%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET074+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.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 14:37:25 EDT 2023

% Result   : Theorem 11.66s 12.00s
% Output   : Proof 11.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET074+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n006.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 09:07:52 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.19/0.48  %----Proving TF0_NAR, FOF, or CNF
% 11.66/12.00  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.PWWKBGtsGI/cvc5---1.0.5_25750.p...
% 11.66/12.00  ------- get file name : TPTP file name is SET074+1
% 11.66/12.00  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25750.smt2...
% 11.66/12.00  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.66/12.00  --- Run --no-e-matching --full-saturate-quant at 5...
% 11.66/12.00  % SZS status Theorem for SET074+1
% 11.66/12.00  % SZS output start Proof for SET074+1
% 11.66/12.00  (
% 11.66/12.00  (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.member Y tptp.universal_class) (not (= (tptp.unordered_pair X Y) tptp.null_class))))))) (let ((_let_2 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_3 (forall ((X $$unsorted)) (not (tptp.member X tptp.null_class))))) (let ((_let_4 (forall ((U $$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_5 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_6 (= tptp.null_class _let_5))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.null_class))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_5))) (let ((_let_9 (not _let_6))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.universal_class))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9))) (let ((_let_13 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))))) (let ((_let_14 (not _let_12))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_16 (or))) (let ((_let_17 (not _let_13))) (let ((_let_18 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_15) :args (_let_17))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_13))) (REFL :args (_let_14)) :args _let_16)) _let_15 :args (_let_14 true _let_13)))) (let ((_let_19 (REFL :args (_let_12)))) (let ((_let_20 (not _let_7))) (let ((_let_21 (_let_3))) (let ((_let_22 (ASSUME :args _let_21))) (let ((_let_23 (= _let_10 _let_8))) (let ((_let_24 (_let_4))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (ASSUME :args (_let_8)))) (let ((_let_27 (ASSUME :args (_let_6)))) (let ((_let_28 (ASSUME :args (_let_20)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_26 _let_27 _let_28) :args (_let_6 _let_20 _let_8)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_28)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (SYMM (SYMM _let_27)) :args (APPLY_UF tptp.member)) (TRUE_INTRO _let_26))) :args (_let_8 _let_6 _let_20)) :args ((not (and _let_6 _let_20 _let_8)) SB_LITERAL))) (CONG (REFL :args (_let_9)) (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_7))) (REFL :args ((not _let_8))) :args _let_16)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_23)) :args ((or _let_11 _let_8 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 0)) (CONG _let_19 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_16)) :args ((or _let_10 _let_12))) _let_18 :args (_let_10 true _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_24))) _let_25 :args (_let_23 false _let_4)) :args (_let_8 false _let_10 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_ENUM)) :args _let_21)) _let_22 :args (_let_20 false _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 1)) (CONG _let_19 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_6))) :args _let_16)) :args ((or _let_6 _let_12))) _let_18 :args (_let_6 true _let_12)) :args (false false _let_8 true _let_7 false _let_6)) :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_4 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (forall ((X $$unsorted)) (= (tptp.singleton X) (tptp.unordered_pair X X))) (forall ((X $$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_2) (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)))) _let_3 (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_2) (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))))) (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_1 true)))))))))))))))))))))))))))))))
% 11.66/12.00  )
% 11.66/12.00  % SZS output end Proof for SET074+1
% 11.66/12.00  % cvc5---1.0.5 exiting
% 11.66/12.00  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------