%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM534+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 10:44:50 EDT 2023

% Result   : Theorem 0.20s 0.63s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : NUM534+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 16:00:02 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.63  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.X8Op1HqWAP/cvc5---1.0.5_3124.p...
% 0.20/0.63  ------- get file name : TPTP file name is NUM534+1
% 0.20/0.63  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3124.smt2...
% 0.20/0.63  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.63  % SZS status Theorem for NUM534+1
% 0.20/0.63  % SZS output start Proof for NUM534+1
% 0.20/0.63  (
% 0.20/0.63  (let ((_let_1 (tptp.sdtmndt0 tptp.xS tptp.xx))) (let ((_let_2 (tptp.sdtpldt0 _let_1 tptp.xx))) (let ((_let_3 (not (= _let_2 tptp.xS)))) (let ((_let_4 (tptp.aElementOf0 tptp.xx tptp.xS))) (let ((_let_5 (tptp.aSet0 tptp.xS))) (let ((_let_6 (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)))))))))))) (let ((_let_7 (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)))))))))))) (let ((_let_8 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_9 (= tptp.xx SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_10 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 tptp.xS))) (let ((_let_11 (or _let_10 _let_9))) (let ((_let_12 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_13 (and _let_12 _let_11))) (let ((_let_14 (not _let_11))) (let ((_let_15 (= _let_10 _let_13))) (let ((_let_16 (not _let_13))) (let ((_let_17 (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W3 tptp.xS))) (= _let_1 (and (tptp.aElement0 W3) (or _let_1 (= W3 tptp.xx)))))))) (let ((_let_18 (= tptp.xx SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_19 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 tptp.xS))) (let ((_let_20 (or _let_19 _let_18))) (let ((_let_21 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_22 (and _let_21 _let_20))) (let ((_let_23 (= _let_19 _let_22))) (let ((_let_24 (not _let_19))) (let ((_let_25 (not _let_5))) (let ((_let_26 (or _let_25 _let_24 _let_21))) (let ((_let_27 (_let_23))) (let ((_let_28 (ASSUME :args (_let_5)))) (let ((_let_29 (forall ((W0 $$unsorted) (BOUND_VARIABLE_788 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_788 W0)) (tptp.aElement0 BOUND_VARIABLE_788))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (_let_29))) (let ((_let_32 ((not (= (tptp.aElementOf0 BOUND_VARIABLE_788 W0) false))))) (let ((_let_33 (ASSUME :args (_let_4)))) (let ((_let_34 (not _let_18))) (let ((_let_35 (not _let_4))) (let ((_let_36 (or))) (let ((_let_37 (ASSUME :args (_let_24)))) (let ((_let_38 (ASSUME :args (_let_18)))) (let ((_let_39 (not _let_17))) (let ((_let_40 (_let_39))) (let ((_let_41 (_let_17))) (let ((_let_42 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_1))) (let ((_let_43 (or _let_42 _let_9))) (let ((_let_44 (and _let_12 _let_43))) (let ((_let_45 (= _let_10 _let_44))) (let ((_let_46 (not _let_10))) (let ((_let_47 (or _let_25 _let_46 _let_12))) (let ((_let_48 (not _let_9))) (let ((_let_49 (and _let_12 _let_10 _let_48))) (let ((_let_50 (= _let_42 _let_49))) (let ((_let_51 (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 tptp.xS) (and (tptp.aElement0 W3) (or (tptp.aElementOf0 W3 (tptp.sdtmndt0 tptp.xS tptp.xx)) (= W3 tptp.xx))))))) (let ((_let_52 (not _let_45))) (let ((_let_53 (and _let_5 _let_51))) (let ((_let_54 (not _let_51))) (let ((_let_55 (= tptp.xS _let_2))) (let ((_let_56 (= _let_55 _let_53))) (let ((_let_57 (not _let_53))) (let ((_let_58 (tptp.aElement0 tptp.xx))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.aSet0 _let_1))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_59 _let_56))) (let ((_let_63 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_935 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElement0 W1)) (= (= (tptp.sdtpldt0 W0 W1) BOUND_VARIABLE_935) (and (tptp.aSet0 BOUND_VARIABLE_935) (forall ((W3 $$unsorted)) (= (and (tptp.aElement0 W3) (or (tptp.aElementOf0 W3 W0) (= W1 W3))) (tptp.aElementOf0 W3 BOUND_VARIABLE_935))))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (forall ((W3 $$unsorted)) (= (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 tptp.xS) (not (= W3 tptp.xx))) (tptp.aElementOf0 W3 (tptp.sdtmndt0 tptp.xS tptp.xx)))))) (let ((_let_66 (and _let_60 _let_65))) (let ((_let_67 (or _let_25 _let_59 _let_66))) (let ((_let_68 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_971 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElement0 W1)) (= (= (tptp.sdtmndt0 W0 W1) BOUND_VARIABLE_971) (and (tptp.aSet0 BOUND_VARIABLE_971) (forall ((W3 $$unsorted)) (= (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 W0) (not (= W1 W3))) (tptp.aElementOf0 W3 BOUND_VARIABLE_971))))))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (or _let_25 _let_35 _let_58))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_25 _let_35 _let_58 (not _let_70)))) _let_28 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.xS tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31)) _let_30 :args (_let_70 false _let_29)) :args (_let_58 false _let_5 false _let_4 false _let_70)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_25 _let_59 _let_66 (not _let_67)))) _let_28 _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.xS tptp.xx _let_1 QUANTIFIERS_INST_E_MATCHING ((tptp.aSet0 BOUND_VARIABLE_971) (tptp.sdtmndt0 W0 W1)))) :args (_let_68)))) _let_69 :args (_let_67 false _let_68)) :args (_let_66 false _let_5 false _let_58 false _let_67)))) (let ((_let_73 (not _let_66))) (let ((_let_74 (_let_54))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_74)) :args _let_74) (REWRITE :args ((=> _let_54 (not (= _let_10 (and _let_12 (or _let_42 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 tptp.xx)))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_51))) (REFL :args (_let_52)) :args _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_53)) :args ((or _let_25 _let_53 _let_54))) _let_28 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_56)) :args ((or _let_55 _let_57 (not _let_56)))) (SYMM (ASSUME :args (_let_3))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_59 _let_61 _let_56 (not _let_62)))) _let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 0)) :args ((or _let_60 _let_73))) _let_72 :args (_let_60 false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_1 tptp.xx tptp.xS QUANTIFIERS_INST_E_MATCHING ((tptp.aSet0 BOUND_VARIABLE_935) (tptp.sdtpldt0 W0 W1)))) :args (_let_63)))) _let_64 :args (_let_62 false _let_63)) :args (_let_56 false _let_58 false _let_60 false _let_62)) :args (_let_57 true _let_55 false _let_56)) :args (_let_54 false _let_5 true _let_53)) :args (_let_52 true _let_51)))) (let ((_let_76 (_let_45))) (let ((_let_77 (_let_65))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_77) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElement0 W3)))) :args _let_77))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 1)) :args ((or _let_65 _let_73))) _let_72 :args (_let_65 false _let_66)) :args (_let_50 false _let_65)))) (let ((_let_79 (not _let_50))) (let ((_let_80 (not _let_49))) (let ((_let_81 (_let_50))) (let ((_let_82 (not _let_12))) (let ((_let_83 (_let_49))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_83) (CONG (REFL :args _let_83) (REFL :args (_let_82)) (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_9))) :args _let_36)) :args ((or _let_9 _let_46 _let_82 _let_49))) (REORDERING (CNF_EQUIV_POS2 :args _let_81) :args ((or _let_42 _let_80 _let_79))) _let_78 (CNF_OR_NEG :args (_let_43 1)) (CNF_OR_NEG :args (_let_43 0)) (CNF_AND_NEG :args (_let_44)) (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_25 _let_12 _let_46 (not _let_47)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.xS SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31)) _let_30 :args (_let_47 false _let_29)) _let_28 (CNF_EQUIV_NEG2 :args _let_76) _let_75 :args (_let_46 true _let_49 false _let_50 true _let_9 true _let_42 true _let_43 false _let_12 false _let_47 false _let_5 true _let_44 true _let_45)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_76) :args ((or _let_10 _let_44 _let_45))) _let_84 _let_75 :args (_let_44 true _let_10 true _let_45)))) (let ((_let_86 (not _let_44))) (let ((_let_87 (not _let_42))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_11 1)) :args ((or _let_48 _let_11))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_9 (not _let_43)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_81) :args ((or _let_87 _let_49 _let_79))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 1)) :args ((or _let_10 _let_80))) _let_84 :args (_let_80 true _let_10)) _let_78 :args (_let_87 true _let_49 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 1)) :args ((or _let_43 _let_86))) _let_85 :args (_let_43 false _let_44)) :args (_let_9 true _let_42 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_13)) :args ((or _let_82 _let_13 _let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 0)) :args ((or _let_12 _let_86))) _let_85 :args (_let_12 false _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_15)) :args ((or _let_10 _let_16 (not _let_15)))) _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_41) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W3 tptp.xS)))) :args _let_41))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_40)) :args _let_40) (REWRITE :args ((=> _let_39 (not (= _let_19 (and _let_21 (or _let_19 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 tptp.xx)))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_17))) (REFL :args ((not _let_23))) :args _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_37 _let_38 _let_33) :args (_let_4 _let_18 _let_24)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_33)) (CONG (SYMM (SYMM _let_38)) (REFL :args (tptp.xS)) :args (APPLY_UF tptp.aElementOf0)) (FALSE_INTRO _let_37))) :args (_let_24 _let_18 _let_4)) :args ((not (and _let_4 _let_18 _let_24)) SB_LITERAL))) (CONG (REFL :args (_let_35)) (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_19))) :args _let_36)) :args ((or _let_35 _let_19 _let_34))) _let_33 (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_18 (not _let_20)))) (CNF_EQUIV_NEG2 :args _let_27) (REORDERING (CNF_AND_POS :args (_let_22 1)) :args ((or _let_20 (not _let_22)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_22)) (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_21 _let_24 (not _let_26)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.xS SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31)) _let_30 :args (_let_26 false _let_29)) _let_28 (CNF_OR_NEG :args (_let_20 0)) (REORDERING (CNF_EQUIV_NEG1 :args _let_27) :args ((or _let_19 _let_22 _let_23))) :args ((or _let_22 _let_23) false _let_21 false _let_26 false _let_5 false _let_20 false _let_19)) :args (_let_23 false _let_4 false _let_18 true _let_19 false _let_20 false _let_22)) :args (_let_17 false _let_23)) :args (_let_15 false _let_17)) :args (_let_16 true _let_10 false _let_15)) :args (_let_14 false _let_12 true _let_13)) :args (false false _let_9 true _let_11)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_8 (forall ((W0 $$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)))) _let_7 _let_6 _let_5 _let_4 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.64  )
% 0.20/0.64  % SZS output end Proof for NUM534+1
% 0.20/0.64  % cvc5---1.0.5 exiting
% 0.20/0.64  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------