TSTP Solution File: SWC084+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC084+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 20:23:07 EDT 2023
% Result : Theorem 41.99s 42.25s
% Output : Proof 42.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC084+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 18:28:40 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 41.99/42.25 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.YpKPiqpiU2/cvc5---1.0.5_6545.p...
% 41.99/42.25 ------- get file name : TPTP file name is SWC084+1
% 41.99/42.25 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6545.smt2...
% 41.99/42.25 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 41.99/42.25 --- Run --no-e-matching --full-saturate-quant at 5...
% 41.99/42.25 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 41.99/42.25 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 41.99/42.25 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 41.99/42.25 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 41.99/42.25 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 41.99/42.25 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 41.99/42.25 % SZS status Theorem for SWC084+1
% 41.99/42.25 % SZS output start Proof for SWC084+1
% 41.99/42.25 (
% 41.99/42.25 (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 $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (and (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (or (not (= (tptp.cons Z tptp.nil) W)) (not (tptp.memberP X Z)) (exists ((X1 $$unsorted)) (and (tptp.ssItem X1) (not (= Z X1)) (tptp.memberP X X1) (tptp.leq Z X1)))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$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)))))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_8 (tptp.ssList tptp.nil))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_11 (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)))))))))))) (let ((_let_12 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12))) (let ((_let_14 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14))) (let ((_let_16 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_17 (= _let_16 (tptp.app _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_18 (tptp.segmentP _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_19 (tptp.segmentP (tptp.app _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (not _let_20))) (let ((_let_22 (not _let_13))) (let ((_let_23 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_21 (not (forall ((X1 $$unsorted)) (or (not (tptp.ssItem X1)) (= X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 X1)) (not (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X1)))))))) (let ((_let_26 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (not _let_26))) (let ((_let_28 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27))) (let ((_let_31 (and _let_25 _let_30))) (let ((_let_32 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_33 (= _let_32 _let_29))) (let ((_let_34 (not _let_8))) (let ((_let_35 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_34 _let_33))) (let ((_let_38 (forall ((U $$unsorted) (BOUND_VARIABLE_3288 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3288)) (= (tptp.neq U BOUND_VARIABLE_3288) (not (= U BOUND_VARIABLE_3288))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Y)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)))))) (let ((_let_42 (not _let_41))) (let ((_let_43 (not _let_32))) (let ((_let_44 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_36 _let_43 _let_42 _let_31))) (let ((_let_47 (forall ((U $$unsorted) (BOUND_VARIABLE_5436 $$unsorted) (BOUND_VARIABLE_5434 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5434)) (not (tptp.neq BOUND_VARIABLE_5434 tptp.nil)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP BOUND_VARIABLE_5434 Y)) (not (tptp.segmentP U Y))))) (and (or (not (tptp.ssItem BOUND_VARIABLE_5436)) (not (= U (tptp.cons BOUND_VARIABLE_5436 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5434 BOUND_VARIABLE_5436)) (not (forall ((X1 $$unsorted)) (or (not (tptp.ssItem X1)) (= X1 BOUND_VARIABLE_5436) (not (tptp.memberP BOUND_VARIABLE_5434 X1)) (not (tptp.leq BOUND_VARIABLE_5436 X1)))))) (or (not (= tptp.nil BOUND_VARIABLE_5434)) (not (= tptp.nil U)))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (or))) (let ((_let_51 (not _let_47))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_49) :args (_let_51))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_47))) (REFL :args (_let_48)) :args _let_50)) _let_49 :args (_let_48 true _let_47)))) (let ((_let_53 (REFL :args (_let_46)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_50)) :args ((or _let_35 _let_46))) _let_52 :args (_let_35 true _let_46)))) (let ((_let_55 (ASSUME :args (_let_8)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_31)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 4)) _let_52 :args ((not _let_31) true _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG (REFL :args (_let_30)) (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_50)) :args ((or _let_28 _let_30))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_33)) :args ((or _let_43 _let_29 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 2)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_32))) :args _let_50)) :args ((or _let_32 _let_46))) _let_52 :args (_let_32 true _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_34 _let_36 _let_33 (not _let_37)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_40))) _let_39 :args (_let_37 false _let_38)) :args (_let_33 false _let_8 false _let_35 false _let_37)) :args (_let_29 false _let_32 false _let_33)) :args (_let_30 true _let_28)) :args ((not _let_25) true _let_31 false _let_30)))) (let ((_let_57 (REFL :args (_let_25)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_13))) :args _let_50)) :args ((or _let_13 _let_25))) _let_56 :args (_let_13 true _let_25)))) (let ((_let_59 (or _let_45 _let_15))) (let ((_let_60 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_50)) :args ((or _let_44 _let_46))) _let_52 :args (_let_44 true _let_46)))) (let ((_let_63 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_24 _let_17))) (let ((_let_66 (forall ((U $$unsorted) (BOUND_VARIABLE_4799 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4799)) (= (tptp.cons BOUND_VARIABLE_4799 U) (tptp.app (tptp.cons BOUND_VARIABLE_4799 tptp.nil) U)))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_16))) (let ((_let_69 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_68))) (let ((_let_70 (not _let_69))) (let ((_let_71 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_64 _let_70))) (let ((_let_74 (forall ((W $$unsorted) (BOUND_VARIABLE_2153 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2153)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2153)))))))) (let ((_let_75 (not _let_73))) (let ((_let_76 (not _let_74))) (let ((_let_77 (= _let_20 _let_76))) (let ((_let_78 (or _let_36 _let_24 _let_77))) (let ((_let_79 (forall ((U $$unsorted) (BOUND_VARIABLE_2179 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2179)) (= (tptp.memberP U BOUND_VARIABLE_2179) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2153 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2153)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2179 BOUND_VARIABLE_2153)))))))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_50)) :args ((or _let_23 _let_25))) _let_56 :args (_let_23 true _let_25)))) (let ((_let_82 (_let_76))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_82)) :args _let_82)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_74))) (REFL :args (_let_75)) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_77)) :args ((or _let_21 _let_76 (not _let_77)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_50)) :args ((or _let_20 _let_25))) _let_56 :args (_let_20 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_36 _let_24 _let_77 (not _let_78)))) _let_54 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.memberP U BOUND_VARIABLE_2179)))) :args (_let_79))) _let_80 :args (_let_78 false _let_79)) :args (_let_77 false _let_35 false _let_23 false _let_78)) :args (_let_76 false _let_20 false _let_77)) :args (_let_75 true _let_74)))) (let ((_let_84 (REFL :args (_let_73)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_73 1)) (CONG _let_84 (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_50)) :args ((or _let_63 _let_73))) _let_83 :args (_let_63 true _let_73)))) (let ((_let_86 (tptp.segmentP (tptp.app _let_68 tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_87 (not _let_18))) (let ((_let_88 (tptp.ssList _let_16))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_89 _let_45 _let_87 _let_72 _let_34 _let_86))) (let ((_let_91 (forall ((U $$unsorted) (BOUND_VARIABLE_4462 $$unsorted) (BOUND_VARIABLE_4460 $$unsorted) (BOUND_VARIABLE_4458 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4458)) (not (tptp.segmentP U BOUND_VARIABLE_4458)) (not (tptp.ssList BOUND_VARIABLE_4462)) (not (tptp.ssList BOUND_VARIABLE_4460)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4462 U) BOUND_VARIABLE_4460) BOUND_VARIABLE_4458))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (_let_91))) (let ((_let_94 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_95 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_96 (not _let_86))) (let ((_let_97 (or _let_36 _let_94))) (let ((_let_98 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 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(ASSUME :args (_let_110)))) (let ((_let_117 (ASSUME :args (_let_13)))) (let ((_let_118 (SYMM _let_117))) (let ((_let_119 (REFL :args (tptp.nil)))) (let ((_let_120 (not _let_107))) (let ((_let_121 (or _let_45 _let_100))) (let ((_let_122 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_121)) :args ((or _let_45 _let_100 (not _let_121)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_123 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_122))) _let_123 :args (_let_121 false _let_122)) :args (_let_100 false _let_44 false _let_121)))) (let ((_let_125 (and _let_102 _let_94 _let_69))) (let ((_let_126 (_let_102 _let_94 _let_69))) (let ((_let_127 (ASSUME :args (_let_102)))) (let 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(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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_5 _let_4 (forall ((U $$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)))))) (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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_3 (forall ((U $$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))))))) _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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 42.10/42.26 )
% 42.10/42.26 % SZS output end Proof for SWC084+1
% 42.10/42.26 % cvc5---1.0.5 exiting
% 42.10/42.26 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------