TSTP Solution File: SWC214+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC214+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:24:03 EDT 2023
% Result : Theorem 77.29s 77.48s
% Output : Proof 77.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC214+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 17:43:09 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 77.29/77.48 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.E3z8wlsyHr/cvc5---1.0.5_30963.p...
% 77.29/77.48 ------- get file name : TPTP file name is SWC214+1
% 77.29/77.48 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_30963.smt2...
% 77.29/77.48 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 77.29/77.48 --- Run --no-e-matching --full-saturate-quant at 5...
% 77.29/77.48 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 77.29/77.48 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 77.29/77.48 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 77.29/77.48 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 77.29/77.48 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 77.29/77.48 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 77.29/77.48 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 77.29/77.48 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 77.29/77.48 --- Run --relevant-triggers --full-saturate-quant at 5...
% 77.29/77.48 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 77.29/77.48 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 77.29/77.48 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 77.29/77.48 % SZS status Theorem for SWC214+1
% 77.29/77.48 % SZS output start Proof for SWC214+1
% 77.29/77.48 (
% 77.29/77.48 (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)) (not (tptp.frontsegP X W)) (not (tptp.strictorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.frontsegP X Y) (tptp.segmentP Y W) (tptp.strictorderedP Y))) (tptp.neq U tptp.nil))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))))) (let ((_let_7 (tptp.singletonP tptp.nil))) (let ((_let_8 (not _let_7))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))))) (let ((_let_12 (tptp.ssList tptp.nil))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_16 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (tptp.cons _let_17 tptp.nil))) (let ((_let_19 (tptp.segmentP _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (tptp.segmentP _let_18 tptp.nil))) (let ((_let_21 (not _let_16))) (let ((_let_22 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (not _let_12))) (let ((_let_25 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24 _let_23))) (let ((_let_28 (forall ((U $$unsorted) (BOUND_VARIABLE_3268 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3268)) (= (tptp.neq U BOUND_VARIABLE_3268) (not (= U BOUND_VARIABLE_3268))))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (_let_28))) (let ((_let_31 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)) (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)) (not (tptp.segmentP Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.strictorderedP Y)))))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_26 _let_22 (not (tptp.strictorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_36 _let_34 (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_32))) (let ((_let_38 (forall ((U $$unsorted) (BOUND_VARIABLE_5274 $$unsorted)) (or (not (tptp.ssList U)) (tptp.neq U tptp.nil) (not (tptp.strictorderedP U)) (not (tptp.ssList BOUND_VARIABLE_5274)) (not (tptp.neq BOUND_VARIABLE_5274 tptp.nil)) (not (tptp.frontsegP BOUND_VARIABLE_5274 U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.frontsegP BOUND_VARIABLE_5274 Y)) (not (tptp.segmentP Y U)) (not (tptp.strictorderedP Y))))))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or))) (let ((_let_42 (not _let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_40) :args (_let_42))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_41)) _let_40 :args (_let_39 true _let_38)))) (let ((_let_44 (REFL :args (_let_37)))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_41)) :args ((or _let_25 _let_37))) _let_43 :args (_let_25 true _let_37)))) (let ((_let_46 (ASSUME :args (_let_12)))) (let ((_let_47 (not _let_23))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_23)) (CONG (REFL :args (_let_47)) (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_16))) :args _let_41)) :args ((or _let_22 _let_16 _let_47))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 1)) _let_43 :args ((not _let_22) true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_24 _let_26 _let_23 (not _let_27)))) _let_46 _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_30))) _let_29 :args (_let_27 false _let_28)) :args (_let_23 false _let_12 false _let_25 false _let_27)) :args (_let_16 true _let_22 false _let_23)))) (let ((_let_49 (tptp.strictorderedP _let_18))) (let ((_let_50 (not _let_49))) (let ((_let_51 (not _let_19))) (let ((_let_52 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_18))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_18))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.ssList _let_18))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55 _let_53 _let_51 _let_50))) (let ((_let_59 (_let_31))) (let ((_let_60 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_61 (tptp.cons _let_17 _let_60))) (let ((_let_62 (tptp.frontsegP _let_61 _let_18))) (let ((_let_63 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_61))) (let ((_let_64 (tptp.frontsegP _let_60 tptp.nil))) (let ((_let_65 (= _let_64 _let_62))) (let ((_let_66 (tptp.ssList _let_60))) (let ((_let_67 (not _let_66))) (let ((_let_68 (tptp.ssItem _let_17))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_69 _let_67 _let_24 _let_65))) (let ((_let_71 (forall ((U $$unsorted) (BOUND_VARIABLE_4121 $$unsorted) (BOUND_VARIABLE_4119 $$unsorted) (BOUND_VARIABLE_4117 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_4117)) (not (tptp.ssList BOUND_VARIABLE_4121)) (not (tptp.ssList BOUND_VARIABLE_4119)) (= (tptp.frontsegP (tptp.cons U BOUND_VARIABLE_4121) (tptp.cons BOUND_VARIABLE_4117 BOUND_VARIABLE_4119)) (and (= U BOUND_VARIABLE_4117) (tptp.frontsegP BOUND_VARIABLE_4121 BOUND_VARIABLE_4119))))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_74 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.tl _let_73)))) (let ((_let_75 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_73))) (let ((_let_76 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_77 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_78 (not _let_77))) (let ((_let_79 (not _let_76))) (let ((_let_80 (or _let_79 _let_78 _let_74))) (let ((_let_81 (forall ((U $$unsorted) (BOUND_VARIABLE_3527 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3527)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3527 U))))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (not _let_75))) (let ((_let_84 (or _let_79 _let_78 _let_83))) (let ((_let_85 (forall ((V $$unsorted) (BOUND_VARIABLE_3438 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3438)) (not (= (tptp.cons BOUND_VARIABLE_3438 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_86 (not _let_84))) (let ((_let_87 (not _let_85))) (let ((_let_88 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_89 (or _let_36 _let_88 _let_87))) (let ((_let_90 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((V $$unsorted) (BOUND_VARIABLE_3438 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3438)) (not (= U (tptp.cons BOUND_VARIABLE_3438 V)))))))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (not _let_88))) (let ((_let_93 (= _let_33 _let_92))) (let ((_let_94 (or _let_36 _let_24 _let_93))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 3)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_41)) :args ((or _let_35 _let_37))) _let_43 :args (_let_35 true _let_37)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_93)) :args ((or _let_34 _let_92 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 4)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_41)) :args ((or _let_33 _let_37))) _let_43 :args (_let_33 true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_24 _let_36 _let_93 (not _let_94)))) _let_46 _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_30))) _let_29 :args (_let_94 false _let_28)) :args (_let_93 false _let_12 false _let_35 false _let_94)) :args (_let_92 false _let_33 false _let_93)))) (let ((_let_97 (_let_87))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_97)) :args _let_97) (REWRITE :args ((=> _let_87 (not (or _let_79 _let_78 (not (= _let_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_85))) (REFL :args (_let_86)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_36 _let_88 _let_87 (not _let_89)))) _let_95 _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_90)))) _let_91 :args (_let_89 false _let_90)) :args (_let_87 false _let_35 true _let_88 false _let_89)) :args (_let_86 true _let_85)))) (let ((_let_99 (REFL :args (_let_84)))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 0)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_76))) :args _let_41)) :args ((or _let_76 _let_84))) _let_98 :args (_let_76 true _let_84)))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_79 _let_78 _let_74 (not _let_80)))) _let_100 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 1)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_77))) :args _let_41)) :args ((or _let_77 _let_84))) _let_98 :args (_let_77 true _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_81))) _let_82 :args (_let_80 false _let_81)) :args (_let_74 false _let_76 false _let_77 false _let_80)))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 2)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_75))) :args _let_41)) :args ((or _let_75 _let_84))) _let_98 :args (_let_75 true _let_84)))) (let ((_let_103 (and _let_76 _let_75 _let_74))) (let ((_let_104 (ASSUME :args (_let_76)))) (let ((_let_105 (ASSUME :args (_let_74)))) (let ((_let_106 (ASSUME :args (_let_75)))) (let ((_let_107 (TRANS (CONG (SYMM (SYMM _let_106)) :args (APPLY_UF tptp.tl)) (SYMM _let_105)))) (let ((_let_108 (or _let_36 _let_88 _let_68))) (let ((_let_109 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_36 _let_88 _let_68 (not _let_108)))) _let_95 _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_109))) _let_110 :args (_let_108 false _let_109)) :args (_let_68 false _let_35 true _let_88 false _let_108)))) (let ((_let_112 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.nil))) (let ((_let_113 (or _let_79 _let_112))) (let ((_let_114 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U tptp.nil))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (and _let_75 _let_74 _let_112))) (let ((_let_117 (ASSUME :args (_let_112)))) (let ((_let_118 (APPLY_UF tptp.frontsegP))) (let ((_let_119 (or _let_36 _let_88 _let_63))) (let ((_let_120 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (and _let_63 _let_62))) (let ((_let_123 (ASSUME :args (_let_62)))) (let ((_let_124 (REFL :args (_let_18)))) (let ((_let_125 (ASSUME :args (_let_63)))) (let ((_let_126 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_18))) (let ((_let_127 (not _let_126))) (let ((_let_128 (= _let_54 _let_127))) (let ((_let_129 (or _let_26 _let_57 _let_128))) (let ((_let_130 (or _let_24 _let_69 _let_56))) (let ((_let_131 (forall ((U $$unsorted) (BOUND_VARIABLE_3291 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3291)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3291 U)))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args 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(= (tptp.app tptp.nil U) U))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) _let_8 (forall ((U $$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)))))))) _let_6 _let_5 (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)))))))))) _let_4 (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 $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) _let_3 (tptp.strictorderedP tptp.nil) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_2 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 77.29/77.49 )
% 77.29/77.49 % SZS output end Proof for SWC214+1
% 77.29/77.49 % cvc5---1.0.5 exiting
% 77.29/77.49 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------