TSTP Solution File: SWC299+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC299+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 20:24:35 EDT 2023
% Result : Theorem 76.91s 77.10s
% Output : Proof 76.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC299+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 16:09:04 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 76.91/77.10 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.EAsBV5JjmH/cvc5---1.0.5_16741.p...
% 76.91/77.10 ------- get file name : TPTP file name is SWC299+1
% 76.91/77.10 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16741.smt2...
% 76.91/77.10 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 76.91/77.10 --- Run --no-e-matching --full-saturate-quant at 5...
% 76.91/77.10 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 76.91/77.10 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 76.91/77.10 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 76.91/77.10 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 76.91/77.10 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 76.91/77.10 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 76.91/77.10 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 76.91/77.10 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 76.91/77.10 --- Run --relevant-triggers --full-saturate-quant at 5...
% 76.91/77.10 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 76.91/77.10 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 76.91/77.10 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 76.91/77.10 % SZS status Theorem for SWC299+1
% 76.91/77.10 % SZS output start Proof for SWC299+1
% 76.91/77.10 (
% 76.91/77.10 (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)) (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (forall ((X2 $$unsorted)) (=> (tptp.ssList X2) (forall ((X3 $$unsorted)) (=> (tptp.ssList X3) (or (not (= (tptp.app (tptp.app (tptp.app (tptp.app X1 (tptp.cons Y tptp.nil)) X2) (tptp.cons Z tptp.nil)) X3) U)) (not (tptp.lt Z Y))))))))))))) (and (forall ((X4 $$unsorted)) (=> (tptp.ssItem X4) (forall ((X5 $$unsorted)) (=> (tptp.ssList X5) (forall ((X6 $$unsorted)) (=> (tptp.ssList X6) (or (not (= (tptp.cons X4 tptp.nil) W)) (not (= (tptp.app (tptp.app X5 W) X6) X)) (exists ((X7 $$unsorted)) (and (tptp.ssItem X7) (tptp.memberP X5 X7) (tptp.lt X4 X7))) (exists ((X8 $$unsorted)) (and (tptp.ssItem X8) (tptp.memberP X6 X8) (tptp.lt X8 X4)))))))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))))))))))))))) (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.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_9 (forall ((U $$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_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_12 (tptp.ssList tptp.nil))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))))) (let ((_let_15 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_15))) (let ((_let_17 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 tptp.nil))) (let ((_let_18 (tptp.app _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_19 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_17))) (let ((_let_20 (tptp.app _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_21 (= _let_20 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_18)))) (let ((_let_22 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.nil))) (let ((_let_23 (tptp.app _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_24 (tptp.app _let_20 _let_22))) (let ((_let_25 (tptp.app _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_26 (= _let_25 (tptp.app _let_20 _let_23)))) (let ((_let_27 (= _let_18 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_15)))) (let ((_let_28 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_29 (= _let_23 _let_28))) (let ((_let_30 (= _let_25 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) _let_28)))) (let ((_let_31 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_16))) (let ((_let_34 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (= tptp.nil _let_25))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or (not (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_37))) (let ((_let_39 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_40 (= _let_25 _let_39))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_41 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((X7 $$unsorted)) (or (not (tptp.ssItem X7)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 X7)) (not (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X7))))) (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_25) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (not (forall ((X8 $$unsorted)) (or (not (tptp.ssItem X8)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X8)) (not (tptp.lt X8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))))) (let ((_let_45 (and _let_44 _let_38))) (let ((_let_46 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.ssList _let_25))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55 _let_53 _let_51 _let_49 _let_32 _let_47 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_45))) (let ((_let_59 (forall ((BOUND_VARIABLE_5794 $$unsorted) (BOUND_VARIABLE_5792 $$unsorted) (BOUND_VARIABLE_5790 $$unsorted) (BOUND_VARIABLE_5788 $$unsorted) (BOUND_VARIABLE_5765 $$unsorted) (BOUND_VARIABLE_5763 $$unsorted) (BOUND_VARIABLE_5761 $$unsorted) (BOUND_VARIABLE_5759 $$unsorted) (BOUND_VARIABLE_5757 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5759 (tptp.cons BOUND_VARIABLE_5757 tptp.nil)) BOUND_VARIABLE_5763) (tptp.cons BOUND_VARIABLE_5765 tptp.nil)) BOUND_VARIABLE_5761))) (or (not (tptp.ssList _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5757)) (not (tptp.ssItem BOUND_VARIABLE_5765)) (not (tptp.lt BOUND_VARIABLE_5765 BOUND_VARIABLE_5757)) (not (tptp.ssList BOUND_VARIABLE_5759)) (not (tptp.ssList BOUND_VARIABLE_5763)) (not (tptp.ssList BOUND_VARIABLE_5761)) (not (tptp.ssList BOUND_VARIABLE_5788)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5794)) (not (= _let_1 (tptp.cons BOUND_VARIABLE_5794 tptp.nil))) (not (tptp.ssList BOUND_VARIABLE_5790)) (not (forall ((X7 $$unsorted)) (or (not (tptp.ssItem X7)) (not (tptp.memberP BOUND_VARIABLE_5790 X7)) (not (tptp.lt BOUND_VARIABLE_5794 X7))))) (not (tptp.ssList BOUND_VARIABLE_5792)) (not (= BOUND_VARIABLE_5788 (tptp.app (tptp.app BOUND_VARIABLE_5790 _let_1) BOUND_VARIABLE_5792))) (not (forall ((X8 $$unsorted)) (or (not (tptp.ssItem X8)) (not (tptp.memberP BOUND_VARIABLE_5792 X8)) (not (tptp.lt X8 BOUND_VARIABLE_5794)))))) (or (not (= tptp.nil BOUND_VARIABLE_5788)) (not (= tptp.nil _let_1))))))))) (let ((_let_60 (not _let_58))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (or))) (let ((_let_63 (not _let_59))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_61) :args (_let_63))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_59))) (REFL :args (_let_60)) :args _let_62)) _let_61 :args (_let_60 true _let_59)))) (let ((_let_65 (REFL :args (_let_58)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 5)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_62)) :args ((or _let_31 _let_58))) _let_64 :args (_let_31 true _let_58)))) (let ((_let_67 (tptp.ssList _let_17))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_49 _let_68 _let_32 _let_21))) (let ((_let_70 (forall ((U $$unsorted) (BOUND_VARIABLE_4886 $$unsorted) (BOUND_VARIABLE_4884 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4884)) (not (tptp.ssList BOUND_VARIABLE_4886)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4884) BOUND_VARIABLE_4886) (tptp.app U (tptp.app BOUND_VARIABLE_4884 BOUND_VARIABLE_4886))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_70))) (let ((_let_73 ((tptp.app (tptp.app U BOUND_VARIABLE_4884) BOUND_VARIABLE_4886)))) (let ((_let_74 (not _let_12))) (let ((_let_75 (or _let_74 _let_55 _let_67))) (let ((_let_76 (forall ((U $$unsorted) (BOUND_VARIABLE_3354 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3354)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3354 U)))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (_let_76))) (let ((_let_79 ((tptp.cons BOUND_VARIABLE_3354 U)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 1)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_62)) :args ((or _let_54 _let_58))) _let_64 :args (_let_54 true _let_58)))) (let ((_let_81 (ASSUME :args (_let_12)))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_74 _let_55 _let_67 (not _let_75)))) _let_81 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_79)) :args _let_78)) _let_77 :args (_let_75 false _let_76)) :args (_let_67 false _let_12 false _let_54 false _let_75)))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 4)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_62)) :args ((or _let_48 _let_58))) _let_64 :args (_let_48 true _let_58)))) (let ((_let_84 (tptp.ssList _let_22))) (let ((_let_85 (not _let_84))) (let ((_let_86 (tptp.ssList _let_20))) (let ((_let_87 (not _let_86))) (let ((_let_88 (or _let_87 _let_85 _let_47 _let_26))) (let ((_let_89 (or _let_74 _let_53 _let_84))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 2)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_62)) :args ((or _let_52 _let_58))) _let_64 :args (_let_52 true _let_58)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_74 _let_53 _let_84 (not _let_89)))) _let_81 _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_79)) :args _let_78)) _let_77 :args (_let_89 false _let_76)) :args (_let_84 false _let_12 false _let_52 false _let_89)))) (let ((_let_92 (tptp.ssList _let_19))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_93 _let_32 _let_86))) (let ((_let_95 (forall ((U $$unsorted) (BOUND_VARIABLE_3612 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3612)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3612)))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (_let_95))) (let ((_let_98 ((tptp.app U BOUND_VARIABLE_3612)))) (let ((_let_99 (or _let_49 _let_68 _let_92))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_32 _let_93 _let_86 (not _let_94)))) _let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_49 _let_68 _let_92 (not _let_99)))) _let_83 _let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_97)) _let_96 :args (_let_99 false _let_95)) :args (_let_92 false _let_48 false _let_67 false _let_99)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (_let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_97)) _let_96 :args (_let_94 false _let_95)) :args (_let_86 false _let_31 false _let_92 false _let_94)))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 6)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_62)) :args ((or _let_46 _let_58))) _let_64 :args (_let_46 true _let_58)))) (let ((_let_102 (or _let_32 _let_74 _let_55 _let_27))) (let ((_let_103 (forall ((U $$unsorted) (BOUND_VARIABLE_3654 $$unsorted) (BOUND_VARIABLE_3652 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3652)) (not (tptp.ssItem BOUND_VARIABLE_3654)) (= (tptp.cons BOUND_VARIABLE_3654 (tptp.app BOUND_VARIABLE_3652 U)) (tptp.app (tptp.cons BOUND_VARIABLE_3654 BOUND_VARIABLE_3652) U)))))) (let ((_let_104 (EQ_RESOLVE 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_let_70)) :args (_let_21 false _let_48 false _let_31 false _let_67 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_16 (not _let_33)))) _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_34))) _let_35 :args (_let_33 false _let_34)) :args (_let_16 false _let_31 false _let_33)) :args (false true _let_30 false _let_29 false _let_27 false _let_26 false _let_21 false _let_16)) :args ((forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))) (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) _let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_13 _let_12 _let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$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)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) _let_10 _let_9 _let_8 _let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) (not (tptp.singletonP tptp.nil)) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (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 $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) _let_6 (tptp.totalorderedP tptp.nil) (forall ((U $$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)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_5 _let_4 _let_3 (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 76.91/77.11 )
% 76.91/77.11 % SZS output end Proof for SWC299+1
% 76.91/77.11 % cvc5---1.0.5 exiting
% 76.91/77.11 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------