TSTP Solution File: SWC346+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC346+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 20:24:55 EDT 2023
% Result : Theorem 1.11s 1.34s
% Output : Proof 1.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SWC346+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n022.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 15:26:54 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 1.11/1.34 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.xC9yBHuv2F/cvc5---1.0.5_27354.p...
% 1.11/1.34 ------- get file name : TPTP file name is SWC346+1
% 1.11/1.34 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27354.smt2...
% 1.11/1.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.11/1.34 % SZS status Theorem for SWC346+1
% 1.11/1.34 % SZS output start Proof for SWC346+1
% 1.11/1.34 (
% 1.11/1.34 (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)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (and (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (forall ((X1 $$unsorted)) (or (not (tptp.ssList X1)) (not (= (tptp.cons Y tptp.nil) W)) (not (= (tptp.app (tptp.app Z W) X1) X)) (exists ((X2 $$unsorted)) (and (tptp.ssItem X2) (tptp.memberP Z X2) (tptp.lt Y X2))) (exists ((X3 $$unsorted)) (and (tptp.ssItem X3) (tptp.memberP X1 X3) (tptp.lt X3 Y))))))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))) (and (tptp.segmentP V U) (tptp.strictorderedP U))))))))))))) (let ((_let_2 (tptp.strictorderedP tptp.nil))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_5 (tptp.ssList tptp.nil))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))))) (let ((_let_7 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U tptp.nil)))))) (let ((_let_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_9 (tptp.strictorderedP _let_8))) (let ((_let_10 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_14 (not _let_12))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_8))) (let ((_let_16 (tptp.strictorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (not _let_9))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_23 (not _let_22))) (let ((_let_24 (not _let_15))) (let ((_let_25 (or _let_11 _let_24 _let_23 (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 X2)) (not (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X2))))) _let_21 _let_19 (not (forall ((X3 $$unsorted)) (or (not (tptp.ssItem X3)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 X3)) (not (tptp.lt X3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))))) (let ((_let_26 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (not _let_26))) (let ((_let_28 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27))) (let ((_let_31 (and _let_25 _let_30))) (let ((_let_32 (tptp.segmentP tptp.nil tptp.nil))) (let ((_let_33 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_34 (and _let_33 _let_16))) (let ((_let_35 (or))) (let ((_let_36 (REFL :args (_let_30)))) (let ((_let_37 (not _let_5))) (let ((_let_38 (or _let_37 _let_32))) (let ((_let_39 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (and _let_28 _let_26 _let_32))) (let ((_let_42 (ASSUME :args (_let_32)))) (let ((_let_43 (APPLY_UF tptp.segmentP))) (let ((_let_44 (ASSUME :args (_let_26)))) (let ((_let_45 (SYMM _let_44))) (let ((_let_46 (ASSUME :args (_let_28)))) (let ((_let_47 (ASSUME :args (_let_2)))) (let ((_let_48 (and _let_2 _let_26))) (let ((_let_49 (_let_2 _let_26))) (let ((_let_50 (APPLY_UF tptp.strictorderedP))) (let ((_let_51 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_52 _let_34 _let_31))) (let ((_let_56 (forall ((U $$unsorted) (BOUND_VARIABLE_5595 $$unsorted) (BOUND_VARIABLE_5593 $$unsorted) (BOUND_VARIABLE_5591 $$unsorted) (BOUND_VARIABLE_5589 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5589)) (and (tptp.segmentP BOUND_VARIABLE_5589 U) (tptp.strictorderedP U)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5595)) (not (= U (tptp.cons BOUND_VARIABLE_5595 tptp.nil))) (not (tptp.ssList BOUND_VARIABLE_5591)) (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP BOUND_VARIABLE_5591 X2)) (not (tptp.lt BOUND_VARIABLE_5595 X2))))) (not (tptp.ssList BOUND_VARIABLE_5593)) (not (= BOUND_VARIABLE_5589 (tptp.app (tptp.app BOUND_VARIABLE_5591 U) BOUND_VARIABLE_5593))) (not (forall ((X3 $$unsorted)) (or (not (tptp.ssItem X3)) (not (tptp.memberP BOUND_VARIABLE_5593 X3)) (not (tptp.lt X3 BOUND_VARIABLE_5595)))))) (or (not (= tptp.nil BOUND_VARIABLE_5589)) (not (= tptp.nil U)))))))) (let ((_let_57 (not _let_55))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (not _let_56))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_58) :args (_let_59))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_56))) (REFL :args (_let_57)) :args _let_35)) _let_58 :args (_let_57 true _let_56)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_55 2)) _let_60 :args ((not _let_34) true _let_55)))) (let ((_let_62 (CNF_AND_NEG :args (_let_34)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_31)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_55 3)) _let_60 :args ((not _let_31) true _let_55)) (MACRO_RESOLUTION_TRUST _let_62 _let_61 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_48)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_47 _let_44) (SCOPE (TRUE_ELIM (TRANS (CONG _let_45 :args _let_50) (TRUE_INTRO _let_47))) :args _let_49)) :args _let_49)) :args (true _let_48)) :args ((or (not _let_2) _let_16 _let_27))) _let_47 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_41)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_42 _let_44 _let_46) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_46) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args _let_43) (CONG (REFL :args (tptp.nil)) _let_45 :args _let_43) (TRUE_INTRO _let_42))) :args (_let_32 _let_26 _let_28))) :args (_let_28 _let_26 _let_32))) :args (true _let_41)) :args ((or _let_33 _let_29 _let_27 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_32 (not _let_38)))) (ASSUME :args (_let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_32 false _let_5 false _let_38)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_35)) :args ((or _let_26 _let_30))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_35)) :args ((or _let_28 _let_30))) :args (_let_30 true _let_34 false _let_16 false _let_2 false _let_33 false _let_32 false _let_26 false _let_28)) :args ((not _let_25) true _let_31 false _let_30)))) (let ((_let_64 (REFL :args (_let_25)))) (let ((_let_65 (not _let_16))) (let ((_let_66 (forall ((W $$unsorted) (BOUND_VARIABLE_2328 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2328)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2328))))))) (let ((_let_67 (not _let_66))) (let ((_let_68 (= _let_33 _let_67))) (let ((_let_69 (or _let_52 _let_54 _let_68))) (let ((_let_70 (forall ((U $$unsorted) (BOUND_VARIABLE_2353 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2353)) (= (tptp.segmentP U BOUND_VARIABLE_2353) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2328 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2328)) (not (= U (tptp.app (tptp.app W BOUND_VARIABLE_2353) BOUND_VARIABLE_2328))))))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (REFL :args (_let_55)))) (let ((_let_73 (or _let_23 _let_21 _let_19))) (let ((_let_74 (not _let_73))) (let ((_let_75 (_let_66))) (let ((_let_76 (not _let_68))) (let ((_let_77 (and _let_15 _let_65))) (let ((_let_78 (ASSUME :args (_let_65)))) (let ((_let_79 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssItem U) false))))) :args (_let_7))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_11 _let_9 _let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_35)) :args ((or _let_10 _let_25))) _let_63 :args (_let_10 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_77)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_78 _let_79) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_79) :args _let_50) (FALSE_INTRO _let_78))) :args (_let_65 _let_15))) :args (_let_15 _let_65))) :args (true _let_77)) (CONG (REFL :args (_let_24)) (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_16))) (REFL :args (_let_17)) :args _let_35)) :args ((or _let_16 _let_24 _let_17))) (MACRO_RESOLUTION_TRUST _let_62 _let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_68)) (CONG (REFL :args (_let_76)) (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_35)) :args ((or _let_33 _let_66 _let_76))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_75) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2328)))) :args _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_23 _let_21 _let_19 _let_74))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_35)) :args ((or _let_22 _let_25))) _let_63 :args (_let_22 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 4)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_35)) :args ((or _let_20 _let_25))) _let_63 :args (_let_20 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 5)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_35)) :args ((or _let_18 _let_25))) _let_63 :args (_let_18 true _let_25)) :args (_let_74 false _let_22 false _let_20 false _let_18)) :args (_let_67 true _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_54 _let_52 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 0)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_35)) :args ((or _let_53 _let_55))) _let_60 :args (_let_53 true _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 1)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_35)) :args ((or _let_51 _let_55))) _let_60 :args (_let_51 true _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.segmentP U BOUND_VARIABLE_2353)))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_68 false _let_53 false _let_51 false _let_69)) :args (_let_33 true _let_66 false _let_68)) :args (_let_65 true _let_34 false _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_15))) :args _let_35)) :args ((or _let_15 _let_25))) _let_63 :args (_let_15 true _let_25)) :args (_let_17 true _let_16 false _let_15)) :args (_let_14 false _let_10 true _let_9)) _let_13 :args (false true _let_12 false _let_7)) :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)))))))) _let_6 (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 $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) _let_5 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))) (forall ((U $$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 $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) _let_3 _let_2 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.16/1.35 )
% 1.16/1.35 % SZS output end Proof for SWC346+1
% 1.16/1.35 % cvc5---1.0.5 exiting
% 1.16/1.35 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------