%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC384+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n020.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 20:25:14 EDT 2023

% Result   : Theorem 10.82s 11.02s
% Output   : Proof 10.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWC384+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n020.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon Aug 28 17:52:44 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 10.82/11.02  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.TDgILGF54V/cvc5---1.0.5_25082.p...
% 10.82/11.02  ------- get file name : TPTP file name is SWC384+1
% 10.82/11.02  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25082.smt2...
% 10.82/11.02  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.82/11.02  --- Run --no-e-matching --full-saturate-quant at 5...
% 10.82/11.02  % SZS status Theorem for SWC384+1
% 10.82/11.02  % SZS output start Proof for SWC384+1
% 10.82/11.02  (
% 10.82/11.02  (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (and (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (or (not (= (tptp.cons Y tptp.nil) W)) (not (= (tptp.app (tptp.app Z W) X1) X)) (exists ((X2 $$unsorted)) (and (tptp.ssItem X2) (tptp.memberP Z X2) (tptp.lt Y X2))) (exists ((X3 $$unsorted)) (and (tptp.ssItem X3) (tptp.memberP X1 X3) (tptp.lt X3 Y)))))))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))) (and (tptp.singletonP U) (tptp.segmentP V U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_4 (tptp.ssList tptp.nil))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_7 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_7))) (let ((_let_9 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (tptp.segmentP _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (not _let_8))) (let ((_let_12 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_15 (not _let_14))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil)))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17 _let_15 (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 X2)) (not (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X2))))) _let_13 _let_11 (not (forall ((X3 $$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_21 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 (not (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_24 (and _let_20 _let_23))) (let ((_let_25 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.nil))) (let ((_let_26 (= _let_25 _let_22))) (let ((_let_27 (not _let_4))) (let ((_let_28 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27 _let_26))) (let ((_let_31 (forall ((U $$unsorted) (BOUND_VARIABLE_3300 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3300)) (= (tptp.neq U BOUND_VARIABLE_3300) (not (= U BOUND_VARIABLE_3300))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (tptp.singletonP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_34 (and _let_33 _let_9))) (let ((_let_35 (not _let_25))) (let ((_let_36 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_29 _let_35 _let_34 _let_24))) (let ((_let_39 (forall ((U $$unsorted) (BOUND_VARIABLE_5605 $$unsorted) (BOUND_VARIABLE_5603 $$unsorted) (BOUND_VARIABLE_5601 $$unsorted) (BOUND_VARIABLE_5599 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5599)) (not (tptp.neq BOUND_VARIABLE_5599 tptp.nil)) (and (tptp.singletonP U) (tptp.segmentP BOUND_VARIABLE_5599 U)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5605)) (not (= U (tptp.cons BOUND_VARIABLE_5605 tptp.nil))) (not (tptp.ssList BOUND_VARIABLE_5601)) (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP BOUND_VARIABLE_5601 X2)) (not (tptp.lt BOUND_VARIABLE_5605 X2))))) (not (tptp.ssList BOUND_VARIABLE_5603)) (not (= BOUND_VARIABLE_5599 (tptp.app (tptp.app BOUND_VARIABLE_5601 U) BOUND_VARIABLE_5603))) (not (forall ((X3 $$unsorted)) (or (not (tptp.ssItem X3)) (not (tptp.memberP BOUND_VARIABLE_5603 X3)) (not (tptp.lt X3 BOUND_VARIABLE_5605)))))) (or (not (= tptp.nil BOUND_VARIABLE_5599)) (not (= tptp.nil U)))))))) (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 (REFL :args (_let_38)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_24)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 4)) _let_44 :args ((not _let_24) true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG (REFL :args (_let_23)) (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_42)) :args ((or _let_21 _let_23))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_26)) :args ((or _let_35 _let_22 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_25))) :args _let_42)) :args ((or _let_25 _let_38))) _let_44 :args (_let_25 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_27 _let_29 _let_26 (not _let_30)))) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_42)) :args ((or _let_28 _let_38))) _let_44 :args (_let_28 true _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args (_let_31)))) _let_32 :args (_let_30 false _let_31)) :args (_let_26 false _let_4 false _let_28 false _let_30)) :args (_let_22 false _let_25 false _let_26)) :args (_let_23 true _let_21)) :args ((not _let_20) true _let_24 false _let_23)))) (let ((_let_47 (REFL :args (_let_20)))) (let ((_let_48 (not _let_9))) (let ((_let_49 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= (tptp.cons V tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_50 (not _let_49))) (let ((_let_51 (= _let_33 _let_50))) (let ((_let_52 (or _let_37 _let_51))) (let ((_let_53 (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_54 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_ENUM))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_45 (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_57 (or _let_19 _let_17))) (let ((_let_58 (not _let_57))) (let ((_let_59 (_let_49))) (let ((_let_60 (not _let_51))) (let ((_let_61 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_62 (not _let_61))) (let ((_let_63 (or _let_37 _let_37 _let_62 _let_15 _let_13 _let_10))) (let ((_let_64 (forall ((U $$unsorted) (BOUND_VARIABLE_4474 $$unsorted) (BOUND_VARIABLE_4472 $$unsorted) (BOUND_VARIABLE_4470 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4470)) (not (tptp.segmentP U BOUND_VARIABLE_4470)) (not (tptp.ssList BOUND_VARIABLE_4474)) (not (tptp.ssList BOUND_VARIABLE_4472)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4474 U) BOUND_VARIABLE_4472) BOUND_VARIABLE_4470))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (or _let_37 _let_61))) (let ((_let_67 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (not _let_10))) (let ((_let_70 (ASSUME :args (_let_10)))) (let ((_let_71 (ASSUME :args (_let_8)))) (let ((_let_72 (ASSUME :args (_let_48)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_70 _let_71 _let_72) :args (_let_8 _let_48 _let_10)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_72)) (CONG (SYMM (SYMM _let_71)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args (APPLY_UF tptp.segmentP)) (TRUE_INTRO _let_70))) :args (_let_10 _let_8 _let_48)) :args ((not (and _let_8 _let_48 _let_10)) SB_LITERAL))) (CONG (REFL :args (_let_11)) (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_9))) (REFL :args (_let_69)) :args _let_42)) :args ((or _let_9 _let_11 _let_69))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_63))) :args ((or _let_37 _let_15 _let_13 _let_62 _let_10 (not _let_63)))) _let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 2)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_42)) :args ((or _let_14 _let_20))) _let_46 :args (_let_14 true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 4)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_42)) :args ((or _let_12 _let_20))) _let_46 :args (_let_12 true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_37 _let_61 (not _let_66)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args _let_55) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_61 false _let_36 false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_64))) _let_65 :args (_let_63 false _let_64)) :args (_let_10 false _let_36 false _let_14 false _let_12 false _let_61 false _let_63)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_34)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 3)) _let_44 :args ((not _let_34) true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_51)) (CONG (REFL :args (_let_60)) (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_42)) :args ((or _let_33 _let_49 _let_60))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_59))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_19 _let_17 _let_58))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 0)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_42)) :args ((or _let_18 _let_20))) _let_46 :args (_let_18 true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 1)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_42)) :args ((or _let_16 _let_20))) _let_46 :args (_let_16 true _let_20)) :args (_let_58 false _let_18 false _let_16)) :args (_let_50 true _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_37 _let_51 (not _let_52)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args _let_55) :args (_let_53)))) _let_54 :args (_let_52 false _let_53)) :args (_let_51 false _let_36 false _let_52)) :args (_let_33 true _let_49 false _let_51)) :args (_let_48 true _let_34 false _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 5)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_8))) :args _let_42)) :args ((or _let_8 _let_20))) _let_46 :args (_let_8 true _let_20)) :args (false false _let_10 true _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 $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))) _let_6 (forall ((U $$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_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) _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)))))))) (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_3 _let_2 (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 $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.85/11.02  )
% 10.85/11.02  % SZS output end Proof for SWC384+1
% 10.85/11.02  % cvc5---1.0.5 exiting
% 10.85/11.02  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------