TSTP Solution File: SWC177+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC177+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 20:23:48 EDT 2023
% Result : Theorem 0.98s 1.29s
% Output : Proof 1.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC177+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 14:32:13 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.98/1.29 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.IUpuQascE3/cvc5---1.0.5_27515.p...
% 0.98/1.29 ------- get file name : TPTP file name is SWC177+1
% 0.98/1.29 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27515.smt2...
% 0.98/1.29 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.98/1.29 % SZS status Theorem for SWC177+1
% 0.98/1.29 % SZS output start Proof for SWC177+1
% 0.98/1.29 (
% 0.98/1.29 (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)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (forall ((X2 $$unsorted)) (=> (tptp.ssList X2) (not (= (tptp.app (tptp.app (tptp.app X1 (tptp.cons Y tptp.nil)) (tptp.cons Z tptp.nil)) X2) U)))))) (tptp.neq Y Z))))) (and (forall ((X3 $$unsorted)) (or (not (tptp.ssItem X3)) (not (= (tptp.cons X3 tptp.nil) W)) (not (tptp.memberP X X3)))) (or (not (= tptp.nil X)) (not (= tptp.nil W))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))) (let ((_let_3 (forall ((U $$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))))))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq 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 $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_10 (tptp.ssList tptp.nil))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_12 (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))))))))))))))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_14 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_14))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_17 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_18 (tptp.app _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_19 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil))) (let ((_let_20 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_19))) (let ((_let_21 (tptp.app _let_20 _let_17))) (let ((_let_22 (tptp.app _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_23 (= _let_22 (tptp.app _let_20 _let_18)))) (let ((_let_24 (= _let_18 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_14)))) (let ((_let_25 (= _let_22 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_17) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_26 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_15))) (let ((_let_29 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (= tptp.nil _let_22))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or (not (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_32))) (let ((_let_34 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_35 (= _let_22 _let_34))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36 (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_40 (and _let_39 _let_33))) (let ((_let_41 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_44 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.ssList _let_22))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47 _let_45 _let_43 _let_42 _let_27 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_40))) (let ((_let_51 (forall ((BOUND_VARIABLE_5478 $$unsorted) (BOUND_VARIABLE_5476 $$unsorted) (BOUND_VARIABLE_5457 $$unsorted) (BOUND_VARIABLE_5455 $$unsorted) (BOUND_VARIABLE_5453 $$unsorted) (BOUND_VARIABLE_5451 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5453 (tptp.cons BOUND_VARIABLE_5451 tptp.nil)) (tptp.cons BOUND_VARIABLE_5457 tptp.nil)) BOUND_VARIABLE_5455))) (or (not (tptp.ssList _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5451)) (not (tptp.ssItem BOUND_VARIABLE_5457)) (tptp.neq BOUND_VARIABLE_5451 BOUND_VARIABLE_5457) (not (tptp.ssList BOUND_VARIABLE_5453)) (not (tptp.ssList BOUND_VARIABLE_5455)) (not (tptp.ssList BOUND_VARIABLE_5476)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5478)) (not (= _let_1 (tptp.cons BOUND_VARIABLE_5478 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5476 BOUND_VARIABLE_5478))) (or (not (= tptp.nil BOUND_VARIABLE_5476)) (not (= tptp.nil _let_1))))))))) (let ((_let_52 (not _let_50))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (or))) (let ((_let_55 (not _let_51))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_53) :args (_let_55))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_51))) (REFL :args (_let_52)) :args _let_54)) _let_53 :args (_let_52 true _let_51)))) (let ((_let_57 (REFL :args (_let_50)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 5)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_54)) :args ((or _let_26 _let_50))) _let_56 :args (_let_26 true _let_50)))) (let ((_let_59 (not _let_16))) (let ((_let_60 (= _let_43 _let_59))) (let ((_let_61 (or _let_47 _let_45 _let_60))) (let ((_let_62 (forall ((U $$unsorted) (BOUND_VARIABLE_2101 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_2101)) (= (tptp.neq U BOUND_VARIABLE_2101) (not (= U BOUND_VARIABLE_2101))))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 2)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_54)) :args ((or _let_44 _let_50))) _let_56 :args (_let_44 true _let_50)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 1)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_54)) :args ((or _let_46 _let_50))) _let_56 :args (_let_46 true _let_50)))) (let ((_let_66 (not _let_60))) (let ((_let_67 (tptp.ssList _let_17))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.ssList _let_20))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_70 _let_68 _let_27 _let_23))) (let ((_let_72 (forall ((U $$unsorted) (BOUND_VARIABLE_4853 $$unsorted) (BOUND_VARIABLE_4851 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4851)) (not (tptp.ssList BOUND_VARIABLE_4853)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4851) BOUND_VARIABLE_4853) (tptp.app U (tptp.app BOUND_VARIABLE_4851 BOUND_VARIABLE_4853))))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (not _let_10))) (let ((_let_75 (or _let_74 _let_45 _let_67))) (let ((_let_76 (forall ((U $$unsorted) (BOUND_VARIABLE_3321 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3321)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3321 U)))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (_let_76))) (let ((_let_79 ((tptp.cons BOUND_VARIABLE_3321 U)))) (let ((_let_80 (ASSUME :args (_let_10)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_74 _let_45 _let_67 (not _let_75)))) _let_80 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_79)) :args _let_78)) _let_77 :args (_let_75 false _let_76)) :args (_let_67 false _let_10 false _let_44 false _let_75)))) (let ((_let_82 (tptp.ssList _let_19))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_42 _let_83 _let_69))) (let ((_let_85 (forall ((U $$unsorted) (BOUND_VARIABLE_3579 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3579)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3579)))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (_let_85))) (let ((_let_88 ((tptp.app U BOUND_VARIABLE_3579)))) (let ((_let_89 (or _let_74 _let_47 _let_82))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 4)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_54)) :args ((or _let_41 _let_50))) _let_56 :args (_let_41 true _let_50)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_42 _let_83 _let_69 (not _let_84)))) _let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_74 _let_47 _let_82 (not _let_89)))) _let_80 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_79)) :args _let_78)) _let_77 :args (_let_89 false _let_76)) :args (_let_82 false _let_10 false _let_46 false _let_89)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_88)) :args _let_87)) _let_86 :args (_let_84 false _let_85)) :args (_let_69 false _let_41 false _let_82 false _let_84)))) (let ((_let_92 (or _let_27 _let_74 _let_45 _let_24))) (let ((_let_93 (forall ((U $$unsorted) (BOUND_VARIABLE_3621 $$unsorted) (BOUND_VARIABLE_3619 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3619)) (not (tptp.ssItem BOUND_VARIABLE_3621)) (= (tptp.cons BOUND_VARIABLE_3621 (tptp.app BOUND_VARIABLE_3619 U)) (tptp.app (tptp.cons BOUND_VARIABLE_3621 BOUND_VARIABLE_3619) U)))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (not _let_25))) (let ((_let_96 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_45 _let_45 _let_97 _let_97 _let_42 _let_74 _let_27 _let_95))) (let ((_let_99 (forall ((V $$unsorted) (BOUND_VARIABLE_2480 $$unsorted) (BOUND_VARIABLE_2478 $$unsorted) (BOUND_VARIABLE_2476 $$unsorted) (BOUND_VARIABLE_2474 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2474)) (not (tptp.leq V BOUND_VARIABLE_2474)) (not (tptp.leq BOUND_VARIABLE_2474 V)) (not (tptp.ssList BOUND_VARIABLE_2480)) (not (tptp.ssList BOUND_VARIABLE_2476)) (not (tptp.ssList BOUND_VARIABLE_2478)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_2480 (tptp.cons V BOUND_VARIABLE_2476)) (tptp.cons BOUND_VARIABLE_2474 BOUND_VARIABLE_2478)) (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))) (let ((_let_100 (tptp.cyclefreeP _let_22))) (let ((_let_101 (= _let_100 _let_99))) (let ((_let_102 (or _let_49 _let_101))) (let ((_let_103 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cyclefreeP U) (forall ((V $$unsorted) (BOUND_VARIABLE_2480 $$unsorted) (BOUND_VARIABLE_2478 $$unsorted) (BOUND_VARIABLE_2476 $$unsorted) (BOUND_VARIABLE_2474 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2474)) (not (tptp.leq V BOUND_VARIABLE_2474)) (not (tptp.leq BOUND_VARIABLE_2474 V)) (not (tptp.ssList BOUND_VARIABLE_2480)) (not (tptp.ssList BOUND_VARIABLE_2476)) (not (tptp.ssList BOUND_VARIABLE_2478)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_2480 (tptp.cons V BOUND_VARIABLE_2476)) (tptp.cons BOUND_VARIABLE_2474 BOUND_VARIABLE_2478))))))))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (tptp.cyclefreeP _let_34))) (let ((_let_106 (or _let_38 _let_105))) (let ((_let_107 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.cyclefreeP (tptp.cons U tptp.nil)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (= tptp.nil _let_21))) (let ((_let_110 (and (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) _let_109))) (let ((_let_111 (= _let_31 _let_110))) (let ((_let_112 (tptp.ssList _let_21))) (let ((_let_113 (not _let_112))) (let ((_let_114 (or _let_113 _let_27 _let_111))) (let ((_let_115 (forall ((U $$unsorted) (BOUND_VARIABLE_4879 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4879)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4879)) (and (= tptp.nil BOUND_VARIABLE_4879) (= tptp.nil U))))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (_let_115))) (let ((_let_118 ((tptp.app U BOUND_VARIABLE_4879)))) (let ((_let_119 (or _let_70 _let_68 _let_112))) (let ((_let_120 (not _let_110))) (let ((_let_121 (= tptp.nil _let_17))) (let ((_let_122 (and _let_121 (= tptp.nil _let_20)))) (let ((_let_123 (= _let_109 _let_122))) (let ((_let_124 (not _let_109))) (let ((_let_125 (or _let_70 _let_68 _let_123))) (let ((_let_126 (not _let_122))) (let ((_let_127 (not _let_121))) (let ((_let_128 (or _let_74 _let_45 _let_127))) (let ((_let_129 (forall ((U $$unsorted) (BOUND_VARIABLE_3346 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3346)) (not (= U (tptp.cons BOUND_VARIABLE_3346 U))))))) (let ((_let_130 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_40)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_50 7)) _let_56 :args ((not _let_40) true _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 1)) (CONG (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_54)) :args ((or _let_31 _let_33))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_111)) :args ((or _let_32 _let_110 (not _let_111)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_110 1)) :args ((or _let_109 _let_120))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_123)) :args ((or _let_122 _let_124 (not _let_123)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_122 0)) :args ((or _let_121 _let_126))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_128)) :args ((or _let_74 _let_45 _let_127 (not _let_128)))) _let_80 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_130 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3346 U)))) :args (_let_129))) _let_130 :args (_let_128 false _let_129)) :args (_let_127 false _let_10 false _let_44 false _let_128)) :args (_let_126 true _let_121)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_125)) :args ((or _let_70 _let_68 _let_123 (not _let_125)))) _let_91 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (_let_20 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_118)) :args _let_117)) _let_116 :args (_let_125 false _let_115)) :args (_let_123 false _let_69 false _let_67 false _let_125)) :args (_let_124 true _let_122 false _let_123)) :args (_let_120 true _let_109)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_27 _let_113 _let_111 (not _let_114)))) _let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_70 _let_68 _let_112 (not _let_119)))) _let_91 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (_let_20 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_88)) :args _let_87)) _let_86 :args (_let_119 false _let_85)) :args (_let_112 false _let_69 false _let_67 false _let_119)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (_let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_118)) :args _let_117)) _let_116 :args (_let_114 false _let_115)) :args (_let_111 false _let_26 false _let_112 false _let_114)) :args (_let_32 true _let_110 false _let_111)) :args (_let_33 true _let_31)) :args ((not _let_39) true _let_40 false _let_33)))) (let ((_let_132 (REFL :args (_let_39)))) (let ((_let_133 (and _let_35 _let_105))) (let ((_let_134 (ASSUME :args (_let_105)))) (let ((_let_135 (ASSUME :args (_let_35)))) (let ((_let_136 (_let_99))) (let ((_let_137 (or _let_45 _let_96))) (let ((_let_138 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.leq U U))))) (let ((_let_139 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_140 (and _let_16 _let_15 _let_23 _let_24))) (let ((_let_141 (APPLY_UF tptp.app))) (let ((_let_142 (APPLY_UF tptp.cons))) (let ((_let_143 (ASSUME :args (_let_16)))) (let ((_let_144 (SYMM _let_143))) (let ((_let_145 (ASSUME :args (_let_15)))) (let ((_let_146 (ASSUME :args (_let_24)))) (let ((_let_147 (ASSUME :args (_let_23)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_140)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_143 _let_145 _let_146 _let_147) (SCOPE (TRANS (SYMM (SYMM _let_147)) (CONG (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (CONG _let_144 (REFL :args (tptp.nil)) :args _let_142) :args _let_141) (TRANS (SYMM (SYMM _let_146)) (CONG _let_143 (SYMM _let_145) :args _let_142) (CONG _let_144 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) :args _let_142)) :args _let_141)) :args (_let_16 _let_15 _let_24 _let_23))) :args (_let_16 _let_15 _let_23 _let_24))) :args (true _let_140)) :args ((or _let_59 (not _let_15) (not _let_23) _let_25 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_98))) :args ((or _let_74 _let_45 _let_42 _let_27 _let_97 _let_95 (not _let_98)))) _let_80 _let_64 _let_90 _let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_137)) :args ((or _let_45 _let_96 (not _let_137)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_139 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssItem U) false))))) :args (_let_138))) _let_139 :args (_let_137 false _let_138)) :args (_let_96 false _let_44 false _let_137)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_136) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app BOUND_VARIABLE_2480 (tptp.cons V BOUND_VARIABLE_2476)) (tptp.cons BOUND_VARIABLE_2474 BOUND_VARIABLE_2478))))) :args _let_136))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_101)) :args ((or _let_99 (not _let_100) (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_133)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_134 _let_135) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_135)) :args (APPLY_UF tptp.cyclefreeP)) (TRUE_INTRO _let_134))) :args (_let_105 _let_35))) :args (_let_35 _let_105))) :args (true _let_133)) :args ((or _let_36 _let_100 (not _let_105)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 1)) (CONG _let_132 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_54)) :args ((or _let_35 _let_39))) _let_131 :args (_let_35 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_38 _let_105 (not _let_106)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG _let_132 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_54)) :args ((or _let_37 _let_39))) _let_131 :args (_let_37 true _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssItem U) false))))) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_105 false _let_37 false _let_106)) :args (_let_100 false _let_35 false _let_105)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_49 _let_101 (not _let_102)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 0)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_54)) :args ((or _let_48 _let_50))) _let_56 :args (_let_48 true _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_103)))) _let_104 :args (_let_102 false _let_103)) :args (_let_101 false _let_48 false _let_102)) :args (_let_99 false _let_100 false _let_101)) :args (_let_98 false _let_99)) :args (_let_95 false _let_10 false _let_44 false _let_41 false _let_26 false _let_96 false _let_98)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_74 _let_45 _let_27 _let_24 (not _let_92)))) _let_80 _let_64 _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.cons BOUND_VARIABLE_3621 BOUND_VARIABLE_3619) U)))) :args (_let_93)))) _let_94 :args (_let_92 false _let_93)) :args (_let_24 false _let_10 false _let_44 false _let_26 false _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_27 _let_70 _let_68 _let_23 (not _let_71)))) _let_58 _let_91 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_17 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app U BOUND_VARIABLE_4851) BOUND_VARIABLE_4853)))) :args (_let_72))) _let_73 :args (_let_71 false _let_72)) :args (_let_23 false _let_26 false _let_69 false _let_67 false _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_60)) (CONG (REFL :args (_let_66)) (REFL :args (_let_43)) (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_16))) :args _let_54)) :args ((or _let_43 _let_16 _let_66))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_50 3)) _let_56 :args ((not _let_43) true _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_47 _let_45 _let_60 (not _let_61)))) _let_65 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_63 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.neq U BOUND_VARIABLE_2101)))) :args (_let_62)))) _let_63 :args (_let_61 false _let_62)) :args (_let_60 false _let_46 false _let_44 false _let_61)) :args (_let_16 true _let_43 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_15 (not _let_28)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_29))) _let_30 :args (_let_28 false _let_29)) :args (_let_15 false _let_26 false _let_28)) :args (false true _let_25 false _let_24 false _let_23 false _let_16 false _let_15)) :args (_let_13 (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)))))))))) _let_12 (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 $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_11 _let_10 _let_9 (forall ((U $$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_8 _let_7 _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 $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) _let_5 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) _let_4 (tptp.cyclefreeP tptp.nil) (forall ((U $$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)))))))) (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_3 _let_2 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.13/1.30 )
% 1.13/1.30 % SZS output end Proof for SWC177+1
% 1.13/1.30 % cvc5---1.0.5 exiting
% 1.13/1.30 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------