TSTP Solution File: SET027+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET027+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 14:36:56 EDT 2023
% Result : Theorem 0.22s 0.59s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET027+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n014.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 : Sat Aug 26 13:40:17 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.59 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Uj16D7H2ao/cvc5---1.0.5_25643.p...
% 0.22/0.59 ------- get file name : TPTP file name is SET027+1
% 0.22/0.59 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25643.smt2...
% 0.22/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.59 % SZS status Theorem for SET027+1
% 0.22/0.59 % SZS output start Proof for SET027+1
% 0.22/0.59 (
% 0.22/0.59 (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.subclass X Y) (tptp.subclass Y Z)) (tptp.subclass X Z)))))) (let ((_let_2 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.subclass X Y) (forall ((U $$unsorted)) (=> (tptp.member U X) (tptp.member U Y))))))) (let ((_let_4 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_5 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_6 (not _let_5))) (let ((_let_7 (or _let_6 _let_4))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_4))) (let ((_let_11 (forall ((U $$unsorted)) (or (not (tptp.member U SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.member U SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_12 (not _let_10))) (let ((_let_13 (tptp.subclass SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (= _let_13 _let_11))) (let ((_let_15 (not _let_11))) (let ((_let_16 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.subclass X Y) (forall ((U $$unsorted)) (or (not (tptp.member U X)) (tptp.member U Y))))))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_18 (_let_16))) (let ((_let_19 ((tptp.subclass X Y)))) (let ((_let_20 (tptp.subclass SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.subclass SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_13))) (let ((_let_25 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y Z)) (tptp.subclass X Z))))) (let ((_let_26 (not _let_24))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (or))) (let ((_let_29 (not _let_25))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_27) :args (_let_29))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_25))) (REFL :args (_let_26)) :args _let_28)) _let_27 :args (_let_26 true _let_25)))) (let ((_let_31 (_let_15))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_31)) :args _let_31)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_11))) (REFL :args (_let_12)) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_14)) :args ((or _let_13 _let_15 (not _let_14)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 2)) _let_30 :args ((not _let_13) true _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_19)) :args _let_18)) _let_17 :args (_let_14 false _let_16)) :args (_let_15 true _let_13 false _let_14)) :args (_let_12 true _let_11)))) (let ((_let_33 (forall ((U $$unsorted)) (or (not (tptp.member U SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.member U SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_34 (= _let_20 _let_33))) (let ((_let_35 (REFL :args (_let_24)))) (let ((_let_36 (_let_33))) (let ((_let_37 (or _let_9 _let_5))) (let ((_let_38 (forall ((U $$unsorted)) (or (not (tptp.member U SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.member U SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_39 (= _let_22 _let_38))) (let ((_let_40 (_let_38))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_7)) :args ((or _let_4 _let_6 (not _let_7)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_9 _let_5 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_10 0)) (CONG (REFL :args (_let_10)) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_28)) :args ((or _let_8 _let_10))) _let_32 :args (_let_8 true _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_40) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member U SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) :args _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or _let_23 _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_28)) :args ((or _let_22 _let_24))) _let_30 :args (_let_22 true _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_19)) :args _let_18)) _let_17 :args (_let_39 false _let_16)) :args (_let_38 false _let_22 false _let_39)) :args (_let_37 false _let_38)) :args (_let_5 false _let_8 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_36) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member U SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) true))))) :args _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_34)) :args ((or _let_21 _let_33 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 1)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_28)) :args ((or _let_20 _let_24))) _let_30 :args (_let_20 true _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_19)) :args _let_18)) _let_17 :args (_let_34 false _let_16)) :args (_let_33 false _let_20 false _let_34)) :args (_let_7 false _let_33)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_10 1)) _let_32 :args ((not _let_4) true _let_10)) :args (false false _let_5 false _let_7 true _let_4)) :args (_let_3 (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)))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.member U (tptp.unordered_pair X Y)) (and (tptp.member U tptp.universal_class) (or (= U X) (= U Y))))) (forall ((X $$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 $$unsorted)) (= (tptp.restrict XR X Y) (tptp.intersection XR (tptp.cross_product X Y)))) (forall ((X $$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_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)))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.59 )
% 0.22/0.59 % SZS output end Proof for SET027+1
% 0.22/0.59 % cvc5---1.0.5 exiting
% 0.22/0.60 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------