TSTP Solution File: SWC325+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC325+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 20:24:46 EDT 2023
% Result : Theorem 0.21s 0.86s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC325+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n025.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 17:46:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.86 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.bRnQZRZcVZ/cvc5---1.0.5_19059.p...
% 0.21/0.86 ------- get file name : TPTP file name is SWC325+1
% 0.21/0.86 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19059.smt2...
% 0.21/0.86 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.86 % SZS status Theorem for SWC325+1
% 0.21/0.86 % SZS output start Proof for SWC325+1
% 0.21/0.86 (
% 0.21/0.86 (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)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (= (tptp.app Y Z) V) (= (tptp.app Z Y) U))))) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (forall ((X1 $$unsorted)) (=> (tptp.ssItem X1) (forall ((X2 $$unsorted)) (let ((_let_1 (tptp.cons X1 tptp.nil))) (=> (tptp.ssList X2) (or (not (= (tptp.app _let_1 X2) W)) (not (= (tptp.app X2 _let_1) X)))))))) (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) (= (tptp.app tptp.nil U) U))))) (let ((_let_4 (tptp.ssList tptp.nil))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_7 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_7))) (let ((_let_9 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_10 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_7))) (let ((_let_12 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_8))) (let ((_let_15 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_17 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil))) (let ((_let_18 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_19 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_18)))) (let ((_let_20 (not _let_19))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24 _let_22 _let_20))) (let ((_let_28 (and _let_27 _let_17))) (let ((_let_29 (not _let_10))) (let ((_let_30 (and _let_29 _let_9))) (let ((_let_31 (forall ((Y $$unsorted) (BOUND_VARIABLE_5244 $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.ssList BOUND_VARIABLE_5244)) (not (= (tptp.app Y BOUND_VARIABLE_5244) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (= (tptp.app BOUND_VARIABLE_5244 Y) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_32 (not _let_31))) (let ((_let_33 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_34 (or _let_33 _let_13 _let_32 _let_30 _let_28))) (let ((_let_35 (forall ((U $$unsorted) (BOUND_VARIABLE_5473 $$unsorted) (BOUND_VARIABLE_5471 $$unsorted) (BOUND_VARIABLE_5469 $$unsorted)) (let ((_let_1 (tptp.cons BOUND_VARIABLE_5473 tptp.nil))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5469)) (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5244 $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.ssList BOUND_VARIABLE_5244)) (not (= (tptp.app Y BOUND_VARIABLE_5244) BOUND_VARIABLE_5469)) (not (= U (tptp.app BOUND_VARIABLE_5244 Y)))))) (and (not (= tptp.nil U)) (= tptp.nil BOUND_VARIABLE_5469)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5473)) (not (tptp.ssList BOUND_VARIABLE_5471)) (not (= U (tptp.app _let_1 BOUND_VARIABLE_5471))) (not (= BOUND_VARIABLE_5469 (tptp.app BOUND_VARIABLE_5471 _let_1)))) (tptp.neq BOUND_VARIABLE_5469 tptp.nil))))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or))) (let ((_let_39 (not _let_35))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_37) :args (_let_39)) (REWRITE :args ((=> _let_39 (not (or _let_33 _let_13 (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5244 $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.ssList BOUND_VARIABLE_5244)) (not (= (tptp.app Y BOUND_VARIABLE_5244) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app BOUND_VARIABLE_5244 Y)))))) _let_30 _let_28))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) (REFL :args (_let_36)) :args _let_38)) _let_37 :args (_let_36 true _let_35)))) (let ((_let_41 (REFL :args (_let_34)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 1)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_38)) :args ((or _let_12 _let_34))) _let_40 :args (_let_12 true _let_34)))) (let ((_let_43 (not _let_9))) (let ((_let_44 (= _let_17 _let_43))) (let ((_let_45 (not _let_4))) (let ((_let_46 (or _let_13 _let_45 _let_44))) (let ((_let_47 (forall ((U $$unsorted) (BOUND_VARIABLE_3290 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3290)) (= (tptp.neq U BOUND_VARIABLE_3290) (not (= U BOUND_VARIABLE_3290))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (ASSUME :args (_let_4)))) (let ((_let_50 (tptp.ssList _let_18))) (let ((_let_51 (or _let_45 _let_26 _let_50))) (let ((_let_52 (not _let_50))) (let ((_let_53 (or _let_24 _let_52 _let_20 _let_22))) (let ((_let_54 (REFL :args (_let_27)))) (let ((_let_55 (forall ((U $$unsorted) (BOUND_VARIABLE_3313 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3313)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3313 U)))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 2)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_38)) :args ((or _let_31 _let_34))) _let_40 :args (_let_31 true _let_34)))) (let ((_let_58 (_let_31))) (let ((_let_59 ((tptp.app Y BOUND_VARIABLE_5244)))) (let ((_let_60 (ASSUME :args _let_58))) (let ((_let_61 (not _let_44))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_44)) (CONG (REFL :args (_let_61)) (REFL :args (_let_17)) (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_9))) :args _let_38)) :args ((or _let_9 _let_17 _let_61))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_28)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 4)) _let_40 :args ((not _let_28) true _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_24 _let_22 _let_20 _let_52 (not _let_53)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_59)) :args _let_58))) _let_57 :args (_let_53 false _let_31)) (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_45 _let_26 _let_50 (not _let_51)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3313 U)))) :args (_let_55))) _let_56 :args (_let_51 false _let_55)) _let_49 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 3)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_38)) :args ((or _let_19 _let_27))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 2)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_38)) :args ((or _let_21 _let_27))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 1)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_38)) :args ((or _let_23 _let_27))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_38)) :args ((or _let_25 _let_27))) :args (_let_27 false _let_53 false _let_50 false _let_51 false _let_4 false _let_19 false _let_21 false _let_23 false _let_25)) :args ((not _let_17) true _let_28 false _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_13 _let_44 (not _let_46)))) _let_49 _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.neq U BOUND_VARIABLE_3290)))) :args (_let_47)))) _let_48 :args (_let_46 false _let_47)) :args (_let_44 false _let_4 false _let_12 false _let_46)) :args (_let_9 true _let_17 false _let_44)))) (let ((_let_63 (REFL :args (_let_43)))) (let ((_let_64 (_let_30))) (let ((_let_65 (not _let_11))) (let ((_let_66 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil)))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_13 _let_45 _let_67 _let_65))) (let ((_let_69 (or _let_13 _let_66))) (let ((_let_70 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (ASSUME :args (_let_65)))) (let ((_let_73 (ASSUME :args (_let_8)))) (let ((_let_74 (ASSUME :args (_let_10)))) (let ((_let_75 (ASSUME :args (_let_9)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_72 _let_74 _let_75 _let_73) :args (_let_10 _let_9 _let_8 _let_65)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (TRANS (SYMM (TRANS (SYMM _let_75) (SYMM (SYMM _let_74)))) (SYMM (SYMM _let_73))))) (FALSE_INTRO _let_72))) :args (_let_65 _let_10 _let_9 _let_8)) :args ((not (and _let_10 _let_9 _let_8 _let_65)) SB_LITERAL))) (CONG (REFL :args (_let_29)) _let_63 (REFL :args ((not _let_8))) (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_11))) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_45 _let_13 _let_67 _let_65 (not _let_68)))) _let_49 _let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_13 _let_66 (not _let_69)))) _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_66 false _let_12 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_59)) :args _let_58))) _let_57 :args (_let_68 false _let_31)) :args (_let_65 false _let_4 false _let_12 false _let_66 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_64) (CONG (REFL :args _let_64) (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_10))) _let_63 :args _let_38)) :args ((or _let_10 _let_30 _let_43))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 3)) _let_40 :args ((not _let_30) true _let_34)) _let_62 :args (_let_10 true _let_30 false _let_9)) _let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_13 _let_8 (not _let_14)))) _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_15))) _let_16 :args (_let_14 false _let_15)) :args (_let_8 false _let_12 false _let_14)) :args (false true _let_11 false _let_10 false _let_9 false _let_8)) :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)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (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 $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) _let_6 _let_5 _let_4 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_3 (forall ((U $$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)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$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))))))) _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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.86 )
% 0.21/0.86 % SZS output end Proof for SWC325+1
% 0.21/0.86 % cvc5---1.0.5 exiting
% 0.21/0.87 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------