TSTP Solution File: SET093+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET093+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 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 14:37:36 EDT 2023
% Result : Theorem 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET093+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n006.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 : Sat Aug 26 10:01:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.56 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Vyi8SszYAE/cvc5---1.0.5_1990.p...
% 0.20/0.56 ------- get file name : TPTP file name is SET093+1
% 0.20/0.56 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1990.smt2...
% 0.20/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.56 % SZS status Theorem for SET093+1
% 0.20/0.56 % SZS output start Proof for SET093+1
% 0.20/0.56 (
% 0.20/0.56 (let ((_let_1 (not (forall ((X $$unsorted)) (=> (= (tptp.singleton (tptp.member_of X)) X) (tptp.member X tptp.universal_class)))))) (let ((_let_2 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_3 (forall ((X $$unsorted)) (= (tptp.singleton X) (tptp.unordered_pair X X))))) (let ((_let_4 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_5 (tptp.member_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_6 (tptp.singleton _let_5))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_6))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.universal_class))) (let ((_let_9 (tptp.unordered_pair _let_5 _let_5))) (let ((_let_10 (= _let_6 _let_9))) (let ((_let_11 (tptp.member _let_9 tptp.universal_class))) (let ((_let_12 (not _let_7))) (let ((_let_13 (or _let_12 _let_8))) (let ((_let_14 (forall ((X $$unsorted)) (or (not (= X (tptp.singleton (tptp.member_of X)))) (tptp.member X tptp.universal_class))))) (let ((_let_15 (not _let_13))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_17 (or))) (let ((_let_18 (not _let_14))) (let ((_let_19 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_16) :args (_let_18))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_14))) (REFL :args (_let_15)) :args _let_17)) _let_16 :args (_let_15 true _let_14)))) (let ((_let_20 (not _let_8))) (let ((_let_21 (_let_3))) (let ((_let_22 (ASSUME :args _let_21))) (let ((_let_23 (_let_4))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 (ASSUME :args (_let_11)))) (let ((_let_26 (ASSUME :args (_let_10)))) (let ((_let_27 (ASSUME :args (_let_7)))) (let ((_let_28 (ASSUME :args (_let_20)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_25 _let_26 _let_27 _let_28) :args (_let_7 _let_20 _let_10 _let_11)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_28)) (CONG (TRANS (SYMM (SYMM _let_27)) (SYMM (SYMM _let_26))) (REFL :args (tptp.universal_class)) :args (APPLY_UF tptp.member)) (TRUE_INTRO _let_25))) :args (_let_11 _let_10 _let_7 _let_20)) :args ((not (and _let_7 _let_20 _let_10 _let_11)) SB_LITERAL))) (CONG (REFL :args (_let_12)) (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_8))) (REFL :args ((not _let_10))) (REFL :args ((not _let_11))) :args _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_5 _let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.unordered_pair X Y)))) :args _let_23)) _let_24 :args (_let_11 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.singleton X)))) :args _let_21)) _let_22 :args (_let_10 false _let_3)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_13 1)) _let_19 :args (_let_20 true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 0)) (CONG (REFL :args (_let_13)) (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_7))) :args _let_17)) :args ((or _let_7 _let_13))) _let_19 :args (_let_7 true _let_13)) :args (false false _let_11 false _let_10 true _let_8 false _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 $$unsorted)) (= (= X Y) (and (tptp.subclass X Y) (tptp.subclass Y X)))) (forall ((U $$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_4 _let_3 (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)))))) (forall ((Y $$unsorted)) (=> (tptp.member Y tptp.universal_class) (tptp.member (tptp.member_of (tptp.singleton Y)) tptp.universal_class))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.singleton Y))) (=> (tptp.member Y tptp.universal_class) (= (tptp.singleton (tptp.member_of _let_1)) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.member_of X))) (or (tptp.member _let_1 tptp.universal_class) (= _let_1 X)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.member_of X))) (or (= (tptp.singleton _let_1) X) (= _let_1 X)))) _let_1 true)))))))))))))))))))))))))))))))
% 0.20/0.56 )
% 0.20/0.56 % SZS output end Proof for SET093+1
% 0.20/0.56 % cvc5---1.0.5 exiting
% 0.20/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------