%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC091+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.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 20:23:10 EDT 2023

% Result   : Theorem 77.54s 77.92s
% Output   : Proof 77.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWC091+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n006.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 16:32:06 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_NAR, FOF, or CNF
% 77.54/77.92  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.MJBAyS9JcM/cvc5---1.0.5_2779.p...
% 77.54/77.92  ------- get file name : TPTP file name is SWC091+1
% 77.54/77.92  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2779.smt2...
% 77.54/77.92  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 77.54/77.92  --- Run --no-e-matching --full-saturate-quant at 5...
% 77.54/77.92  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 77.54/77.92  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 77.54/77.92  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 77.54/77.92  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 77.54/77.92  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 77.54/77.92  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 77.54/77.92  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 77.54/77.92  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 77.54/77.92  --- Run --relevant-triggers --full-saturate-quant at 5...
% 77.54/77.92  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 77.54/77.92  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 77.54/77.92  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 77.54/77.92  % SZS status Theorem for SWC091+1
% 77.54/77.92  % SZS output start Proof for SWC091+1
% 77.54/77.92  (
% 77.54/77.92  (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)) (not (tptp.frontsegP X W)) (not (tptp.totalorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (tptp.neq W Z) (tptp.frontsegP X Z) (tptp.segmentP Z W) (tptp.totalorderedP Z))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))))) (let ((_let_9 (tptp.singletonP tptp.nil))) (let ((_let_10 (not _let_9))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))))) (let ((_let_15 (tptp.ssList tptp.nil))) (let ((_let_16 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_17 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_18 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))))) (let ((_let_19 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_20 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (tptp.cons _let_21 tptp.nil))) (let ((_let_23 (tptp.segmentP _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_24 (tptp.segmentP _let_22 tptp.nil))) (let ((_let_25 (not _let_20))) (let ((_let_26 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_27 (= _let_26 _let_25))) (let ((_let_28 (not _let_15))) (let ((_let_29 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28 _let_27))) (let ((_let_32 (forall ((U $$unsorted) (BOUND_VARIABLE_3275 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3275)) (= (tptp.neq U BOUND_VARIABLE_3275) (not (= U BOUND_VARIABLE_3275))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (_let_32))) (let ((_let_35 (forall ((Z $$unsorted)) (or (not (tptp.ssList Z)) (not (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Z)) (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Z)) (not (tptp.segmentP Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.totalorderedP Z)))))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (not _let_37))) (let ((_let_39 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)))))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_30 (not (tptp.totalorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_44 _let_42 _let_40 _let_38 _let_36))) (let ((_let_46 (forall ((U $$unsorted) (BOUND_VARIABLE_5290 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.totalorderedP U)) (not (tptp.ssList BOUND_VARIABLE_5290)) (not (tptp.neq BOUND_VARIABLE_5290 tptp.nil)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP BOUND_VARIABLE_5290 Y)) (not (tptp.segmentP U Y))))) (not (tptp.frontsegP BOUND_VARIABLE_5290 U)) (not (forall ((Z $$unsorted)) (or (not (tptp.ssList Z)) (not (tptp.neq U Z)) (not (tptp.frontsegP BOUND_VARIABLE_5290 Z)) (not (tptp.segmentP Z U)) (not (tptp.totalorderedP Z))))))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or))) (let ((_let_50 (not _let_46))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_48) :args (_let_50))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_46))) (REFL :args (_let_47)) :args _let_49)) _let_48 :args (_let_47 true _let_46)))) (let ((_let_52 (REFL :args (_let_45)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_49)) :args ((or _let_29 _let_45))) _let_51 :args (_let_29 true _let_45)))) (let ((_let_54 (ASSUME :args (_let_15)))) (let ((_let_55 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_56 (not _let_55))) (let ((_let_57 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_58 (not _let_57))) (let ((_let_59 (not _let_26))) (let ((_let_60 (or _let_30 _let_59 _let_58 _let_56))) (let ((_let_61 (_let_39))) (let ((_let_62 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_63 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_62))) (let ((_let_64 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_65 (tptp.segmentP (tptp.app _let_62 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_66 (or _let_30 _let_63))) (let ((_let_67 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (not _let_64))) (let ((_let_70 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_71 _let_69))) (let ((_let_73 (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 W))))))) (let ((_let_74 (not _let_72))) (let ((_let_75 (not _let_73))) (let ((_let_76 (= _let_37 _let_75))) (let ((_let_77 (or _let_44 _let_30 _let_76))) (let ((_let_78 (forall ((U $$unsorted) (BOUND_VARIABLE_2226 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2226)) (= (tptp.frontsegP U BOUND_VARIABLE_2226) (not (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U (tptp.app BOUND_VARIABLE_2226 W))))))))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 2)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_49)) :args ((or _let_43 _let_45))) _let_51 :args (_let_43 true _let_45)))) (let ((_let_81 (_let_75))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_81)) :args _let_81)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_73))) (REFL :args (_let_74)) :args _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_76)) :args ((or _let_38 _let_75 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 5)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_49)) :args ((or _let_37 _let_45))) _let_51 :args (_let_37 true _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_30 _let_44 _let_76 (not _let_77)))) _let_53 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.frontsegP U BOUND_VARIABLE_2226)))) :args (_let_78))) _let_79 :args (_let_77 false _let_78)) :args (_let_76 false _let_29 false _let_43 false _let_77)) :args (_let_75 false _let_37 false _let_76)) :args (_let_74 true _let_73)))) (let ((_let_83 (REFL :args (_let_72)))) (let ((_let_84 (or _let_30 _let_30 _let_56 _let_28 _let_71 _let_65))) (let ((_let_85 (forall ((U $$unsorted) (BOUND_VARIABLE_4449 $$unsorted) (BOUND_VARIABLE_4447 $$unsorted) (BOUND_VARIABLE_4445 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4445)) (not (tptp.segmentP U BOUND_VARIABLE_4445)) (not (tptp.ssList BOUND_VARIABLE_4449)) (not (tptp.ssList BOUND_VARIABLE_4447)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4449 U) BOUND_VARIABLE_4447) BOUND_VARIABLE_4445))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (or _let_30 _let_55))) (let ((_let_88 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_30 _let_55 (not _let_87)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_55 false _let_29 false _let_87)))) (let ((_let_91 (and _let_63 _let_64 _let_65))) (let ((_let_92 (ASSUME :args (_let_65)))) (let ((_let_93 (APPLY_UF tptp.segmentP))) (let ((_let_94 (ASSUME :args (_let_63)))) (let ((_let_95 (ASSUME :args (_let_64)))) (let ((_let_96 (not _let_27))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_27)) (CONG (REFL :args (_let_96)) (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_20))) :args _let_49)) :args ((or _let_20 _let_26 _let_96))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_30 _let_56 _let_59 _let_58 (not _let_60)))) _let_53 _let_90 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_91)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_92 _let_94 _let_95) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (SYMM (SYMM _let_95)) (CONG (SYMM (SYMM _let_94)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) :args (APPLY_UF tptp.app))) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args _let_93) (TRUE_INTRO _let_92))) :args (_let_65 _let_63 _let_64))) :args (_let_63 _let_64 _let_65))) :args (true _let_91)) :args ((or _let_57 (not _let_63) _let_69 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_84))) :args ((or _let_28 _let_30 _let_56 _let_71 _let_65 (not _let_84)))) _let_54 _let_53 _let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_49)) :args ((or _let_70 _let_72))) _let_82 :args (_let_70 true _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_85))) _let_86 :args (_let_84 false _let_85)) :args (_let_65 false _let_15 false _let_29 false _let_55 false _let_70 false _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 1)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_64))) :args _let_49)) :args ((or _let_64 _let_72))) _let_82 :args (_let_64 true _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_30 _let_63 (not _let_66)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_63 false _let_29 false _let_66)) :args (_let_57 false _let_65 false _let_64 false _let_63)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_61) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList Y) false))))) :args _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 4)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_49)) :args ((or _let_39 _let_45))) _let_51 :args (_let_39 true _let_45)) :args (_let_60 false _let_39)) :args (_let_59 false _let_29 false _let_55 false _let_57 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_28 _let_30 _let_27 (not _let_31)))) _let_54 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_34))) _let_33 :args (_let_31 false _let_32)) :args (_let_27 false _let_15 false _let_29 false _let_31)) :args (_let_20 true _let_26 false _let_27)))) (let ((_let_98 (tptp.totalorderedP _let_22))) (let ((_let_99 (not _let_98))) (let ((_let_100 (not _let_23))) (let ((_let_101 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_22))) (let ((_let_102 (not _let_101))) (let ((_let_103 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22))) 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(IMPLIES_ELIM (SCOPE (INSTANTIATE _let_164 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_163))) _let_164 :args (_let_162 false _let_163)) :args (_let_161 false _let_122 false _let_162)) :args (_let_113 false _let_124 false _let_125 false _let_161)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_119))) :args ((or _let_28 _let_118 _let_116 _let_114 (not _let_119)))) _let_54 _let_160 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_151)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_152 _let_153 _let_155) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS _let_156 (SYMM (SYMM _let_154))) :args (APPLY_UF tptp.ssList)) (TRUE_INTRO _let_152))) :args (_let_122 _let_125 _let_124))) :args (_let_122 _let_124 _let_125))) :args (true _let_151)) _let_150 _let_146 _let_145 :args (_let_115 false _let_125 false _let_124 false _let_122)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_121 :args (_let_21 _let_109 tptp.nil _let_21 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_120)))) _let_121 :args (_let_119 false _let_120)) :args (_let_114 false _let_15 false _let_117 false _let_115 false _let_119)) :args (_let_111 false _let_113 false _let_114)) :args (_let_101 false _let_112 false _let_111)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_108) :args (_let_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.totalorderedP Z) false))))) :args _let_108)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 6)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_49)) :args ((or _let_35 _let_45))) _let_51 :args (_let_35 true _let_45)) :args (_let_107 false _let_35)) :args (_let_100 false _let_98 false _let_105 false _let_103 false _let_101 false _let_107)) _let_97 :args (false false _let_24 true _let_23 false _let_20)) :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 $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))) _let_19 _let_18 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) _let_17 _let_16 _let_15 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) _let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) _let_12 (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 $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_11 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) _let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) _let_8 _let_7 (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_6 _let_5 _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) _let_3 (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))) (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 77.54/77.92  )
% 77.54/77.92  % SZS output end Proof for SWC091+1
% 77.54/77.92  % cvc5---1.0.5 exiting
% 77.54/77.93  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------