TSTP Solution File: SWC079+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC079+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 20:23:04 EDT 2023
% Result : Theorem 31.08s 31.30s
% Output : Proof 31.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC079+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 19:05:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 31.08/31.30 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.FVcwrbbzSC/cvc5---1.0.5_24747.p...
% 31.08/31.30 ------- get file name : TPTP file name is SWC079+1
% 31.08/31.30 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24747.smt2...
% 31.08/31.30 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.08/31.30 --- Run --no-e-matching --full-saturate-quant at 5...
% 31.08/31.30 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.08/31.30 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.08/31.30 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.08/31.30 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.08/31.30 % SZS status Theorem for SWC079+1
% 31.08/31.30 % SZS output start Proof for SWC079+1
% 31.08/31.30 (
% 31.08/31.30 (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)) (let ((_let_1 (not (tptp.neq V tptp.nil)))) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (and (or _let_1 (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (not (= W Z)) (exists ((X1 $$unsorted)) (and (tptp.ssItem X1) (= (tptp.cons X1 tptp.nil) Z) (= (tptp.hd X) X1) (tptp.neq tptp.nil X)))))) (or _let_1 (tptp.neq X tptp.nil)))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$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) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_9 (forall ((U $$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_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_11 (tptp.ssList tptp.nil))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_14 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (tptp.cons _let_14 tptp.nil))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_15))) (let ((_let_17 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17))) (let ((_let_19 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (tptp.cons _let_14 _let_19))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20))) (let ((_let_22 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_23 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_22))) (let ((_let_24 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.tl _let_22)))) (let ((_let_26 (= _let_20 (tptp.app _let_15 _let_19)))) (let ((_let_27 (tptp.segmentP (tptp.app _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_28 (tptp.ssList _let_15))) (let ((_let_29 (tptp.ssItem _let_14))) (let ((_let_30 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_31 (not _let_16))) (let ((_let_32 (and _let_30 _let_29 _let_28 _let_31))) (let ((_let_33 (not _let_29))) (let ((_let_34 (not _let_11))) (let ((_let_35 (or _let_34 _let_33 _let_28))) (let ((_let_36 (forall ((U $$unsorted) (BOUND_VARIABLE_3306 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3306)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3306 U)))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_39 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38 _let_29))) (let ((_let_42 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (not _let_38))) (let ((_let_45 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_46 (= _let_45 _let_44))) (let ((_let_47 (or _let_40 _let_34 _let_46))) (let ((_let_48 (forall ((U $$unsorted) (BOUND_VARIABLE_3283 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3283)) (= (tptp.neq U BOUND_VARIABLE_3283) (not (= U BOUND_VARIABLE_3283))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_48))) (let ((_let_51 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)))))) (let ((_let_52 (not _let_51))) (let ((_let_53 (not _let_45))) (let ((_let_54 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_40 _let_53 _let_52 _let_32))) (let ((_let_57 (forall ((U $$unsorted) (BOUND_VARIABLE_5345 $$unsorted)) (let ((_let_1 (tptp.hd BOUND_VARIABLE_5345))) (let ((_let_2 (tptp.cons _let_1 tptp.nil))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5345)) (not (tptp.neq BOUND_VARIABLE_5345 tptp.nil)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP BOUND_VARIABLE_5345 Y)) (not (tptp.segmentP U Y))))) (and (tptp.neq tptp.nil BOUND_VARIABLE_5345) (tptp.ssItem _let_1) (tptp.ssList _let_2) (not (= U _let_2))))))))) (let ((_let_58 (not _let_56))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (or))) (let ((_let_61 (not _let_57))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_59) :args (_let_61))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_57))) (REFL :args (_let_58)) :args _let_60)) _let_59 :args (_let_58 true _let_57)))) (let ((_let_63 (REFL :args (_let_56)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 1)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_60)) :args ((or _let_39 _let_56))) _let_62 :args (_let_39 true _let_56)))) (let ((_let_65 (ASSUME :args (_let_11)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_46)) :args ((or _let_53 _let_44 (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 2)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_45))) :args _let_60)) :args ((or _let_45 _let_56))) _let_62 :args (_let_45 true _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_34 _let_40 _let_46 (not _let_47)))) _let_65 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_50))) _let_49 :args (_let_47 false _let_48)) :args (_let_46 false _let_11 false _let_39 false _let_47)) :args (_let_44 false _let_45 false _let_46)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_29 _let_38 (not _let_41)))) _let_64 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_29 false _let_39 true _let_38 false _let_41)))) (let ((_let_68 (= _let_30 _let_44))) (let ((_let_69 (or _let_34 _let_40 _let_68))) (let ((_let_70 (not _let_68))) (let ((_let_71 (not _let_28))) (let ((_let_72 (not _let_30))) (let ((_let_73 (_let_32))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_73) (CONG (REFL :args _let_73) (REFL :args (_let_72)) (REFL :args (_let_33)) (REFL :args (_let_71)) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_16))) :args _let_60)) :args ((or _let_16 _let_32 _let_72 _let_33 _let_71))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_56 4)) _let_62 :args ((not _let_32) true _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_68)) (CONG (REFL :args (_let_70)) (REFL :args (_let_30)) (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_38))) :args _let_60)) :args ((or _let_30 _let_38 _let_70))) _let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_34 _let_40 _let_68 (not _let_69)))) _let_65 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP)) :args _let_50)) _let_49 :args (_let_69 false _let_48)) :args (_let_68 false _let_11 false _let_39 false _let_69)) :args (_let_30 true _let_38 false _let_68)) _let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_28 _let_33 (not _let_35)))) _let_65 _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.nil _let_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_36))) _let_37 :args (_let_35 false _let_36)) :args (_let_28 false _let_11 false _let_29 false _let_35)) :args (_let_16 true _let_32 false _let_30 false _let_29 false _let_28)))) (let ((_let_75 (or _let_55 _let_18))) (let ((_let_76 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_60)) :args ((or _let_54 _let_56))) _let_62 :args (_let_54 true _let_56)))) (let ((_let_79 (or _let_40 _let_38 _let_21))) (let ((_let_80 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (not _let_23))) (let ((_let_83 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_84 (not _let_83))) (let ((_let_85 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_86 _let_84 _let_82))) (let ((_let_88 (forall ((V $$unsorted) (BOUND_VARIABLE_3453 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3453)) (not (= (tptp.cons BOUND_VARIABLE_3453 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_89 (not _let_87))) (let ((_let_90 (not _let_88))) (let ((_let_91 (or _let_40 _let_38 _let_90))) (let ((_let_92 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((V $$unsorted) (BOUND_VARIABLE_3453 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3453)) (not (= U (tptp.cons BOUND_VARIABLE_3453 V)))))))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (_let_90))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_94)) :args _let_94) (REWRITE :args ((=> _let_90 (not (or _let_86 _let_84 (not (= _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_90) _let_88))) (REFL :args (_let_89)) :args _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_40 _let_38 _let_90 (not _let_91)))) _let_64 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_93 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_92)))) _let_93 :args (_let_91 false _let_92)) :args (_let_90 false _let_39 true _let_38 false _let_91)) :args (_let_89 true _let_88)))) (let ((_let_96 (REFL :args (_let_87)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_87 2)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_23))) :args _let_60)) :args ((or _let_23 _let_87))) _let_95 :args (_let_23 true _let_87)))) (let ((_let_98 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_99 (not _let_98))) (let ((_let_100 (not _let_24))) (let ((_let_101 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_102 (not _let_101))) (let ((_let_103 (or _let_55 _let_102 _let_100 _let_99))) (let ((_let_104 (_let_51))) (let ((_let_105 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_106 (not _let_105))) (let ((_let_107 (= _let_101 _let_106))) (let ((_let_108 (or _let_55 _let_34 _let_107))) (let ((_let_109 (= tptp.nil _let_15))) (let ((_let_110 (not _let_109))) (let ((_let_111 (or _let_34 _let_33 _let_110))) (let ((_let_112 (forall ((U $$unsorted) (BOUND_VARIABLE_3331 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3331)) (not (= U (tptp.cons BOUND_VARIABLE_3331 U))))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (REFL :args (_let_31)))) (let ((_let_115 (and _let_16 _let_110))) (let ((_let_116 (ASSUME :args (_let_110)))) (let ((_let_117 (ASSUME :args (_let_16)))) (let ((_let_118 (SYMM _let_117))) (let ((_let_119 (not _let_107))) (let ((_let_120 (or _let_55 _let_98))) (let ((_let_121 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_122 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_55 _let_98 (not _let_120)))) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_122 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_121))) _let_122 :args (_let_120 false _let_121)) :args (_let_98 false _let_54 false _let_120)))) (let ((_let_124 (or _let_86 _let_84 _let_25))) (let ((_let_125 (forall ((U $$unsorted) (BOUND_VARIABLE_3542 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3542)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3542 U))))))) (let ((_let_126 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_87 0)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_85))) :args _let_60)) :args ((or _let_85 _let_87))) _let_95 :args (_let_85 true _let_87)))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_124)) :args ((or _let_86 _let_84 _let_25 (not _let_124)))) _let_127 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_87 1)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_84) _let_83))) :args _let_60)) :args ((or _let_83 _let_87))) _let_95 :args (_let_83 true _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_126 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_125))) _let_126 :args (_let_124 false _let_125)) :args (_let_25 false _let_85 false _let_83 false _let_124)))) (let ((_let_129 (tptp.ssList _let_19))) (let ((_let_130 (not _let_129))) (let ((_let_131 (or _let_130 _let_33 _let_26))) (let ((_let_132 (forall ((U $$unsorted) (BOUND_VARIABLE_4794 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4794)) (= (tptp.cons BOUND_VARIABLE_4794 U) (tptp.app (tptp.cons BOUND_VARIABLE_4794 tptp.nil) U)))))) (let ((_let_133 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_134 (and _let_85 _let_23 _let_25))) (let ((_let_135 (ASSUME :args (_let_85)))) (let ((_let_136 (ASSUME :args (_let_25)))) (let ((_let_137 (ASSUME :args (_let_23)))) (let ((_let_138 (TRANS (CONG (SYMM (SYMM _let_137)) :args (APPLY_UF tptp.tl)) (SYMM _let_136)))) (let ((_let_139 (or _let_55 _let_55 _let_99 _let_34 _let_86 _let_27))) (let ((_let_140 (forall ((U $$unsorted) (BOUND_VARIABLE_4457 $$unsorted) (BOUND_VARIABLE_4455 $$unsorted) (BOUND_VARIABLE_4453 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4453)) (not (tptp.segmentP U BOUND_VARIABLE_4453)) (not (tptp.ssList BOUND_VARIABLE_4457)) (not (tptp.ssList BOUND_VARIABLE_4455)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4457 U) BOUND_VARIABLE_4455) BOUND_VARIABLE_4453))))) (let ((_let_141 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_142 (not _let_27))) (let ((_let_143 (not _let_26))) (let ((_let_144 (not _let_25))) (let ((_let_145 (not _let_21))) (let ((_let_146 (not _let_18))) (let ((_let_147 (ASSUME :args (_let_27)))) (let ((_let_148 (APPLY_UF tptp.app))) (let ((_let_149 (ASSUME :args (_let_18)))) (let ((_let_150 (ASSUME :args (_let_26)))) (let ((_let_151 (ASSUME :args (_let_21)))) (let ((_let_152 (ASSUME :args (_let_100)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_147 _let_149 _let_117 _let_136 _let_137 _let_150 _let_151 _let_152) :args (_let_16 _let_18 _let_21 _let_100 _let_23 _let_25 _let_26 _let_27)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_152)) (CONG (TRANS (SYMM (SYMM _let_151)) (SYMM (SYMM _let_150)) (CONG _let_118 _let_138 :args _let_148) (CONG (SYMM (SYMM _let_149)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) :args _let_148)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args (APPLY_UF tptp.segmentP)) (TRUE_INTRO _let_147))) :args (_let_27 _let_18 _let_16 _let_25 _let_23 _let_26 _let_21 _let_100)) :args ((not (and _let_16 _let_18 _let_21 _let_100 _let_23 _let_25 _let_26 _let_27)) SB_LITERAL))) (CONG _let_114 (REFL :args (_let_146)) (REFL :args (_let_145)) (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_24))) (REFL :args (_let_82)) (REFL :args (_let_144)) (REFL :args (_let_143)) (REFL :args (_let_142)) :args _let_60)) :args ((or _let_31 _let_24 _let_146 _let_145 _let_82 _let_144 _let_143 _let_142))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_139))) :args ((or _let_34 _let_55 _let_99 _let_86 _let_27 (not _let_139)))) _let_65 _let_78 _let_123 _let_127 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_141 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_140))) _let_141 :args (_let_139 false _let_140)) :args (_let_27 false _let_11 false _let_54 false _let_98 false _let_85 false _let_139)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_131)) :args ((or _let_33 _let_130 _let_26 (not _let_131)))) _let_67 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_134)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_135 _let_136 _let_137) (SCOPE (TRUE_ELIM (TRANS (CONG _let_138 :args (APPLY_UF tptp.ssList)) (TRUE_INTRO _let_135))) :args (_let_85 _let_25 _let_23))) :args (_let_85 _let_23 _let_25))) :args (true _let_134)) _let_127 _let_97 _let_128 :args (_let_129 false _let_85 false _let_23 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_133 :args (_let_19 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_4794 U)))) :args (_let_132))) _let_133 :args (_let_131 false _let_132)) :args (_let_26 false _let_29 false _let_129 false _let_131)) _let_128 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_55 _let_99 _let_102 _let_100 (not _let_103)))) _let_78 _let_123 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_107)) (CONG (REFL :args (_let_119)) (REFL :args (_let_101)) (MACRO_SR_PRED_INTRO :args ((= (not _let_106) _let_105))) :args _let_60)) :args ((or _let_105 _let_101 _let_119))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_115)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_116 _let_117) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.nil)) (SYMM _let_118) :args (=)) (FALSE_INTRO _let_116))) :args (_let_110 _let_16))) :args (_let_16 _let_110))) :args (true _let_115)) (CONG _let_114 (MACRO_SR_PRED_INTRO :args ((= (not _let_110) _let_109))) (REFL :args (_let_106)) :args _let_60)) _let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_34 _let_33 _let_110 (not _let_111)))) _let_65 _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (tptp.nil _let_14 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_112))) _let_113 :args (_let_111 false _let_112)) :args (_let_110 false _let_11 false _let_29 false _let_111)) :args (_let_106 false _let_16 true _let_109)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_34 _let_55 _let_107 (not _let_108)))) _let_65 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_50))) _let_49 :args (_let_108 false _let_48)) :args (_let_107 false _let_11 false _let_54 false _let_108)) :args (_let_101 true _let_105 false _let_107)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_104) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList Y) false))))) :args _let_104)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 3)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_60)) :args ((or _let_51 _let_56))) _let_62 :args (_let_51 true _let_56)) :args (_let_103 false _let_51)) :args (_let_100 false _let_54 false _let_98 false _let_101 false _let_103)) _let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_40 _let_38 _let_21 (not _let_79)))) _let_64 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_80))) _let_81 :args (_let_79 false _let_80)) :args (_let_21 false _let_39 true _let_38 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_55 _let_18 (not _let_75)))) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_76))) _let_77 :args (_let_75 false _let_76)) :args (_let_18 false _let_54 false _let_75)) _let_74 :args (false false _let_27 false _let_26 false _let_25 true _let_24 false _let_23 false _let_21 false _let_18 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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) (forall ((U $$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))))))))))))) _let_13 _let_12 _let_11 _let_10 (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))))))))))) _let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) _let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))) (forall ((U $$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_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_5 _let_4 (forall ((U $$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)))))) _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)))))))) _let_2 (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))))))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.08/31.30 )
% 31.08/31.30 % SZS output end Proof for SWC079+1
% 31.08/31.30 % cvc5---1.0.5 exiting
% 31.08/31.30 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------