%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET103+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 14:37:42 EDT 2023

% Result   : Theorem 1.86s 2.28s
% Output   : Proof 1.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET103+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n013.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat Aug 26 13:04:32 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 1.86/2.28  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.pKKz55Jt4v/cvc5---1.0.5_10144.p...
% 1.86/2.28  ------- get file name : TPTP file name is SET103+1
% 1.86/2.28  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10144.smt2...
% 1.86/2.28  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.86/2.28  % SZS status Theorem for SET103+1
% 1.86/2.28  % SZS output start Proof for SET103+1
% 1.86/2.28  (
% 1.86/2.28  (let ((_let_1 (forall ((X $$unsorted) (Y $$unsorted)) (or (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X tptp.null_class)) (tptp.ordered_pair X Y)) (tptp.member Y tptp.universal_class))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (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_4 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))))))) (let ((_let_6 (forall ((X $$unsorted)) (= (tptp.singleton X) (tptp.unordered_pair X X))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_8 (forall ((U $$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_9 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_10 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (= (tptp.unordered_pair _let_10 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.null_class)) _let_9))) (let ((_let_12 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (= _let_9 (tptp.unordered_pair _let_10 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12))))) (let ((_let_14 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (= _let_12 _let_14))) (let ((_let_16 (= tptp.null_class _let_14))) (let ((_let_17 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.universal_class))) (let ((_let_18 (or _let_11 _let_17))) (let ((_let_19 (not _let_18))) (let ((_let_20 (_let_2))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (or))) (let ((_let_23 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_21) :args _let_20)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_19)) :args _let_22)) _let_21 :args (_let_19 true _let_1)))) (let ((_let_24 (_let_5))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (_let_6))) (let ((_let_27 (ASSUME :args _let_26))) (let ((_let_28 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14))) (let ((_let_29 (tptp.member _let_28 _let_14))) (let ((_let_30 (tptp.member _let_14 tptp.universal_class))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_16 _let_29))) (let ((_let_33 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y) Y))))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or (not (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_34))) (let ((_let_36 (forall ((XF $$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_37 (not _let_35))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (not _let_36))) (let ((_let_40 (_let_33))) (let ((_let_41 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_28))) (let ((_let_42 (tptp.member _let_28 tptp.universal_class))) (let ((_let_43 (and _let_42 _let_41))) (let ((_let_44 (= _let_29 _let_43))) (let ((_let_45 (not _let_29))) (let ((_let_46 (_let_8))) (let ((_let_47 (ASSUME :args _let_46))) (let ((_let_48 (not _let_43))) (let ((_let_49 (not _let_17))) (let ((_let_50 (ASSUME :args (_let_49)))) (let ((_let_51 (ASSUME :args (_let_41)))) (let ((_let_52 (ASSUME :args (_let_42)))) (let ((_let_53 (_let_7))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 (and _let_13 _let_15 _let_16))) (let ((_let_56 (_let_13 _let_15 _let_16))) (let ((_let_57 (ASSUME :args (_let_13)))) (let ((_let_58 (APPLY_UF tptp.unordered_pair))) (let ((_let_59 (ASSUME :args (_let_15)))) (let ((_let_60 (ASSUME :args (_let_16)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_55)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_57 _let_59 _let_60) (SCOPE (TRANS (CONG (REFL :args (_let_10)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (TRANS (SYMM (SYMM _let_60)) (SYMM _let_59)) :args _let_58) :args _let_58) (SYMM _let_57)) :args _let_56)) :args _let_56)) :args (true _let_55)) :args ((or _let_11 (not _let_13) (not _let_15) (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_16 _let_29 (not _let_32)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.unordered_pair X Y)))) :args _let_53)) _let_54 :args (_let_30 false _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_44)) :args ((or _let_45 _let_43 (not _let_44)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_50 _let_51 _let_52) :args (_let_49 _let_42 _let_41)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_52)) (CONG (SYMM _let_51) (REFL :args (tptp.universal_class)) :args (APPLY_UF tptp.member)) (FALSE_INTRO _let_50))) :args (_let_49 _let_41 _let_42)) :args ((not (and _let_49 _let_42 _let_41)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_17))) (REFL :args ((not _let_42))) (REFL :args ((not _let_41))) :args _let_22)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_18 1)) _let_23 :args (_let_49 true _let_18)) (REORDERING (CNF_AND_POS :args (_let_43 1)) :args ((or _let_41 _let_48))) (REORDERING (CNF_AND_POS :args (_let_43 0)) :args ((or _let_42 _let_48))) :args (_let_48 true _let_17 false _let_41 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.member U (tptp.unordered_pair X Y))))) :args _let_46))) _let_47 :args (_let_44 false _let_8)) :args (_let_45 true _let_43 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_40) :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y tptp.universal_class) false))))) :args _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 1)) (CONG (REFL :args (_let_35)) (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_22)) :args ((or _let_33 _let_35))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_38) :args (_let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_36))) (REFL :args (_let_37)) :args _let_22)) _let_38 :args (_let_37 true _let_36)) :args (_let_33 true _let_35)) :args (_let_32 false _let_33)) :args (_let_16 false _let_30 true _let_29 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.singleton X)))) :args _let_26)) _let_27 :args (_let_15 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordered_pair X Y)))) :args _let_24)) _let_25 :args (_let_13 false _let_5)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_18 0)) _let_23 :args ((not _let_11) true _let_18)) :args (false false _let_16 false _let_15 false _let_13 true _let_11)) :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 $$unsorted)) (= (= X Y) (and (tptp.subclass X Y) (tptp.subclass Y X)))) _let_8 _let_7 _let_6 _let_5 (forall ((U $$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_4) (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 $$unsorted)) (= (tptp.successor X) (tptp.union X (tptp.singleton X)))) (tptp.subclass tptp.successor_relation _let_4) (forall ((X $$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_3 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.86/2.29  )
% 1.86/2.29  % SZS output end Proof for SET103+1
% 1.86/2.29  % cvc5---1.0.5 exiting
% 1.86/2.30  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------