TSTP Solution File: SWC093+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC093+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 20:23:11 EDT 2023
% Result : Theorem 31.60s 31.83s
% Output : Proof 31.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC093+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 15:45:01 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 31.60/31.83 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xpXprhUw2k/cvc5---1.0.5_539.p...
% 31.60/31.83 ------- get file name : TPTP file name is SWC093+1
% 31.60/31.83 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_539.smt2...
% 31.60/31.83 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.60/31.83 --- Run --no-e-matching --full-saturate-quant at 5...
% 31.60/31.83 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.60/31.83 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.60/31.83 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.60/31.83 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.60/31.83 % SZS status Theorem for SWC093+1
% 31.60/31.83 % SZS output start Proof for SWC093+1
% 31.60/31.83 (
% 31.60/31.83 (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 $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (or (not (= (tptp.cons Z tptp.nil) W)) (not (tptp.memberP X Z))))) (tptp.neq X tptp.nil)))))))))))))) (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 $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))) (let ((_let_12 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12))) (let ((_let_14 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14))) (let ((_let_16 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_17 (= _let_16 (tptp.app _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_18 (tptp.segmentP _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_19 (tptp.segmentP (tptp.app _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (not _let_20))) (let ((_let_22 (not _let_13))) (let ((_let_23 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_21))) (let ((_let_26 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_27 (and _let_25 _let_26))) (let ((_let_28 (not _let_25))) (let ((_let_29 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_30 (not _let_29))) (let ((_let_31 (forall ((Y $$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_32 (not _let_31))) (let ((_let_33 (not _let_26))) (let ((_let_34 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_33 _let_32 (and _let_30 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_27))) (let ((_let_39 (forall ((U $$unsorted) (BOUND_VARIABLE_5374 $$unsorted) (BOUND_VARIABLE_5372 $$unsorted)) (let ((_let_1 (tptp.neq BOUND_VARIABLE_5372 tptp.nil))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5372)) (not _let_1) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP BOUND_VARIABLE_5372 Y)) (not (tptp.segmentP U Y))))) (and (not (= tptp.nil U)) (= tptp.nil BOUND_VARIABLE_5372)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5374)) (not (= U (tptp.cons BOUND_VARIABLE_5374 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5372 BOUND_VARIABLE_5374))) _let_1)))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (or))) (let ((_let_43 (not _let_39))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_41) :args (_let_43))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_39))) (REFL :args (_let_40)) :args _let_42)) _let_41 :args (_let_40 true _let_39)))) (let ((_let_45 (REFL :args (_let_38)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_27)) :args ((or _let_33 _let_27 _let_28))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_26))) :args _let_42)) :args ((or _let_26 _let_38))) _let_44 :args (_let_26 true _let_38)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 5)) _let_44 :args ((not _let_27) true _let_38)) :args (_let_28 false _let_26 true _let_27)))) (let ((_let_47 (REFL :args (_let_25)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_13))) :args _let_42)) :args ((or _let_13 _let_25))) _let_46 :args (_let_13 true _let_25)))) (let ((_let_49 (or _let_37 _let_15))) (let ((_let_50 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_42)) :args ((or _let_36 _let_38))) _let_44 :args (_let_36 true _let_38)))) (let ((_let_53 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_24 _let_17))) (let ((_let_56 (forall ((U $$unsorted) (BOUND_VARIABLE_4790 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4790)) (= (tptp.cons BOUND_VARIABLE_4790 U) (tptp.app (tptp.cons BOUND_VARIABLE_4790 tptp.nil) U)))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_16))) (let ((_let_59 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_58))) (let ((_let_60 (not _let_59))) (let ((_let_61 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_62 (not _let_61))) (let ((_let_63 (or _let_62 _let_54 _let_60))) (let ((_let_64 (forall ((W $$unsorted) (BOUND_VARIABLE_2144 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2144)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2144)))))))) (let ((_let_65 (not _let_63))) (let ((_let_66 (not _let_64))) (let ((_let_67 (= _let_20 _let_66))) (let ((_let_68 (or _let_35 _let_24 _let_67))) (let ((_let_69 (forall ((U $$unsorted) (BOUND_VARIABLE_2170 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2170)) (= (tptp.memberP U BOUND_VARIABLE_2170) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2144 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2144)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2170 BOUND_VARIABLE_2144)))))))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_42)) :args ((or _let_23 _let_25))) _let_46 :args (_let_23 true _let_25)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_42)) :args ((or _let_34 _let_38))) _let_44 :args (_let_34 true _let_38)))) (let ((_let_73 (_let_66))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_73)) :args _let_73)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_64))) (REFL :args (_let_65)) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_67)) :args ((or _let_21 _let_66 (not _let_67)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_42)) :args ((or _let_20 _let_25))) _let_46 :args (_let_20 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_35 _let_24 _let_67 (not _let_68)))) _let_72 _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.memberP U BOUND_VARIABLE_2170)))) :args (_let_69))) _let_70 :args (_let_68 false _let_69)) :args (_let_67 false _let_34 false _let_23 false _let_68)) :args (_let_66 false _let_20 false _let_67)) :args (_let_65 true _let_64)))) (let ((_let_75 (REFL :args (_let_63)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_63 1)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_42)) :args ((or _let_53 _let_63))) _let_74 :args (_let_53 true _let_63)))) (let ((_let_77 (tptp.segmentP (tptp.app _let_58 tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_78 (not _let_8))) (let ((_let_79 (not _let_18))) (let ((_let_80 (tptp.ssList _let_16))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_81 _let_37 _let_79 _let_62 _let_78 _let_77))) (let ((_let_83 (forall ((U $$unsorted) (BOUND_VARIABLE_4453 $$unsorted) (BOUND_VARIABLE_4451 $$unsorted) (BOUND_VARIABLE_4449 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4449)) (not (tptp.segmentP U BOUND_VARIABLE_4449)) (not (tptp.ssList BOUND_VARIABLE_4453)) (not (tptp.ssList BOUND_VARIABLE_4451)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4453 U) BOUND_VARIABLE_4451) BOUND_VARIABLE_4449))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (_let_83))) (let ((_let_86 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_87 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_88 (not _let_77))) (let ((_let_89 (or _let_35 _let_86))) (let ((_let_90 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_93 (not _let_92))) (let ((_let_94 (not _let_87))) (let ((_let_95 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_96 (not _let_95))) (let ((_let_97 (or _let_37 _let_96 _let_94 _let_93))) (let ((_let_98 (_let_31))) (let ((_let_99 (= _let_30 _let_95))) (let ((_let_100 (or _let_37 _let_78 _let_99))) (let ((_let_101 (forall ((U $$unsorted) (BOUND_VARIABLE_3279 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3279)) (= (tptp.neq U BOUND_VARIABLE_3279) (not (= U BOUND_VARIABLE_3279))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (ASSUME :args (_let_8)))) (let ((_let_104 (= tptp.nil _let_12))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_78 _let_24 _let_105))) (let ((_let_107 (forall ((U $$unsorted) (BOUND_VARIABLE_3327 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3327)) (not (= U (tptp.cons BOUND_VARIABLE_3327 U))))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (REFL :args (_let_22)))) (let ((_let_110 (and _let_13 _let_105))) (let ((_let_111 (ASSUME :args (_let_105)))) (let ((_let_112 (ASSUME :args (_let_13)))) (let ((_let_113 (SYMM _let_112))) (let ((_let_114 (REFL :args (tptp.nil)))) (let ((_let_115 (not _let_99))) (let ((_let_116 (or _let_37 _let_92))) (let ((_let_117 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_116)) :args ((or _let_37 _let_92 (not _let_116)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_117))) _let_118 :args (_let_116 false _let_117)) :args (_let_92 false _let_36 false _let_116)))) (let ((_let_120 (not _let_86))) (let ((_let_121 (and _let_86 _let_94 _let_59))) (let ((_let_122 (ASSUME :args (_let_94)))) (let ((_let_123 (APPLY_UF tptp.segmentP))) (let ((_let_124 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_125 (ASSUME :args (_let_86)))) (let ((_let_126 (APPLY_UF tptp.app))) (let ((_let_127 (ASSUME :args (_let_59)))) (let ((_let_128 (or _let_54 _let_24 _let_80))) (let ((_let_129 (forall ((U $$unsorted) (BOUND_VARIABLE_3302 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3302)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3302 U)))))) (let ((_let_130 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_131 (or _let_37 _let_37 _let_93 _let_78 _let_54 _let_19))) (let ((_let_132 (ASSUME :args (_let_19)))) (let ((_let_133 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_134 (ASSUME :args (_let_15)))) (let ((_let_135 (ASSUME :args (_let_17)))) (let ((_let_136 (ASSUME :args (_let_79)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_132 _let_134 _let_112 _let_135 _let_136) :args (_let_13 _let_15 _let_79 _let_17 _let_19)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_136)) (CONG (TRANS (SYMM (SYMM _let_135)) (CONG _let_113 _let_133 :args _let_126) (CONG (SYMM (SYMM _let_134)) _let_133 :args _let_126)) _let_124 :args _let_123) (TRUE_INTRO _let_132))) :args (_let_19 _let_15 _let_13 _let_17 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(tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.60/31.84 )
% 31.60/31.84 % SZS output end Proof for SWC093+1
% 31.60/31.84 % cvc5---1.0.5 exiting
% 31.60/31.84 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------