TSTP Solution File: SWC031+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC031+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 20:22:44 EDT 2023
% Result : Theorem 77.59s 77.83s
% Output : Proof 77.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC031+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n007.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 17:11:13 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 77.59/77.83 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.84ranzZL5g/cvc5---1.0.5_8531.p...
% 77.59/77.83 ------- get file name : TPTP file name is SWC031+1
% 77.59/77.83 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_8531.smt2...
% 77.59/77.83 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 77.59/77.83 --- Run --no-e-matching --full-saturate-quant at 5...
% 77.59/77.83 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 77.59/77.83 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 77.59/77.83 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 77.59/77.83 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 77.59/77.83 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 77.59/77.83 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 77.59/77.83 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 77.59/77.83 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 77.59/77.83 --- Run --relevant-triggers --full-saturate-quant at 5...
% 77.59/77.83 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 77.59/77.83 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 77.59/77.83 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 77.59/77.83 % SZS status Theorem for SWC031+1
% 77.59/77.83 % SZS output start Proof for SWC031+1
% 77.59/77.83 (
% 77.59/77.83 (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)) (let ((_let_1 (= tptp.nil V))) (let ((_let_2 (= tptp.nil U))) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.frontsegP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.frontsegP X Y) (tptp.segmentP Y W) (tptp.totalorderedP Y))) (and (or (not _let_1) _let_2) (or (not _let_2) _let_1)))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))))) (let ((_let_7 (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_8 (tptp.singletonP tptp.nil))) (let ((_let_9 (not _let_8))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_12 (forall ((U $$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_13 (tptp.ssList tptp.nil))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_16 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_17 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_18 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (tptp.cons _let_18 tptp.nil))) (let ((_let_20 (tptp.segmentP _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (tptp.segmentP _let_19 tptp.nil))) (let ((_let_22 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_17))) (let ((_let_24 (or _let_23 _let_22))) (let ((_let_25 (not _let_22))) (let ((_let_26 (or _let_25 _let_17))) (let ((_let_27 (and _let_26 _let_24))) (let ((_let_28 (tptp.frontsegP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_29 (= _let_17 _let_28))) (let ((_let_30 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_31 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)) (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)) (not (tptp.segmentP Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.totalorderedP Y)))))) (let ((_let_32 (not _let_31))) (let ((_let_33 (not _let_30))) (let ((_let_34 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 (not (tptp.totalorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_35 _let_27 _let_33 _let_32))) (let ((_let_39 (forall ((U $$unsorted) (BOUND_VARIABLE_5277 $$unsorted)) (let ((_let_1 (= tptp.nil BOUND_VARIABLE_5277))) (let ((_let_2 (= tptp.nil U))) (or (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.ssList BOUND_VARIABLE_5277)) (and (or (not _let_1) _let_2) (or (not _let_2) _let_1)) (not (tptp.frontsegP BOUND_VARIABLE_5277 U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.frontsegP BOUND_VARIABLE_5277 Y)) (not (tptp.segmentP Y U)) (not (tptp.totalorderedP Y))))))))))) (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 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 3)) _let_44 :args ((not _let_27) true _let_38)))) (let ((_let_46 (CNF_AND_NEG :args (_let_27)))) (let ((_let_47 (or _let_37 _let_29))) (let ((_let_48 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (REFL :args (_let_38)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_50 (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_52 (and _let_22 _let_30))) (let ((_let_53 (ASSUME :args (_let_30)))) (let ((_let_54 (APPLY_UF tptp.frontsegP))) (let ((_let_55 (ASSUME :args (_let_22)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_52)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_53 _let_55) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_55)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args _let_54) (TRUE_INTRO _let_53))) :args (_let_30 _let_22))) :args (_let_22 _let_30))) :args (true _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 4)) (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_30))) :args _let_42)) :args ((or _let_30 _let_38))) _let_44 :args (_let_30 true _let_38)) (REORDERING (CNF_EQUIV_POS2 :args (_let_29)) :args ((or _let_17 (not _let_28) (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_37 _let_29 (not _let_47)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_48)))) _let_49 :args (_let_47 false _let_48)) :args (_let_29 false _let_36 false _let_47)) (CNF_OR_NEG :args (_let_26 1)) _let_46 _let_45 (REORDERING (CNF_OR_NEG :args (_let_24 1)) :args ((or _let_25 _let_24))) :args (_let_25 false _let_30 true _let_28 false _let_29 true _let_17 true _let_26 true _let_27 false _let_24)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG (REFL :args (_let_24)) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_17))) :args _let_42)) :args ((or _let_17 _let_24))) (MACRO_RESOLUTION_TRUST _let_46 _let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_22))) :args _let_42)) :args ((or _let_22 _let_26))) _let_56 :args (_let_26 true _let_22)) :args ((not _let_24) true _let_27 false _let_26)) :args (_let_17 true _let_24)))) (let ((_let_58 (tptp.totalorderedP _let_19))) (let ((_let_59 (not _let_58))) (let ((_let_60 (not _let_20))) (let ((_let_61 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_19))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_19))) (let ((_let_64 (not _let_63))) (let ((_let_65 (tptp.ssList _let_19))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_66 _let_64 _let_62 _let_60 _let_59))) (let ((_let_68 (_let_31))) (let ((_let_69 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_70 (tptp.cons _let_18 _let_69))) (let ((_let_71 (tptp.frontsegP _let_70 _let_19))) (let ((_let_72 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_70))) (let ((_let_73 (tptp.frontsegP _let_69 tptp.nil))) (let ((_let_74 (= _let_73 _let_71))) (let ((_let_75 (not _let_13))) (let ((_let_76 (tptp.ssList _let_69))) (let ((_let_77 (not _let_76))) (let ((_let_78 (tptp.ssItem _let_18))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_79 _let_77 _let_75 _let_74))) (let ((_let_81 (forall ((U $$unsorted) (BOUND_VARIABLE_4125 $$unsorted) (BOUND_VARIABLE_4123 $$unsorted) (BOUND_VARIABLE_4121 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_4121)) (not (tptp.ssList BOUND_VARIABLE_4125)) (not (tptp.ssList BOUND_VARIABLE_4123)) (= (tptp.frontsegP (tptp.cons U BOUND_VARIABLE_4125) (tptp.cons BOUND_VARIABLE_4121 BOUND_VARIABLE_4123)) (and (= U BOUND_VARIABLE_4121) (tptp.frontsegP BOUND_VARIABLE_4125 BOUND_VARIABLE_4123))))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_84 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_85 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_84))) (let ((_let_86 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.tl _let_84)))) (let ((_let_87 (not _let_85))) (let ((_let_88 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_89 (not _let_88))) (let ((_let_90 (not _let_83))) (let ((_let_91 (or _let_90 _let_89 _let_87))) (let ((_let_92 (forall ((V $$unsorted) (BOUND_VARIABLE_3442 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3442)) (not (= (tptp.cons BOUND_VARIABLE_3442 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_93 (not _let_91))) (let ((_let_94 (not _let_92))) (let ((_let_95 (or _let_35 _let_22 _let_94))) (let ((_let_96 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((V $$unsorted) (BOUND_VARIABLE_3442 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3442)) (not (= U (tptp.cons BOUND_VARIABLE_3442 V)))))))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_50 (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_99 (_let_94))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_99)) :args _let_99) (REWRITE :args ((=> _let_94 (not (or _let_90 _let_89 (not (= _let_84 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_92))) (REFL :args (_let_93)) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_35 _let_22 _let_94 (not _let_95)))) _let_98 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_97 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_96)))) _let_97 :args (_let_95 false _let_96)) :args (_let_94 false _let_34 true _let_22 false _let_95)) :args (_let_93 true _let_92)))) (let ((_let_101 (REFL :args (_let_91)))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_91 0)) (CONG _let_101 (MACRO_SR_PRED_INTRO :args ((= (not _let_90) _let_83))) :args _let_42)) :args ((or _let_83 _let_91))) _let_100 :args (_let_83 true _let_91)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_91 2)) (CONG _let_101 (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_85))) :args _let_42)) :args ((or _let_85 _let_91))) _let_100 :args (_let_85 true _let_91)))) (let ((_let_104 (or _let_90 _let_89 _let_86))) (let ((_let_105 (forall ((U $$unsorted) (BOUND_VARIABLE_3531 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3531)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3531 U))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_90 _let_89 _let_86 (not _let_104)))) _let_102 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_91 1)) (CONG _let_101 (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_88))) :args _let_42)) :args ((or _let_88 _let_91))) _let_100 :args (_let_88 true _let_91)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 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(forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) _let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_11 (forall ((U $$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_10 (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 $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (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_9 (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 $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) _let_7 _let_6 _let_5 (forall ((U $$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) _let_3 (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_2 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 77.59/77.84 )
% 77.59/77.84 % SZS output end Proof for SWC031+1
% 77.59/77.84 % cvc5---1.0.5 exiting
% 77.64/77.85 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------