TSTP Solution File: NUM556+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM556+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 10:45:03 EDT 2023
% Result : Theorem 0.22s 0.74s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM556+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n005.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 : Fri Aug 25 10:13:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.74 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.lbJgHSwJUZ/cvc5---1.0.5_32571.p...
% 0.22/0.74 ------- get file name : TPTP file name is NUM556+3
% 0.22/0.74 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32571.smt2...
% 0.22/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.74 % SZS status Theorem for NUM556+3
% 0.22/0.74 % SZS output start Proof for NUM556+3
% 0.22/0.74 (
% 0.22/0.74 (let ((_let_1 (tptp.sbrdtbr0 tptp.xP))) (let ((_let_2 (tptp.aSubsetOf0 tptp.xP tptp.xS))) (let ((_let_3 (not (and (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xP) (tptp.aElementOf0 W0 tptp.xS))) _let_2) (= _let_1 tptp.xk))))) (let ((_let_4 (tptp.sdtmndt0 tptp.xQ tptp.xy))) (let ((_let_5 (tptp.aSet0 _let_4))) (let ((_let_6 (tptp.aElementOf0 tptp.xx _let_4))) (let ((_let_7 (and (not _let_6) _let_5 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 tptp.xQ) (not (= W0 tptp.xy)))))))) (let ((_let_8 (tptp.sdtpldt0 _let_4 tptp.xx))) (let ((_let_9 (= tptp.xP _let_8))) (let ((_let_10 (and _let_5 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 tptp.xQ) (not (= W0 tptp.xy))))) (tptp.aSet0 tptp.xP) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xP) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (= W0 tptp.xx))))) _let_9))) (let ((_let_11 (not (tptp.aElementOf0 tptp.xx tptp.xQ)))) (let ((_let_12 (tptp.aElementOf0 tptp.xy tptp.xQ))) (let ((_let_13 (tptp.aElement0 tptp.xy))) (let ((_let_14 (and _let_13 _let_12))) (let ((_let_15 (tptp.sbrdtbr0 tptp.xQ))) (let ((_let_16 (= _let_15 tptp.xk))) (let ((_let_17 (tptp.isFinite0 tptp.xQ))) (let ((_let_18 (tptp.aSet0 tptp.xQ))) (let ((_let_19 (and _let_18 _let_17 _let_16))) (let ((_let_20 (tptp.slbdtsldtrb0 tptp.xS tptp.xk))) (let ((_let_21 (and _let_18 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 tptp.xS))) (tptp.aSubsetOf0 tptp.xQ tptp.xS) _let_16 (tptp.aElementOf0 tptp.xQ _let_20)))) (let ((_let_22 (tptp.aElementOf0 tptp.xx tptp.xS))) (let ((_let_23 (tptp.slbdtsldtrb0 tptp.xT tptp.xk))) (let ((_let_24 (tptp.aSet0 tptp.xS))) (let ((_let_25 (and _let_24 (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00))))) (let ((_let_26 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aElementOf0 W1 W0)) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 W1))) (tptp.sbrdtbr0 W0)))))))) (let ((_let_27 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (=> (not (tptp.aElementOf0 W1 W0)) (= (tptp.sbrdtbr0 (tptp.sdtpldt0 W0 W1)) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 W0)))))))))) (let ((_let_28 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))))) (let ((_let_29 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_30 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xS))) (let ((_let_31 (= tptp.xx SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_32 (ASSUME :args (_let_22)))) (let ((_let_33 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xP))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_30))) (let ((_let_36 (not _let_30))) (let ((_let_37 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xP)) (tptp.aElementOf0 W0 tptp.xS))))) (let ((_let_38 (not _let_35))) (let ((_let_39 (or _let_37 _let_2))) (let ((_let_40 (not _let_37))) (let ((_let_41 (= tptp.xk _let_1))) (let ((_let_42 (tptp.szszuzczcdt0 (tptp.sbrdtbr0 _let_4)))) (let ((_let_43 (= _let_15 _let_42))) (let ((_let_44 (= _let_42 (tptp.sbrdtbr0 _let_8)))) (let ((_let_45 (= tptp.xk _let_15))) (let ((_let_46 (not _let_12))) (let ((_let_47 (not _let_17))) (let ((_let_48 (not _let_18))) (let ((_let_49 (or _let_48 _let_47 _let_46 _let_43))) (let ((_let_50 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isFinite0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_2038 W0)) (= (tptp.sbrdtbr0 W0) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 BOUND_VARIABLE_2038)))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (1))) (let ((_let_53 (ASSUME :args (_let_14)))) (let ((_let_54 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))) :args _let_52))) (let ((_let_55 (0))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (AND_ELIM _let_56 :args _let_55))) (let ((_let_58 (tptp.aElement0 tptp.xx))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.isFinite0 _let_4))) (let ((_let_61 (not _let_60))) (let ((_let_62 (not _let_5))) (let ((_let_63 (or _let_62 _let_61 _let_59 _let_6 _let_44))) (let ((_let_64 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2007 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isFinite0 W0)) (not (tptp.aElement0 BOUND_VARIABLE_2007)) (tptp.aElementOf0 BOUND_VARIABLE_2007 W0) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 W0)) (tptp.sbrdtbr0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_2007))))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (not _let_22))) (let ((_let_67 (not _let_24))) (let ((_let_68 (or _let_67 _let_66 _let_58))) (let ((_let_69 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1531 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1531 W0)) (tptp.aElement0 BOUND_VARIABLE_1531))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (not _let_13))) (let ((_let_72 (or _let_71 _let_48 _let_47 _let_60))) (let ((_let_73 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1860 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aSet0 BOUND_VARIABLE_1860)) (not (tptp.isFinite0 BOUND_VARIABLE_1860)) (tptp.isFinite0 (tptp.sdtmndt0 BOUND_VARIABLE_1860 W0)))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (3))) (let ((_let_77 (and _let_9 _let_45 _let_44 _let_43))) (let ((_let_78 (ASSUME :args (_let_9)))) (let ((_let_79 (ASSUME :args (_let_44)))) (let ((_let_80 (ASSUME :args (_let_43)))) (let ((_let_81 (ASSUME :args (_let_45)))) (let ((_let_82 (or))) (let ((_let_83 (_let_40))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_83)) :args _let_83)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_37))) (REFL :args (_let_38)) :args _let_82)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 0)) (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_77)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_78 _let_79 _let_80 _let_81) (SCOPE (TRANS (SYMM (SYMM _let_81)) (SYMM (SYMM _let_80)) (SYMM (SYMM _let_79)) (CONG (SYMM _let_78) :args (APPLY_UF tptp.sbrdtbr0))) :args (_let_9 _let_44 _let_43 _let_45))) :args (_let_9 _let_45 _let_44 _let_43))) :args (true _let_77)) :args ((or _let_41 (not _let_45) (not _let_9) (not _let_44) (not _let_43)))) (AND_ELIM _let_56 :args _let_76) (AND_ELIM _let_75 :args (4)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_6 _let_62 _let_61 _let_59 _let_44 (not _let_63)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) :args _let_55) (AND_ELIM _let_75 :args _let_55) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_48 _let_47 _let_71 _let_60 (not _let_72)))) _let_57 _let_54 (AND_ELIM _let_53 :args _let_55) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (tptp.xy tptp.xQ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtmndt0 BOUND_VARIABLE_1860 W0)))) :args (_let_73))) _let_74 :args (_let_72 false _let_73)) :args (_let_60 false _let_18 false _let_17 false _let_13 false _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_66 _let_58 (not _let_68)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))) :args _let_55) _let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.xS tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1531 W0) false))))) :args (_let_69))) _let_70 :args (_let_68 false _let_69)) :args (_let_58 false _let_24 false _let_22 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_4 tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_2007 W0) true))))) :args (_let_64))) _let_65 :args (_let_63 false _let_64)) :args (_let_44 true _let_6 false _let_5 false _let_60 false _let_58 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_47 _let_46 _let_43 (not _let_49)))) _let_57 _let_54 (AND_ELIM _let_53 :args _let_52) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.xQ tptp.xy QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_2038 W0) false))))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_43 false _let_18 false _let_17 false _let_12 false _let_49)) :args (_let_41 false _let_45 false _let_9 false _let_44 false _let_43)) :args ((not _let_39) false _let_41)) :args (_let_40 true _let_39)) :args (_let_38 true _let_37)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 1)) _let_84 :args (_let_36 true _let_35)))) (let ((_let_86 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_4))) (let ((_let_87 (or _let_86 _let_31))) (let ((_let_88 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_89 (and _let_88 _let_87))) (let ((_let_90 (= _let_33 _let_89))) (let ((_let_91 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xP) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (= tptp.xx W0))))))) (let ((_let_92 (_let_91))) (let ((_let_93 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xQ))) (let ((_let_94 (and _let_88 _let_93 (not (= tptp.xy SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_95 (= _let_86 _let_94))) (let ((_let_96 (not _let_86))) (let ((_let_97 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 tptp.xQ) (not (= tptp.xy W0))))))) (let ((_let_98 (_let_97))) (let ((_let_99 (not _let_94))) (let ((_let_100 (not _let_93))) (let ((_let_101 (or _let_100 _let_30))) (let ((_let_102 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xQ)) (tptp.aElementOf0 W0 tptp.xS))))) (let ((_let_103 (_let_102))) (let ((_let_104 (ASSUME :args (_let_36)))) (let ((_let_105 (ASSUME :args (_let_31)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_104 _let_105 _let_32) :args (_let_22 _let_36 _let_31)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_32)) (CONG (SYMM (SYMM _let_105)) (REFL :args (tptp.xS)) :args (APPLY_UF tptp.aElementOf0)) (FALSE_INTRO _let_104))) :args (_let_36 _let_31 _let_22)) :args ((not (and _let_22 _let_36 _let_31)) SB_LITERAL))) (CONG (REFL :args (_let_66)) (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_30))) (REFL :args ((not _let_31))) :args _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_86 _let_31 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_95)) :args ((or _let_96 _let_94 (not _let_95)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_94 1)) :args ((or _let_93 _let_99))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_30 _let_100 (not _let_101)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_103) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 tptp.xS) true))))) :args _let_103)) (AND_ELIM _let_56 :args _let_52) :args (_let_101 false _let_102)) :args (_let_100 true _let_30 false _let_101)) :args (_let_99 true _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_98) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W0 _let_4)))) :args _let_98)) (AND_ELIM _let_75 :args _let_52) :args (_let_95 false _let_97)) :args (_let_96 true _let_94 false _let_95)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_89 1)) :args ((or _let_87 (not _let_89)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_90)) :args ((or _let_34 _let_89 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 0)) (CONG (REFL :args (_let_35)) (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_82)) :args ((or _let_33 _let_35))) _let_84 :args (_let_33 true _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_92) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W0 tptp.xP)))) :args _let_92)) (AND_ELIM _let_75 :args _let_76) :args (_let_90 false _let_91)) :args (_let_89 false _let_33 false _let_90)) :args (_let_87 false _let_89)) :args (_let_31 true _let_86 false _let_87)) _let_85 _let_32 :args (false false _let_31 true _let_30 false _let_22)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_29 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))) (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isCountable0 W0) true))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (tptp.isFinite0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aSubsetOf0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1) (tptp.aSet0 W2)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (or (tptp.aElementOf0 W3 W0) (= W3 W1)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 W0) (not (= W3 W1)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (= (tptp.sdtpldt0 (tptp.sdtmndt0 W0 W1) W1) W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aSet0 W1)) (=> (not (tptp.aElementOf0 W0 W1)) (= (tptp.sdtmndt0 (tptp.sdtpldt0 W1 W0) W0) W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtmndt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtpldt0 W1 W0)))))) _let_28 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)) (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (or (= W0 tptp.sz00) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= W0 (tptp.szszuzczcdt0 W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (= W0 (tptp.szszuzczcdt0 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 tptp.sz00 W0))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.sz00)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W2 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aElement0 (tptp.sbrdtbr0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))) _let_27 _let_26 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aSubsetOf0 W1 W0)) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 W1) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.isFinite0 W0) (tptp.sdtlseqdt0 W1 (tptp.sbrdtbr0 W0))) (exists ((W2 $$unsorted)) (and (tptp.aSubsetOf0 W2 W0) (= (tptp.sbrdtbr0 W2) W1)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzizndt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 W0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzazxdt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W2 W1)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 W1))) (let ((_let_2 (tptp.szmzizndt0 W0))) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 W1 tptp.szNzAzT0) (not (= W0 tptp.slcrc0)) (not (= W1 tptp.slcrc0))) (=> (and (tptp.aElementOf0 _let_2 W1) (tptp.aElementOf0 _let_1 W0)) (= _let_2 _let_1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slbdtrb0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtrb0 W0)))) (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 (tptp.szszuzczcdt0 W1))) (or (tptp.aElementOf0 W0 (tptp.slbdtrb0 W1)) (= W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.aSubsetOf0 (tptp.slbdtrb0 W0) (tptp.slbdtrb0 W1))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 W0)) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aSubsetOf0 W0 (tptp.slbdtrb0 W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sbrdtbr0 (tptp.slbdtrb0 W0)) W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.slbdtsldtrb0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aSubsetOf0 W3 W0) (= (tptp.sbrdtbr0 W3) W1))))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtsldtrb0 W0 W1)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (not (tptp.isFinite0 W0))) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= (tptp.slbdtsldtrb0 W0 W1) tptp.slcrc0)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (forall ((W1 $$unsorted)) (=> (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W1 tptp.sz00))) (tptp.isCountable0 (tptp.slbdtsldtrb0 W0 W1)))))) (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) _let_25 (and (tptp.aSet0 _let_20) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (tptp.aSet0 _let_23) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xT))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xT))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xT)))) _let_3) _let_2) _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))) (tptp.aSubsetOf0 _let_20 _let_23) (not (=> (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (or (not (exists ((W0 $$unsorted)) (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (= _let_20 tptp.slcrc0))))) _let_22 _let_21 _let_19 _let_14 _let_11 _let_11 _let_10 _let_7 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.75 )
% 0.22/0.75 % SZS output end Proof for NUM556+3
% 0.22/0.75 % cvc5---1.0.5 exiting
% 0.22/0.75 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------