TSTP Solution File: SET067^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET067^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 14:37:21 EDT 2023
% Result : Theorem 0.23s 0.53s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET067^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 09:31:45 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.50 %----Proving TH0
% 0.23/0.51 %------------------------------------------------------------------------------
% 0.23/0.51 % File : SET067^1 : TPTP v8.1.2. Released v3.6.0.
% 0.23/0.51 % Domain : Set Theory
% 0.23/0.51 % Problem : If one argument is a proper class, pair contains only the other
% 0.23/0.51 % Version : [BS+08] axioms.
% 0.23/0.51 % English :
% 0.23/0.51
% 0.23/0.51 % Refs : [BS+05] Benzmueller et al. (2005), Can a Higher-Order and a Fi
% 0.23/0.51 % : [BS+08] Benzmueller et al. (2008), Combined Reasoning by Autom
% 0.23/0.51 % : [Ben08] Benzmueller (2008), Email to Geoff Sutcliffe
% 0.23/0.51 % Source : [Ben08]
% 0.23/0.51 % Names :
% 0.23/0.51
% 0.23/0.51 % Status : Theorem
% 0.23/0.51 % Rating : 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.23/0.51 % Syntax : Number of formulae : 29 ( 14 unt; 14 typ; 14 def)
% 0.23/0.51 % Number of atoms : 38 ( 18 equ; 0 cnn)
% 0.23/0.51 % Maximal formula atoms : 3 ( 2 avg)
% 0.23/0.51 % Number of connectives : 42 ( 5 ~; 3 |; 6 &; 27 @)
% 0.23/0.51 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.23/0.51 % Maximal formula depth : 7 ( 1 avg)
% 0.23/0.51 % Number of types : 2 ( 0 usr)
% 0.23/0.51 % Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% 0.23/0.51 % Number of symbols : 18 ( 16 usr; 3 con; 0-3 aty)
% 0.23/0.51 % Number of variables : 37 ( 32 ^; 3 !; 2 ?; 37 :)
% 0.23/0.51 % SPC : TH0_THM_EQU_NAR
% 0.23/0.51
% 0.23/0.51 % Comments :
% 0.23/0.51 %------------------------------------------------------------------------------
% 0.23/0.51 %----Basic set theory definitions
% 0.23/0.51 %------------------------------------------------------------------------------
% 0.23/0.51 thf(in_decl,type,
% 0.23/0.51 in: $i > ( $i > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(in,definition,
% 0.23/0.51 ( in
% 0.23/0.51 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(is_a_decl,type,
% 0.23/0.51 is_a: $i > ( $i > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(is_a,definition,
% 0.23/0.51 ( is_a
% 0.23/0.51 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(emptyset_decl,type,
% 0.23/0.51 emptyset: $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(emptyset,definition,
% 0.23/0.51 ( emptyset
% 0.23/0.51 = ( ^ [X: $i] : $false ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(unord_pair_decl,type,
% 0.23/0.51 unord_pair: $i > $i > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(unord_pair,definition,
% 0.23/0.51 ( unord_pair
% 0.23/0.51 = ( ^ [X: $i,Y: $i,U: $i] :
% 0.23/0.51 ( ( U = X )
% 0.23/0.51 | ( U = Y ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(singleton_decl,type,
% 0.23/0.51 singleton: $i > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(singleton,definition,
% 0.23/0.51 ( singleton
% 0.23/0.51 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(union_decl,type,
% 0.23/0.51 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(union,definition,
% 0.23/0.51 ( union
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.51 ( ( X @ U )
% 0.23/0.51 | ( Y @ U ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(excl_union_decl,type,
% 0.23/0.51 excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(excl_union,definition,
% 0.23/0.51 ( excl_union
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.51 ( ( ( X @ U )
% 0.23/0.51 & ~ ( Y @ U ) )
% 0.23/0.51 | ( ~ ( X @ U )
% 0.23/0.51 & ( Y @ U ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(intersection_decl,type,
% 0.23/0.51 intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(intersection,definition,
% 0.23/0.51 ( intersection
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.51 ( ( X @ U )
% 0.23/0.51 & ( Y @ U ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(setminus_decl,type,
% 0.23/0.51 setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(setminus,definition,
% 0.23/0.51 ( setminus
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.51 ( ( X @ U )
% 0.23/0.51 & ~ ( Y @ U ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(complement_decl,type,
% 0.23/0.51 complement: ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(complement,definition,
% 0.23/0.51 ( complement
% 0.23/0.51 = ( ^ [X: $i > $o,U: $i] :
% 0.23/0.51 ~ ( X @ U ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(disjoint_decl,type,
% 0.23/0.51 disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(disjoint,definition,
% 0.23/0.51 ( disjoint
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.23/0.51 ( ( intersection @ X @ Y )
% 0.23/0.51 = emptyset ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(subset_decl,type,
% 0.23/0.51 subset: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(subset,definition,
% 0.23/0.51 ( subset
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.23/0.51 ! [U: $i] :
% 0.23/0.51 ( ( X @ U )
% 0.23/0.51 => ( Y @ U ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(meets_decl,type,
% 0.23/0.51 meets: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(meets,definition,
% 0.23/0.51 ( meets
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.23/0.51 ? [U: $i] :
% 0.23/0.51 ( ( X @ U )
% 0.23/0.51 & ( Y @ U ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(misses_decl,type,
% 0.23/0.51 misses: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(misses,definition,
% 0.23/0.53 ( misses
% 0.23/0.53 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.23/0.53 ~ ? [U: $i] :
% 0.23/0.53 ( ( X @ U )
% 0.23/0.53 & ( Y @ U ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 thf(thm,conjecture,
% 0.23/0.53 ! [X: $i,Y: $i] : ( subset @ ( unord_pair @ X @ Y ) @ ( unord_pair @ Y @ X ) ) ).
% 0.23/0.53
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.kGANavALxL/cvc5---1.0.5_28855.p...
% 0.23/0.53 (declare-sort $$unsorted 0)
% 0.23/0.53 (declare-fun tptp.in ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.23/0.53 (assert (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.23/0.53 (declare-fun tptp.is_a ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.23/0.53 (assert (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.23/0.53 (declare-fun tptp.emptyset ($$unsorted) Bool)
% 0.23/0.53 (assert (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.23/0.53 (declare-fun tptp.unord_pair ($$unsorted $$unsorted $$unsorted) Bool)
% 0.23/0.53 (assert (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))
% 0.23/0.53 (declare-fun tptp.singleton ($$unsorted $$unsorted) Bool)
% 0.23/0.53 (assert (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.23/0.53 (declare-fun tptp.union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.53 (assert (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.23/0.53 (declare-fun tptp.excl_union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.53 (assert (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (let ((_let_1 (@ Y U))) (let ((_let_2 (@ X U))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))
% 0.23/0.53 (declare-fun tptp.intersection ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.53 (assert (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.23/0.53 (declare-fun tptp.setminus ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.53 (assert (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))
% 0.23/0.53 (declare-fun tptp.complement ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.53 (assert (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.23/0.53 (declare-fun tptp.disjoint ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.23/0.53 (assert (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))
% 0.23/0.53 (declare-fun tptp.subset ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.23/0.53 (assert (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))
% 0.23/0.53 (declare-fun tptp.meets ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.23/0.53 (assert (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))
% 0.23/0.53 (declare-fun tptp.misses ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.23/0.53 (assert (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))
% 0.23/0.53 (assert (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.unord_pair X) Y)) (@ (@ tptp.unord_pair Y) X)))))
% 0.23/0.53 (set-info :filename cvc5---1.0.5_28855)
% 0.23/0.53 (check-sat-assuming ( true ))
% 0.23/0.53 ------- get file name : TPTP file name is SET067^1
% 0.23/0.53 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28855.smt2...
% 0.23/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.53 % SZS status Theorem for SET067^1
% 0.23/0.53 % SZS output start Proof for SET067^1
% 0.23/0.53 (
% 0.23/0.53 (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.unord_pair X) Y)) (@ (@ tptp.unord_pair Y) X)))))) (let ((_let_2 (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) (let ((_let_3 (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (let ((_let_4 (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))) (let ((_let_5 (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))) (let ((_let_6 (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_7 (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))) (let ((_let_8 (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_9 (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (let ((_let_1 (@ Y U))) (let ((_let_2 (@ X U))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))) (let ((_let_10 (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_11 (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))) (let ((_let_12 (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))) (let ((_let_13 (= tptp.emptyset (lambda ((X $$unsorted)) false)))) (let ((_let_14 (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) (let ((_let_15 (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) (let ((_let_16 (ASSUME :args (_let_15)))) (let ((_let_17 (ASSUME :args (_let_14)))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (ASSUME :args (_let_10)))) (let ((_let_22 (ASSUME :args (_let_9)))) (let ((_let_23 (ASSUME :args (_let_8)))) (let ((_let_24 (ASSUME :args (_let_7)))) (let ((_let_25 (ASSUME :args (_let_6)))) (SCOPE (SCOPE (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16) :args ((= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) SB_DEFAULT SBA_FIXPOINT))) _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16) :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))
% 0.23/0.53 )
% 0.23/0.53 % SZS output end Proof for SET067^1
% 0.23/0.53 % cvc5---1.0.5 exiting
% 0.23/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------