TSTP Solution File: NUM595+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM595+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 10:45:26 EDT 2023
% Result : Theorem 26.60s 26.87s
% Output : Proof 26.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : NUM595+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 14:54:10 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 26.60/26.87 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.AjSI0okFi2/cvc5---1.0.5_8755.p...
% 26.60/26.87 ------- get file name : TPTP file name is NUM595+3
% 26.60/26.87 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8755.smt2...
% 26.60/26.87 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.60/26.87 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.60/26.87 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.60/26.87 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.60/26.87 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.60/26.87 % SZS status Theorem for NUM595+3
% 26.60/26.87 % SZS output start Proof for NUM595+3
% 26.60/26.87 (
% 26.60/26.87 (let ((_let_1 (not (tptp.aElementOf0 tptp.xx tptp.xT)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))) (let ((_let_3 (tptp.slbdtsldtrb0 _let_2 tptp.xk))) (let ((_let_4 (= tptp.xX _let_3))) (let ((_let_5 (tptp.aSet0 tptp.xX))) (let ((_let_6 (and _let_5 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 tptp.xX))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi))))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi))))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))))) _let_3) _let_2) _let_1))))))) _let_4 (not (not (exists ((W0 $$unsorted)) (tptp.aElementOf0 W0 tptp.xX))))))) (let ((_let_7 (tptp.sdtlpdtrp0 tptp.xd tptp.xi))) (let ((_let_8 (tptp.aElementOf0 tptp.xi tptp.szNzAzT0))) (let ((_let_9 (and _let_8 (= _let_7 tptp.xx)))) (let ((_let_10 (tptp.szDzozmdt0 tptp.xd))) (let ((_let_11 (tptp.sdtlcdtrc0 tptp.xd _let_10))) (let ((_let_12 (tptp.aFunction0 tptp.xd))) (let ((_let_13 (and _let_12 (= _let_10 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (=> (and (tptp.aSet0 W1) (or (and (or (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0))))) (tptp.aSubsetOf0 W1 _let_1)) (= (tptp.sbrdtbr0 W1) tptp.xk)) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= (tptp.sdtlpdtrp0 tptp.xd W0) (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1)))))))))) (let ((_let_14 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xT) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (=> (and (tptp.aSet0 W2) (or (and (or (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W2) (tptp.aElementOf0 W3 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0))))) (tptp.aSubsetOf0 W2 _let_1)) (= (tptp.sbrdtbr0 W2) tptp.xk)) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W2) W1)))))))))) (let ((_let_15 (tptp.szDzozmdt0 tptp.xN))) (let ((_let_16 (and (tptp.aFunction0 tptp.xN) (= _let_15 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_3 (tptp.szmzizndt0 _let_2))) (let ((_let_4 (tptp.sdtmndt0 _let_2 _let_3))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (=> (and (or (and (tptp.aSet0 _let_2) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.aElementOf0 W1 tptp.szNzAzT0)))) (tptp.aSubsetOf0 _let_2 tptp.szNzAzT0)) (tptp.isCountable0 _let_2)) (and (tptp.aElementOf0 _let_3 _let_2) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W1)))) (tptp.aSet0 _let_4) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W1 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W1) (tptp.aElementOf0 W1 _let_1) (not (= W1 _let_2))))))) (tptp.aSet0 _let_1) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0))) (tptp.aElementOf0 W1 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 _let_1 _let_4) (tptp.isCountable0 _let_1)))))))))))) (let ((_let_17 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK)))) (let ((_let_18 (not (= tptp.xK tptp.sz00)))) (let ((_let_19 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_20 (tptp.sdtlcdtrc0 tptp.xc _let_19))) (let ((_let_21 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0))) (let ((_let_22 (tptp.aElementOf0 _let_7 tptp.xT))) (let ((_let_23 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.xT))) (let ((_let_24 (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC tptp.xi) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_25 (= _let_7 _let_24))) (let ((_let_26 (= _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_27 (SYMM (ASSUME :args (_let_21))))) (let ((_let_28 (1))) (let ((_let_29 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) :args _let_28))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (AND_ELIM _let_30 :args _let_28))) (let ((_let_32 (2))) (let ((_let_33 (AND_ELIM _let_30 :args _let_32))) (let ((_let_34 (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_35 (ASSUME :args (_let_9)))) (let ((_let_36 (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_37 (ASSUME :args (_let_6)))) (let ((_let_38 (AND_INTRO (AND_ELIM (EQ_RESOLVE _let_37 _let_36) :args _let_28) (AND_ELIM (EQ_RESOLVE _let_35 _let_34) :args _let_28) _let_33 _let_31 _let_29 _let_27))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO _let_38 :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))) (or (not (tptp.aSet0 W2)) (and (or (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 W2)) (tptp.aElementOf0 W3 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))))) (not (tptp.aSubsetOf0 W2 _let_1))) (not (= tptp.xk (tptp.sbrdtbr0 W2)))) (not (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC tptp.xi) W2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))))) (let ((_let_41 (not _let_40))) (let ((_let_42 (not _let_23))) (let ((_let_43 (or _let_42 _let_41))) (let ((_let_44 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xT)) (not (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))) (or (not (tptp.aSet0 W2)) (and (or (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 W2)) (tptp.aElementOf0 W3 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))))) (not (tptp.aSubsetOf0 W2 _let_1))) (not (= tptp.xk (tptp.sbrdtbr0 W2)))) (not (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= W1 (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC tptp.xi) W2)))))))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (not _let_44))) (let ((_let_47 (tptp.aElementOf0 tptp.xi _let_15))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_46))) (let ((_let_50 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xN))) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xT)) (not (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (or (not (tptp.aSet0 W2)) (and (or (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 W2)) (tptp.aElementOf0 W3 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))))) (not (tptp.aSubsetOf0 W2 _let_1))) (not (= tptp.xk (tptp.sbrdtbr0 W2)))) (not (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= W1 (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W2))))))))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_33 _let_31 _let_29 _let_27) :args ((forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xT)) (not (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (or (not (tptp.aSet0 W2)) (and (or (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 W2)) (tptp.aElementOf0 W3 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))))) (not (tptp.aSubsetOf0 W2 _let_1))) (not (= tptp.xk (tptp.sbrdtbr0 W2)))) (not (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= W1 (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W2))))))))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_52 (EQ_RESOLVE _let_35 (TRANS _let_34 (MACRO_SR_EQ_INTRO _let_38 :args ((and _let_8 (= tptp.xx _let_7)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_53 (or))) (let ((_let_54 (_let_46))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_54)) :args _let_54) (REWRITE :args ((=> _let_46 (not (or _let_42 (not (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))) (or (not (tptp.aSet0 W2)) (and (or (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 W2)) (tptp.aElementOf0 W3 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))))) (not (tptp.aSubsetOf0 W2 _let_1))) (not (= tptp.xk (tptp.sbrdtbr0 W2)))) (not (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC tptp.xi) W2))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_44))) (REFL :args (_let_45)) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_46 (not _let_49)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.xi QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 _let_15) false))))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_46 false _let_47 false _let_49)) :args (_let_45 true _let_44)))) (let ((_let_56 (REFL :args (_let_43)))) (let ((_let_57 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_3))) (let ((_let_58 (not _let_57))) (let ((_let_59 (= tptp.xk (tptp.sbrdtbr0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_60 (not _let_59))) (let ((_let_61 (tptp.aSubsetOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_2))) (let ((_let_62 (not _let_61))) (let ((_let_63 (and (or (and (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))))) _let_62) _let_60) _let_58))) (let ((_let_64 (tptp.aSet0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_48 _let_65 _let_63 _let_25))) (let ((_let_67 (forall ((W0 $$unsorted) (BOUND_VARIABLE_5355 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (or (not (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xN))) (not (tptp.aSet0 BOUND_VARIABLE_5355)) (and (or (and (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_5355)) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))))) (not (tptp.aSubsetOf0 BOUND_VARIABLE_5355 _let_1))) (not (= tptp.xk (tptp.sbrdtbr0 BOUND_VARIABLE_5355)))) (not (tptp.aElementOf0 BOUND_VARIABLE_5355 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= (tptp.sdtlpdtrp0 tptp.xd W0) (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) BOUND_VARIABLE_5355))))))) (let ((_let_68 (_let_67))) (let ((_let_69 (not _let_63))) (let ((_let_70 (forall ((W0 $$unsorted)) (not (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)) tptp.xk)))))) (let ((_let_71 (EQ_RESOLVE _let_37 (TRANS _let_36 (MACRO_SR_EQ_INTRO _let_38 :args ((and _let_5 _let_4 (not (forall ((W0 $$unsorted)) (not (tptp.aElementOf0 W0 tptp.xX)))) (forall ((BOUND_VARIABLE_5445 $$unsorted) (BOUND_VARIABLE_5482 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))) (or (not (tptp.aElementOf0 BOUND_VARIABLE_5445 tptp.xX)) (and (tptp.aSet0 BOUND_VARIABLE_5445) (or (not (tptp.aElementOf0 BOUND_VARIABLE_5482 BOUND_VARIABLE_5445)) (tptp.aElementOf0 BOUND_VARIABLE_5482 _let_1)) (tptp.aSubsetOf0 BOUND_VARIABLE_5445 _let_1) (= tptp.xk (tptp.sbrdtbr0 BOUND_VARIABLE_5445)))))) (forall ((BOUND_VARIABLE_5461 $$unsorted)) (or (and (or (not (tptp.aSet0 BOUND_VARIABLE_5461)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 BOUND_VARIABLE_5461)) (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi))))))) (not (tptp.aSubsetOf0 BOUND_VARIABLE_5461 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi))))) (not (= tptp.xk (tptp.sbrdtbr0 BOUND_VARIABLE_5461))) (tptp.aElementOf0 BOUND_VARIABLE_5461 tptp.xX)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_72 (not _let_70))) (let ((_let_73 (_let_72))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_73)) :args _let_73) (REWRITE :args ((=> _let_72 (not _let_58)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_70))) (REFL :args (_let_57)) :args _let_53)) (AND_ELIM _let_71 :args _let_28) :args (_let_57 true _let_70)))) (let ((_let_75 (and _let_64 (or (not (tptp.aElementOf0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.aElementOf0 tptp.sz00 _let_2)) _let_61 _let_59))) (let ((_let_76 (or _let_58 _let_75))) (let ((_let_77 (forall ((BOUND_VARIABLE_5445 $$unsorted) (BOUND_VARIABLE_5482 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xi)))) (or (not (tptp.aElementOf0 BOUND_VARIABLE_5445 (tptp.slbdtsldtrb0 _let_1 tptp.xk))) (and (tptp.aSet0 BOUND_VARIABLE_5445) (or (not (tptp.aElementOf0 BOUND_VARIABLE_5482 BOUND_VARIABLE_5445)) (tptp.aElementOf0 BOUND_VARIABLE_5482 _let_1)) (tptp.aSubsetOf0 BOUND_VARIABLE_5445 _let_1) (= tptp.xk (tptp.sbrdtbr0 BOUND_VARIABLE_5445)))))))) (let ((_let_78 (_let_77))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or _let_64 (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_58 _let_75 (not _let_76)))) _let_74 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:args (_let_23 true _let_43)) _let_39 :args (false false _let_26 false _let_25 false _let_23 true _let_22)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$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 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall 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(and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$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 $$unsorted)) (=> 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(tptp.szszuzczcdt0 W0))))) (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) 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(tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (=> (not (tptp.aElementOf0 W1 W0)) (= (tptp.sbrdtbr0 (tptp.sdtpldt0 W0 W1)) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 W0)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aElementOf0 W1 W0)) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 W1))) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$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)))) _let_21 (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 $$unsorted)) (=> (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W1 tptp.sz00))) (tptp.isCountable0 (tptp.slbdtsldtrb0 W0 W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.slbdtsldtrb0 W1 W0))) (=> (and (tptp.aSet0 W1) (tptp.aSet0 W2) (not (= W0 tptp.sz00))) (=> (and (tptp.aSubsetOf0 _let_1 (tptp.slbdtsldtrb0 W2 W0)) (not (= _let_1 tptp.slcrc0))) (tptp.aSubsetOf0 W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (forall ((W2 $$unsorted)) (=> (and (tptp.aSubsetOf0 W2 (tptp.slbdtsldtrb0 W0 W1)) (tptp.isFinite0 W2)) (exists ((W3 $$unsorted)) (and (tptp.aSubsetOf0 W3 W0) (tptp.isFinite0 W3) (tptp.aSubsetOf0 W2 (tptp.slbdtsldtrb0 W3 W1)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (tptp.aSet0 (tptp.szDzozmdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.aElement0 (tptp.sdtlpdtrp0 W0 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aFunction0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtlbdtrb0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 (tptp.szDzozmdt0 W0)) (= (tptp.sdtlpdtrp0 W0 W3) W1))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aFunction0 W0) (tptp.aElement0 W1)) (tptp.aSubsetOf0 (tptp.sdtlbdtrb0 W0 W1) (tptp.szDzozmdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtlcdtrc0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (exists ((W4 $$unsorted)) (and (tptp.aElementOf0 W4 W1) (= (tptp.sdtlpdtrp0 W0 W4) W3)))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.aElementOf0 (tptp.sdtlpdtrp0 W0 W1) (tptp.sdtlcdtrc0 W0 _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtexdt0 W0 W1)) (and (tptp.aFunction0 W2) (= (tptp.szDzozmdt0 W2) W1) (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W1) (= (tptp.sdtlpdtrp0 W2 W3) (tptp.sdtlpdtrp0 W0 W3))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.isCountable0 W1)) (=> (forall ((W2 $$unsorted) (W3 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (and (tptp.aElementOf0 W2 _let_1) (tptp.aElementOf0 W3 _let_1) (not (= W2 W3))) (not (= (tptp.sdtlpdtrp0 W0 W2) (tptp.sdtlpdtrp0 W0 W3)))))) (tptp.isCountable0 (tptp.sdtlcdtrc0 W0 W1))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 W0))) (let ((_let_2 (tptp.szDzozmdt0 W0))) (=> (tptp.aFunction0 W0) (=> (and (tptp.isCountable0 _let_2) (tptp.isFinite0 (tptp.sdtlcdtrc0 W0 _let_2))) (and (tptp.aElement0 _let_1) (tptp.isCountable0 (tptp.sdtlbdtrb0 W0 _let_1)))))))) (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT)) (tptp.aElementOf0 tptp.xK tptp.szNzAzT0) (and (tptp.aSet0 tptp.xS) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xS) (tptp.aElementOf0 W0 tptp.szNzAzT0))) (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS)) (and (tptp.aFunction0 tptp.xc) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xc)))) (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))))))) (= _let_19 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSet0 _let_20) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xc (tptp.szDzozmdt0 tptp.xc))) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xc)) (= (tptp.sdtlpdtrp0 tptp.xc W1) W0))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xc (tptp.szDzozmdt0 tptp.xc))) (tptp.aElementOf0 W0 tptp.xT))) (tptp.aSubsetOf0 _let_20 tptp.xT)) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (or (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 tptp.szNzAzT0)))) (tptp.aSubsetOf0 W1 tptp.szNzAzT0)) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W2))) (let ((_let_2 (tptp.sdtlcdtrc0 W2 _let_1))) (=> (and (tptp.aFunction0 W2) (or (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W3 (tptp.szDzozmdt0 W2)))) (let ((_let_2 (= (tptp.sbrdtbr0 W3) W0))) (let ((_let_3 (tptp.aSubsetOf0 W3 W1))) (let ((_let_4 (tptp.aSet0 W3))) (and (=> _let_1 (and (or (and _let_4 (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W1)))) _let_3) _let_2)) (=> (and _let_4 (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W1))) _let_3 _let_2) _let_1))))))) (= _let_1 (tptp.slbdtsldtrb0 W1 W0))) (=> (and (tptp.aSet0 _let_2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 (tptp.sdtlcdtrc0 W2 (tptp.szDzozmdt0 W2))) (exists ((W4 $$unsorted)) (and (tptp.aElementOf0 W4 (tptp.szDzozmdt0 W2)) (= (tptp.sdtlpdtrp0 W2 W4) W3)))))) (or (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 (tptp.sdtlcdtrc0 W2 (tptp.szDzozmdt0 W2))) (tptp.aElementOf0 W3 tptp.xT))) (tptp.aSubsetOf0 _let_2 tptp.xT)))) (=> (tptp.iLess0 W0 tptp.xK) (exists ((W3 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xT) (exists ((W4 $$unsorted)) (and (tptp.aSet0 W4) (forall ((W5 $$unsorted)) (=> (tptp.aElementOf0 W5 W4) (tptp.aElementOf0 W5 W1))) (tptp.aSubsetOf0 W4 W1) (tptp.isCountable0 W4) (forall ((W5 $$unsorted)) (=> (or (and (or (and (tptp.aSet0 W5) (forall ((W6 $$unsorted)) (=> (tptp.aElementOf0 W6 W5) (tptp.aElementOf0 W6 W4)))) (tptp.aSubsetOf0 W5 W4)) (= (tptp.sbrdtbr0 W5) W0)) (tptp.aElementOf0 W5 (tptp.slbdtsldtrb0 W4 W0))) (= (tptp.sdtlpdtrp0 W2 W5) W3)))))))))))))))) _let_18 _let_18 _let_17 _let_16 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aSet0 _let_1) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.aElementOf0 W1 tptp.szNzAzT0))) (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W1 W0) (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN W1)))) (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN W0) (tptp.sdtlpdtrp0 tptp.xN W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W1))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_3 (tptp.szmzizndt0 _let_2))) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W0 W1))) (not (=> (and (tptp.aElementOf0 _let_3 _let_2) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))) (or (and (tptp.aElementOf0 _let_3 _let_1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN W1)) (tptp.sdtlseqdt0 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)) W2)))) (= _let_3 (tptp.szmzizndt0 _let_1)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtpldt0 W1 _let_2))) (let ((_let_4 (tptp.aElementOf0 _let_2 _let_1))) (let ((_let_5 (tptp.sdtmndt0 _let_1 _let_2))) (=> (and (tptp.aSet0 W1) (=> (and _let_4 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))) (=> (and (tptp.aSet0 _let_5) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W2) (tptp.aElementOf0 W2 _let_1) (not (= W2 _let_2)))))))) (or (and (or (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 W1 _let_5)) (= (tptp.sbrdtbr0 W1) tptp.xk)) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 _let_5 tptp.xk)))))) (and _let_4 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2)))) (tptp.aSet0 _let_3) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))) (= (tptp.aElementOf0 W2 (tptp.sdtpldt0 W1 _let_1)) (and (tptp.aElement0 W2) (or (tptp.aElementOf0 W2 W1) (= W2 _let_1)))))) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.sdtpldt0 W1 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))) (tptp.aElementOf0 W2 tptp.xS))) (tptp.aSubsetOf0 _let_3 tptp.xS) (= (tptp.sbrdtbr0 _let_3) tptp.xK) (tptp.aElementOf0 _let_3 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)))))))))))) (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtmndt0 _let_1 _let_2))) (let ((_let_4 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aFunction0 _let_4) (tptp.aElementOf0 _let_2 _let_1) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W1)))) (tptp.aSet0 _let_3) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W1 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W1) (tptp.aElementOf0 W1 _let_1) (not (= W1 _let_2))))))) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W1 (tptp.szDzozmdt0 (tptp.sdtlpdtrp0 tptp.xC W0))))) (let ((_let_2 (= (tptp.sbrdtbr0 W1) tptp.xk))) (let ((_let_3 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_4 (tptp.aSubsetOf0 W1 (tptp.sdtmndt0 _let_3 (tptp.szmzizndt0 _let_3))))) (let ((_let_5 (tptp.aSet0 W1))) (and (=> _let_1 (and _let_5 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) _let_4 _let_2)) (=> (and (or (and _let_5 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))))))) _let_4) _let_2) _let_1)))))))) (= (tptp.szDzozmdt0 _let_4) (tptp.slbdtsldtrb0 _let_3 tptp.xk)) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.aElementOf0 _let_2 _let_1))) (let ((_let_4 (tptp.sdtmndt0 _let_1 _let_2))) (=> (and (tptp.aSet0 W1) (=> (and _let_3 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))) (=> (and (tptp.aSet0 _let_4) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W2) (tptp.aElementOf0 W2 _let_1) (not (= W2 _let_2)))))))) (or (and (or (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 W1 _let_4)) (= (tptp.sbrdtbr0 W1) tptp.xk)) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 _let_4 tptp.xk)))))) (and _let_3 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2)))) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))) (= (tptp.aElementOf0 W2 (tptp.sdtpldt0 W1 _let_1)) (and (tptp.aElement0 W2) (or (tptp.aElementOf0 W2 W1) (= W2 _let_1)))))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 W1 _let_2)))))))))))))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (let ((_let_2 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1)))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aSet0 _let_2) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (= (tptp.aElementOf0 W1 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1))) (exists ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (and (tptp.aElementOf0 W2 (tptp.szDzozmdt0 _let_1)) (= (tptp.sdtlpdtrp0 _let_1 W2) W1))))))) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W1 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1))) (tptp.aElementOf0 W1 tptp.xT)))) (tptp.aSubsetOf0 _let_2 tptp.xT)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtmndt0 _let_1 _let_2))) (=> (and (=> (and (tptp.aElementOf0 _let_2 _let_1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))) (=> (and (tptp.aSet0 _let_3) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W2) (tptp.aElementOf0 W2 _let_1) (not (= W2 _let_2)))))))) (or (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))))))) (tptp.aSubsetOf0 W1 _let_3)))) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtmndt0 _let_1 _let_2))) (=> (and (tptp.aSet0 W2) (or (and (or (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W2) (tptp.aElementOf0 W3 W1))) (tptp.aSubsetOf0 W2 W1)) (= (tptp.sbrdtbr0 W2) tptp.xk)) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 W1 tptp.xk)))) (and (tptp.aElementOf0 _let_2 _let_1) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W3 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W3)))) (tptp.aSet0 _let_3) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 _let_1) (not (= W3 _let_2))))))) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W3 W2) (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 W2 _let_3) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 _let_3 tptp.xk))))))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xT) (exists ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtmndt0 _let_1 _let_2))) (and (tptp.aElementOf0 _let_2 _let_1) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W3 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W3)))) (tptp.aSet0 _let_3) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 _let_1) (not (= W3 _let_2))))))) (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W3 W2) (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 W2 _let_3) (tptp.isCountable0 W2) (forall ((W3 $$unsorted)) (=> (and (tptp.aSet0 W3) (or (and (or (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W2))) (tptp.aSubsetOf0 W3 W2)) (= (tptp.sbrdtbr0 W3) tptp.xk)) (tptp.aElementOf0 W3 (tptp.slbdtsldtrb0 W2 tptp.xk)))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W3) W1)))))))))))) _let_14 (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xe W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_2 _let_1) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xe W0) W1))) (= _let_2 (tptp.szmzizndt0 _let_1)))))))) _let_13 (and (tptp.aSet0 _let_11) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xd (tptp.szDzozmdt0 tptp.xd))) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xd)) (= (tptp.sdtlpdtrp0 tptp.xd W1) W0)))))) (and (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xd)) (= (tptp.sdtlpdtrp0 tptp.xd W0) tptp.xx))) (tptp.aElementOf0 tptp.xx _let_11)) _let_9 _let_6 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.60/26.88 )
% 26.60/26.88 % SZS output end Proof for NUM595+3
% 26.60/26.88 % cvc5---1.0.5 exiting
% 26.60/26.88 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------