TSTP Solution File: SWC277+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC277+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 20:24:26 EDT 2023
% Result : Theorem 0.21s 0.77s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC277+1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 17:36:34 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.77 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ZyeH62q32x/cvc5---1.0.5_3363.p...
% 0.21/0.77 ------- get file name : TPTP file name is SWC277+1
% 0.21/0.77 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3363.smt2...
% 0.21/0.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.77 % SZS status Theorem for SWC277+1
% 0.21/0.77 % SZS output start Proof for SWC277+1
% 0.21/0.77 (
% 0.21/0.77 (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.segmentP X W)) (tptp.totalorderedP U) (and (not (tptp.singletonP W)) (tptp.neq X tptp.nil)))))))))))))) (let ((_let_2 (tptp.totalorderedP tptp.nil))) (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 $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))))) (let ((_let_6 (tptp.ssList tptp.nil))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_9 (tptp.totalorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 tptp.nil))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_10))) (let ((_let_12 (tptp.totalorderedP _let_10))) (let ((_let_13 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_14 (tptp.singletonP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (not _let_14))) (let ((_let_16 (and _let_15 _let_13))) (let ((_let_17 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_9 _let_20 _let_18 _let_16))) (let ((_let_24 (not _let_9))) (let ((_let_25 (forall ((U $$unsorted) (BOUND_VARIABLE_5242 $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderedP U) (not (tptp.ssList BOUND_VARIABLE_5242)) (not (tptp.segmentP BOUND_VARIABLE_5242 U)) (and (not (tptp.singletonP U)) (tptp.neq BOUND_VARIABLE_5242 tptp.nil)))))) (let ((_let_26 (not _let_23))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (or))) (let ((_let_29 (not _let_25))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_27) :args (_let_29))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_25))) (REFL :args (_let_26)) :args _let_28)) _let_27 :args (_let_26 true _let_25)))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 1)) _let_30 :args (_let_24 true _let_23)))) (let ((_let_32 (not _let_11))) (let ((_let_33 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32))) (let ((_let_36 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= (tptp.cons V tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_37 (not _let_35))) (let ((_let_38 (not _let_36))) (let ((_let_39 (= _let_14 _let_38))) (let ((_let_40 (or _let_22 _let_39))) (let ((_let_41 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.singletonP U) (not (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= U (tptp.cons V tptp.nil))))))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (REFL :args (_let_23)))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_28)) :args ((or _let_21 _let_23))) _let_30 :args (_let_21 true _let_23)))) (let ((_let_45 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_46 (not _let_45))) (let ((_let_47 (= _let_13 _let_46))) (let ((_let_48 (not _let_6))) (let ((_let_49 (or _let_20 _let_48 _let_47))) (let ((_let_50 (forall ((U $$unsorted) (BOUND_VARIABLE_3259 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3259)) (= (tptp.neq U BOUND_VARIABLE_3259) (not (= U BOUND_VARIABLE_3259))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 2)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_28)) :args ((or _let_19 _let_23))) _let_30 :args (_let_19 true _let_23)))) (let ((_let_53 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_54 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_55 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_56 (not _let_54))) (let ((_let_57 (or _let_20 _let_22 _let_18 _let_56 _let_55))) (let ((_let_58 (or _let_22 _let_53))) (let ((_let_59 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U tptp.nil))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (and _let_45 _let_53))) (let ((_let_62 (ASSUME :args (_let_53)))) (let ((_let_63 (ASSUME :args (_let_45)))) (let ((_let_64 (SYMM _let_63))) (let ((_let_65 (forall ((U $$unsorted) (BOUND_VARIABLE_4353 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4353)) (not (tptp.segmentP U BOUND_VARIABLE_4353)) (not (tptp.segmentP BOUND_VARIABLE_4353 U)) (= U BOUND_VARIABLE_4353))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (ASSUME :args (_let_2)))) (let ((_let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_9))))) (let ((_let_69 (APPLY_UF tptp.totalorderedP))) (let ((_let_70 (ASSUME :args (_let_55)))) (let ((_let_71 (ASSUME :args (_let_24)))) (let ((_let_72 (SYMM (FALSE_INTRO _let_71)))) (let ((_let_73 (not _let_47))) (let ((_let_74 (not _let_13))) (let ((_let_75 (_let_16))) (let ((_let_76 (_let_38))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_76)) :args _let_76) (REWRITE :args ((=> _let_38 (not (or _let_34 (not (= _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_36))) (REFL :args (_let_37)) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or _let_15 _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_75) (CONG (REFL :args _let_75) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) (REFL :args (_let_74)) :args _let_28)) :args ((or _let_14 _let_16 _let_74))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 4)) _let_30 :args ((not _let_16) true _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_47)) (CONG (REFL :args (_let_73)) (REFL :args (_let_13)) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_28)) :args ((or _let_13 _let_45 _let_73))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_67 _let_63 _let_70 _let_71) :args (_let_2 _let_24 _let_45 _let_55)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_72 (CONG (SYMM (SYMM _let_70)) :args _let_69) (CONG _let_64 :args _let_69) (TRUE_INTRO _let_67))) :args (_let_2 _let_45 _let_55 _let_24)) :args ((not (and _let_2 _let_24 _let_45 _let_55)) SB_LITERAL))) (CONG (REFL :args ((not _let_2))) _let_68 (REFL :args (_let_46)) (REFL :args ((not _let_55))) :args _let_28)) _let_31 _let_67 (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_22 _let_20 _let_18 _let_56 _let_55 (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.segmentP U BOUND_VARIABLE_4353) false))))) :args (_let_65)))) _let_66 :args (_let_57 false _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 3)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_28)) :args ((or _let_17 _let_23))) _let_30 :args (_let_17 true _let_23)) _let_52 _let_44 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_61)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_62 _let_63) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_64 :args (APPLY_UF tptp.segmentP)) (TRUE_INTRO _let_62))) :args (_let_53 _let_45))) :args (_let_45 _let_53))) :args (true _let_61)) :args ((or _let_46 _let_54 (not _let_53)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_22 _let_53 (not _let_58)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_53 false _let_21 false _let_58)) :args (_let_46 true _let_9 false _let_2 false _let_55 false _let_57 false _let_17 false _let_19 false _let_21 false _let_54 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_20 _let_47 (not _let_49)))) (ASSUME :args (_let_6)) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.neq U BOUND_VARIABLE_3259)))) :args (_let_50)))) _let_51 :args (_let_49 false _let_50)) :args (_let_47 false _let_6 false _let_19 false _let_49)) :args (_let_13 true _let_45 false _let_47)) :args (_let_14 true _let_16 false _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_22 _let_39 (not _let_40)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_41)))) _let_42 :args (_let_40 false _let_41)) :args (_let_39 false _let_21 false _let_40)) :args (_let_38 false _let_14 false _let_39)) :args (_let_37 true _let_36)))) (let ((_let_78 (REFL :args (_let_35)))) (let ((_let_79 (or _let_34 _let_12))) (let ((_let_80 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U tptp.nil)))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (ASSUME :args (_let_12)))) (let ((_let_83 (ASSUME :args (_let_11)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_82 _let_83 _let_71) :args (_let_24 _let_11 _let_12)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_72 (CONG (SYMM (SYMM _let_83)) :args _let_69) (TRUE_INTRO _let_82))) :args (_let_12 _let_11 _let_24)) :args ((not (and _let_24 _let_11 _let_12)) SB_LITERAL))) (CONG _let_68 (REFL :args (_let_32)) (REFL :args ((not _let_12))) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_34 _let_12 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 0)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_28)) :args ((or _let_33 _let_35))) _let_77 :args (_let_33 true _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssItem U) false))))) :args (_let_80))) _let_81 :args (_let_79 false _let_80)) :args (_let_12 false _let_33 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 1)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_11))) :args _let_28)) :args ((or _let_11 _let_35))) _let_77 :args (_let_11 true _let_35)) _let_31 :args (false false _let_12 false _let_11 true _let_9)) :args ((forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))) (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))) _let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) _let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) _let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$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))))))))))) (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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) (not (tptp.singletonP tptp.nil)) (forall ((U $$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)))))))) _let_5 (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 $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) _let_3 _let_2 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.77 )
% 0.21/0.77 % SZS output end Proof for SWC277+1
% 0.21/0.77 % cvc5---1.0.5 exiting
% 0.21/0.77 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------