 false _let_73)) :args (_let_54 false _let_69 false _let_68 false _let_67)))) (let ((_let_93 (tptp.ssList _let_50))) (let ((_let_94 (not _let_93))) (let ((_let_95 (or _let_94 _let_61))) (let ((_let_96 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (or _let_56 _let_19 _let_93))) (let ((_let_99 (forall ((U $$unsorted) (BOUND_VARIABLE_3321 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3321)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3321 U)))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (ASSUME :args (_let_9)))) (let ((_let_102 (or _let_23 _let_21 _let_62))) (let ((_let_103 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (and _let_62 _let_61 _let_60))) (let ((_let_106 (ASSUME :args (_let_61)))) (let ((_let_107 (ASSUME :args (_let_60)))) (let ((_let_108 (ASSUME :args (_let_62)))) (let ((_let_109 (_let_49))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_109)) :args _let_109)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_47))) (REFL :args (_let_48)) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_56 _let_19 _let_55 _let_49 _let_53 (not _let_57)))) _let_101 _let_43 _let_92 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_105)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_106 _let_107 _let_108) (SCOPE (TRANS (SYMM (SYMM _let_108)) (SYMM (SYMM _let_107)) (CONG (SYMM (SYMM _let_106)) (REFL :args (_let_45)) :args (APPLY_UF tptp.app))) :args (_let_61 _let_60 _let_62))) :args (_let_62 _let_61 _let_60))) :args (true _let_105)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_23 _let_21 _let_62 (not 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(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_4 (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)))))))) _let_3 (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 $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (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))))))) _let_2 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 79.68/79.90 )
% 79.68/79.90 % SZS output end Proof for SWC247+1
% 79.68/79.90 % cvc5---1.0.5 exiting
% 79.68/79.90 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------