%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 14:37:30 EDT 2023

% Result   : Theorem 0.21s 0.76s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n017.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   : Sat Aug 26 08:55:10 EDT 2023
% 0.21/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.76  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.snKXKoRRez/cvc5---1.0.5_15715.p...
% 0.21/0.76  ------- get file name : TPTP file name is SET082+1
% 0.21/0.76  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15715.smt2...
% 0.21/0.76  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.76  % SZS status Theorem for SET082+1
% 0.21/0.76  % SZS output start Proof for SET082+1
% 0.21/0.76  (
% 0.21/0.76  (let ((_let_1 (not (forall ((X $$unsorted)) (=> (not (tptp.member X tptp.universal_class)) (= (tptp.singleton X) tptp.null_class)))))) (let ((_let_2 (exists ((XF $$unsorted)) (and (tptp.function XF) (forall ((Y $$unsorted)) (=> (tptp.member Y tptp.universal_class) (or (= Y tptp.null_class) (tptp.member (tptp.apply XF Y) Y)))))))) (let ((_let_3 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_4 (forall ((X $$unsorted)) (= (tptp.singleton X) (tptp.unordered_pair X X))))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_6 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.member U (tptp.unordered_pair X Y)) (and (tptp.member U tptp.universal_class) (or (= U X) (= U Y))))))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.universal_class))) (let ((_let_8 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8))) (let ((_let_10 (tptp.member _let_9 tptp.universal_class))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9))) (let ((_let_12 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (= tptp.null_class _let_12))) (let ((_let_14 (or _let_7 _let_13))) (let ((_let_15 (not _let_7))) (let ((_let_16 (forall ((X $$unsorted)) (or (tptp.member X tptp.universal_class) (= tptp.null_class (tptp.singleton X)))))) (let ((_let_17 (not _let_14))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (or))) (let ((_let_20 (not _let_16))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_18) :args (_let_20))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_16))) (REFL :args (_let_17)) :args _let_19)) _let_18 :args (_let_17 true _let_16)))) (let ((_let_22 (and _let_10 _let_11))) (let ((_let_23 (tptp.member _let_9 _let_8))) (let ((_let_24 (= _let_23 _let_22))) (let ((_let_25 (_let_6))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (= tptp.null_class _let_8))) (let ((_let_28 (tptp.member _let_8 tptp.universal_class))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27 _let_23))) (let ((_let_31 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y) Y))))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or (not (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_32))) (let ((_let_34 (forall ((XF $$unsorted)) (or (not (tptp.function XF)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply XF Y) Y)))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (not _let_34))) (let ((_let_38 (_let_31))) (let ((_let_39 (= _let_12 _let_8))) (let ((_let_40 (not _let_27))) (let ((_let_41 (_let_4))) (let ((_let_42 (ASSUME :args _let_41))) (let ((_let_43 (not _let_13))) (let ((_let_44 (and _let_43 _let_39))) (let ((_let_45 (_let_43 _let_39))) (let ((_let_46 (ASSUME :args (_let_43)))) (let ((_let_47 (ASSUME :args (_let_39)))) (let ((_let_48 (_let_5))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_24)) :args ((or (not _let_23) _let_22 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_27 _let_23 (not _let_30)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.unordered_pair X Y)))) :args _let_48)) _let_49 :args (_let_28 false _let_5)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_44)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_46 _let_47) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.null_class)) (SYMM _let_47) :args (=)) (FALSE_INTRO _let_46))) :args _let_45)) :args _let_45)) :args (true _let_44)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_13))) (REFL :args ((not _let_39))) (REFL :args (_let_40)) :args _let_19)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_14 1)) _let_21 :args (_let_43 true _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.singleton X)))) :args _let_41)) _let_42 :args (_let_39 false _let_4)) :args (_let_40 true _let_13 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args (_let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y tptp.universal_class) false))))) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 1)) (CONG (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_19)) :args ((or _let_31 _let_33))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_36) :args (_let_37))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_34))) (REFL :args (_let_35)) :args _let_19)) _let_36 :args (_let_35 true _let_34)) :args (_let_31 true _let_33)) :args (_let_30 false _let_31)) :args (_let_23 false _let_28 true _let_27 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_26 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.member U (tptp.unordered_pair X Y))))) :args _let_25))) _let_26 :args (_let_24 false _let_6)) :args (_let_22 false _let_23 false _let_24)))) (let ((_let_51 (not _let_22))) (let ((_let_52 (ASSUME :args (_let_15)))) (let ((_let_53 (ASSUME :args (_let_11)))) (let ((_let_54 (ASSUME :args (_let_10)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_52 _let_53 _let_54) :args (_let_15 _let_10 _let_11)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_54)) (CONG (SYMM _let_53) (REFL :args (tptp.universal_class)) :args (APPLY_UF tptp.member)) (FALSE_INTRO _let_52))) :args (_let_15 _let_11 _let_10)) :args ((not (and _let_15 _let_10 _let_11)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_7))) (REFL :args ((not _let_10))) (REFL :args ((not _let_11))) :args _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_22 1)) :args ((or _let_11 _let_51))) _let_50 :args (_let_11 false _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_22 0)) :args ((or _let_10 _let_51))) _let_50 :args (_let_10 false _let_22)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_14 0)) _let_21 :args (_let_15 true _let_14)) :args (false false _let_11 false _let_10 true _let_7)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.subclass X Y) (forall ((U $$unsorted)) (=> (tptp.member U X) (tptp.member U Y))))) (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (forall ((X $$unsorted) (Y $$unsorted)) (= (= X Y) (and (tptp.subclass X Y) (tptp.subclass Y X)))) _let_6 _let_5 _let_4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) (and (tptp.member U X) (tptp.member V Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (=> (and (tptp.member X tptp.universal_class) (tptp.member Y tptp.universal_class)) (and (= (tptp.first _let_1) X) (= (tptp.second _let_1) Y))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.member Z (tptp.cross_product X Y)) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.member (tptp.ordered_pair X Y) tptp.element_relation) (and (tptp.member Y tptp.universal_class) (tptp.member X Y)))) (tptp.subclass tptp.element_relation _let_3) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.intersection X Y)) (and (tptp.member Z X) (tptp.member Z Y)))) (forall ((X $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.complement X)) (and (tptp.member Z tptp.universal_class) (not (tptp.member Z X))))) (forall ((X $$unsorted) (XR $$unsorted) (Y $$unsorted)) (= (tptp.restrict XR X Y) (tptp.intersection XR (tptp.cross_product X Y)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.null_class))) (forall ((X $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.domain_of X)) (and (tptp.member Z tptp.universal_class) (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class))))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (= (tptp.member _let_1 (tptp.rotate X)) (and (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (= (tptp.member _let_1 (tptp.flip X)) (and (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.union X Y)) (or (tptp.member Z X) (tptp.member Z Y)))) (forall ((X $$unsorted)) (= (tptp.successor X) (tptp.union X (tptp.singleton X)))) (tptp.subclass tptp.successor_relation _let_3) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation) (and (tptp.member X tptp.universal_class) (tptp.member Y tptp.universal_class) (= (tptp.successor X) Y)))) (forall ((Y $$unsorted)) (= (tptp.inverse Y) (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))))) (forall ((Z $$unsorted)) (= (tptp.range_of Z) (tptp.domain_of (tptp.inverse Z)))) (forall ((X $$unsorted) (XR $$unsorted)) (= (tptp.image XR X) (tptp.range_of (tptp.restrict XR X tptp.universal_class)))) (forall ((X $$unsorted)) (= (tptp.inductive X) (and (tptp.member tptp.null_class X) (tptp.subclass (tptp.image tptp.successor_relation X) X)))) (exists ((X $$unsorted)) (and (tptp.member X tptp.universal_class) (tptp.inductive X) (forall ((Y $$unsorted)) (=> (tptp.inductive Y) (tptp.subclass X Y))))) (forall ((U $$unsorted) (X $$unsorted)) (= (tptp.member U (tptp.sum_class X)) (exists ((Y $$unsorted)) (and (tptp.member U Y) (tptp.member Y X))))) (forall ((X $$unsorted)) (=> (tptp.member X tptp.universal_class) (tptp.member (tptp.sum_class X) tptp.universal_class))) (forall ((U $$unsorted) (X $$unsorted)) (= (tptp.member U (tptp.power_class X)) (and (tptp.member U tptp.universal_class) (tptp.subclass U X)))) (forall ((U $$unsorted)) (=> (tptp.member U tptp.universal_class) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((XR $$unsorted) (YR $$unsorted)) (tptp.subclass (tptp.compose YR XR) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((XR $$unsorted) (YR $$unsorted) (U $$unsorted) (V $$unsorted)) (= (tptp.member (tptp.ordered_pair U V) (tptp.compose YR XR)) (and (tptp.member U tptp.universal_class) (tptp.member V (tptp.image YR (tptp.image XR (tptp.singleton U))))))) (forall ((Z $$unsorted)) (= (tptp.member Z tptp.identity_relation) (exists ((X $$unsorted)) (and (tptp.member X tptp.universal_class) (= Z (tptp.ordered_pair X X)))))) (forall ((XF $$unsorted)) (= (tptp.function XF) (and (tptp.subclass XF (tptp.cross_product tptp.universal_class tptp.universal_class)) (tptp.subclass (tptp.compose XF (tptp.inverse XF)) tptp.identity_relation)))) (forall ((X $$unsorted) (XF $$unsorted)) (=> (and (tptp.member X tptp.universal_class) (tptp.function XF)) (tptp.member (tptp.image XF X) tptp.universal_class))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.disjoint X Y) (forall ((U $$unsorted)) (not (and (tptp.member U X) (tptp.member U Y)))))) (forall ((X $$unsorted)) (=> (not (= X tptp.null_class)) (exists ((U $$unsorted)) (and (tptp.member U tptp.universal_class) (tptp.member U X) (tptp.disjoint U X))))) (forall ((XF $$unsorted) (Y $$unsorted)) (= (tptp.apply XF Y) (tptp.sum_class (tptp.image XF (tptp.singleton Y))))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.77  )
% 0.21/0.77  % SZS output end Proof for SET082+1
% 0.21/0.77  % cvc5---1.0.5 exiting
% 0.56/0.77  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------