TSTP Solution File: SET926^20 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET926^20 : TPTP v8.1.2. Released v8.1.0.
% 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 14:41:03 EDT 2023
% Result : Theorem 0.23s 0.60s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET926^20 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n018.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 08:29:00 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.23/0.50 %----Proving TH0
% 0.23/0.51 %------------------------------------------------------------------------------
% 0.23/0.51 % File : SET926^20 : TPTP v8.1.2. Released v8.1.0.
% 0.23/0.51 % Domain : Set Theory
% 0.23/0.51 % Problem : TPTP problem SET926+1.p with axiomatized equality
% 0.23/0.51 % Version : [BP13] axioms.
% 0.23/0.51 % English :
% 0.23/0.51
% 0.23/0.51 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.23/0.51 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.23/0.51 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.23/0.51 % Source : [TPTP]
% 0.23/0.51 % Names : SET926+1 [QMLTP]
% 0.23/0.51
% 0.23/0.51 % Status : Theorem
% 0.23/0.51 % Rating : 0.23 v8.1.0
% 0.23/0.51 % Syntax : Number of formulae : 49 ( 12 unt; 20 typ; 10 def)
% 0.23/0.51 % Number of atoms : 128 ( 10 equ; 0 cnn)
% 0.23/0.51 % Maximal formula atoms : 9 ( 4 avg)
% 0.23/0.51 % Number of connectives : 211 ( 1 ~; 1 |; 4 &; 200 @)
% 0.23/0.51 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.23/0.51 % Maximal formula depth : 14 ( 7 avg)
% 0.23/0.51 % Number of types : 3 ( 1 usr)
% 0.23/0.51 % Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% 0.23/0.51 % Number of symbols : 20 ( 19 usr; 2 con; 0-3 aty)
% 0.23/0.51 % Number of variables : 65 ( 55 ^; 7 !; 3 ?; 65 :)
% 0.23/0.51 % SPC : TH0_THM_EQU_NAR
% 0.23/0.51
% 0.23/0.51 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.23/0.51 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.23/0.51 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.23/0.51 % $modal == [$constants == $rigid,$quantification == $decreasing,
% 0.23/0.51 % $modalities == $modal_system_T].
% 0.23/0.51 %------------------------------------------------------------------------------
% 0.23/0.51 thf(mworld,type,
% 0.23/0.51 mworld: $tType ).
% 0.23/0.51
% 0.23/0.51 thf(mrel_type,type,
% 0.23/0.51 mrel: mworld > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mactual_type,type,
% 0.23/0.51 mactual: mworld ).
% 0.23/0.51
% 0.23/0.51 thf(mlocal_type,type,
% 0.23/0.51 mlocal: ( mworld > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mlocal_def,definition,
% 0.23/0.51 ( mlocal
% 0.23/0.51 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mnot_type,type,
% 0.23/0.51 mnot: ( mworld > $o ) > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mand_type,type,
% 0.23/0.51 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mor_type,type,
% 0.23/0.51 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mimplies_type,type,
% 0.23/0.51 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mequiv_type,type,
% 0.23/0.51 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mnot_def,definition,
% 0.23/0.51 ( mnot
% 0.23/0.51 = ( ^ [A: mworld > $o,W: mworld] :
% 0.23/0.51 ~ ( A @ W ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mand_def,definition,
% 0.23/0.51 ( mand
% 0.23/0.51 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.23/0.51 ( ( A @ W )
% 0.23/0.51 & ( B @ W ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mor_def,definition,
% 0.23/0.51 ( mor
% 0.23/0.51 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.23/0.51 ( ( A @ W )
% 0.23/0.51 | ( B @ W ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mimplies_def,definition,
% 0.23/0.51 ( mimplies
% 0.23/0.51 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.23/0.51 ( ( A @ W )
% 0.23/0.51 => ( B @ W ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mequiv_def,definition,
% 0.23/0.51 ( mequiv
% 0.23/0.51 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.23/0.51 ( ( A @ W )
% 0.23/0.51 <=> ( B @ W ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mbox_type,type,
% 0.23/0.51 mbox: ( mworld > $o ) > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mbox_def,definition,
% 0.23/0.51 ( mbox
% 0.23/0.51 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.23/0.51 ! [V: mworld] :
% 0.23/0.51 ( ( mrel @ W @ V )
% 0.23/0.51 => ( Phi @ V ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mdia_type,type,
% 0.23/0.51 mdia: ( mworld > $o ) > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mdia_def,definition,
% 0.23/0.51 ( mdia
% 0.23/0.51 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.23/0.51 ? [V: mworld] :
% 0.23/0.51 ( ( mrel @ W @ V )
% 0.23/0.51 & ( Phi @ V ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mrel_reflexive,axiom,
% 0.23/0.51 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.23/0.51
% 0.23/0.51 thf(eiw_di_type,type,
% 0.23/0.51 eiw_di: $i > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(eiw_di_nonempty,axiom,
% 0.23/0.51 ! [W: mworld] :
% 0.23/0.51 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.23/0.51
% 0.23/0.51 thf(eiw_di_decr,axiom,
% 0.23/0.51 ! [W: mworld,V: mworld,X: $i] :
% 0.23/0.51 ( ( ( eiw_di @ X @ W )
% 0.23/0.51 & ( mrel @ V @ W ) )
% 0.23/0.51 => ( eiw_di @ X @ V ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mforall_di_type,type,
% 0.23/0.51 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mforall_di_def,definition,
% 0.23/0.51 ( mforall_di
% 0.23/0.51 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.23/0.51 ! [X: $i] :
% 0.23/0.51 ( ( eiw_di @ X @ W )
% 0.23/0.51 => ( A @ X @ W ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(mexists_di_type,type,
% 0.23/0.51 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(mexists_di_def,definition,
% 0.23/0.51 ( mexists_di
% 0.23/0.51 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.23/0.51 ? [X: $i] :
% 0.23/0.51 ( ( eiw_di @ X @ W )
% 0.23/0.51 & ( A @ X @ W ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(empty_set_decl,type,
% 0.23/0.51 empty_set: $i ).
% 0.23/0.51
% 0.23/0.51 thf(qmltpeq_decl,type,
% 0.23/0.51 qmltpeq: $i > $i > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(in_decl,type,
% 0.23/0.51 in: $i > $i > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(empty_decl,type,
% 0.23/0.51 empty: $i > mworld > $o ).
% 0.23/0.51
% 0.23/0.51 thf(singleton_decl,type,
% 0.23/0.51 singleton: $i > $i ).
% 0.23/0.51
% 0.23/0.51 thf(set_difference_decl,type,
% 0.23/0.51 set_difference: $i > $i > $i ).
% 0.23/0.51
% 0.23/0.51 thf(reflexivity,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(symmetry,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [X: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(transitivity,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [X: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [Y: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(set_difference_substitution_1,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(set_difference_substitution_2,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(singleton_substitution_1,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(empty_substitution_1,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(in_substitution_1,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(in_substitution_2,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(antisymmetry_r2_hidden,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(fc1_xboole_0,axiom,
% 0.23/0.51 mlocal @ ( empty @ empty_set ) ).
% 0.23/0.51
% 0.23/0.51 thf(l34_zfmisc_1,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(l36_zfmisc_1,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(rc1_xboole_0,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mexists_di
% 0.23/0.51 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(rc2_xboole_0,axiom,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mexists_di
% 0.23/0.51 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(t69_zfmisc_1,conjecture,
% 0.23/0.51 ( mlocal
% 0.23/0.51 @ ( mforall_di
% 0.23/0.51 @ ^ [A: $i] :
% 0.23/0.51 ( mforall_di
% 0.23/0.51 @ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.8URyjKBA4I/cvc5---1.0.5_9494.p...
% 0.23/0.52 (declare-sort $$unsorted 0)
% 0.23/0.52 (declare-sort tptp.mworld 0)
% 0.23/0.52 (declare-fun tptp.mrel (tptp.mworld tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mactual () tptp.mworld)
% 0.23/0.52 (declare-fun tptp.mlocal ((-> tptp.mworld Bool)) Bool)
% 0.23/0.52 (assert (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))
% 0.23/0.52 (declare-fun tptp.mnot ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mand ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mor ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mimplies ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mequiv ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (assert (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))
% 0.23/0.52 (assert (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))
% 0.23/0.52 (assert (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))
% 0.23/0.52 (assert (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))
% 0.23/0.52 (assert (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))
% 0.23/0.52 (declare-fun tptp.mbox ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (assert (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.23/0.52 (declare-fun tptp.mdia ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (assert (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.23/0.52 (assert (forall ((W tptp.mworld)) (@ (@ tptp.mrel W) W)))
% 0.23/0.52 (declare-fun tptp.eiw_di ($$unsorted tptp.mworld) Bool)
% 0.23/0.52 (assert (forall ((W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ tptp.eiw_di X) W))))
% 0.23/0.52 (assert (forall ((W tptp.mworld) (V tptp.mworld) (X $$unsorted)) (let ((_let_1 (@ tptp.eiw_di X))) (=> (and (@ _let_1 W) (@ (@ tptp.mrel V) W)) (@ _let_1 V)))))
% 0.23/0.52 (declare-fun tptp.mforall_di ((-> $$unsorted tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (assert (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (=> (@ (@ tptp.eiw_di X) W) (@ (@ A X) W))))))
% 0.23/0.52 (declare-fun tptp.mexists_di ((-> $$unsorted tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (assert (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (and (@ (@ tptp.eiw_di X) W) (@ (@ A X) W))))))
% 0.23/0.52 (declare-fun tptp.empty_set () $$unsorted)
% 0.23/0.52 (declare-fun tptp.qmltpeq ($$unsorted $$unsorted tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.in ($$unsorted $$unsorted tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.empty ($$unsorted tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.singleton ($$unsorted) $$unsorted)
% 0.23/0.52 (declare-fun tptp.set_difference ($$unsorted $$unsorted) $$unsorted)
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.qmltpeq X) X) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq X) Y)) (@ (@ tptp.qmltpeq Y) X)) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Z $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ _let_1 Y)) (@ (@ tptp.qmltpeq Y) Z))) (@ _let_1 Z)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference A) C)) (@ (@ tptp.set_difference B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.set_difference C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.singleton A)) (@ tptp.singleton B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ tptp.empty A))) (@ tptp.empty B)) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.in A) C))) (@ (@ tptp.in B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.in C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.in A) B)) (@ tptp.mnot (@ (@ tptp.in B) A))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.empty tptp.empty_set)))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.singleton A))) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference _let_1) B)) _let_1)) (@ tptp.mnot (@ (@ tptp.in A) B))) __flatten_var_0)))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton A)) B)) tptp.empty_set)) (@ (@ tptp.in A) B)) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mexists_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.empty A) __flatten_var_0)))))
% 0.23/0.52 (assert (@ tptp.mlocal (@ tptp.mexists_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mnot (@ tptp.empty A)) __flatten_var_0)))))
% 0.23/0.52 (assert (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.singleton A))) (let ((_let_2 (@ tptp.qmltpeq (@ (@ tptp.set_difference _let_1) B)))) (@ (@ (@ tptp.mor (@ _let_2 tptp.empty_set)) (@ _let_2 _let_1)) __flatten_var_0))))) __flatten_var_0))))))
% 0.23/0.52 (set-info :filename cvc5---1.0.5_9494)
% 0.23/0.60 (check-sat-assuming ( true ))
% 0.23/0.60 ------- get file name : TPTP file name is SET926^20
% 0.23/0.60 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9494.smt2...
% 0.23/0.60 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.60 % SZS status Theorem for SET926^20
% 0.23/0.60 % SZS output start Proof for SET926^20
% 0.23/0.60 (
% 0.23/0.60 (let ((_let_1 (@ tptp.mlocal (@ tptp.mexists_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mnot (@ tptp.empty A)) __flatten_var_0)))))) (let ((_let_2 (@ tptp.mlocal (@ tptp.mexists_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.empty A) __flatten_var_0)))))) (let ((_let_3 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ tptp.empty A))) (@ tptp.empty B)) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_4 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.qmltpeq X) X) __flatten_var_0)))))) (let ((_let_5 (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (and (@ (@ tptp.eiw_di X) W) (@ (@ A X) W))))))) (let ((_let_6 (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (=> (@ (@ tptp.eiw_di X) W) (@ (@ A X) W))))))) (let ((_let_7 (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))) (let ((_let_8 (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))) (let ((_let_9 (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))) (let ((_let_10 (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))) (let ((_let_11 (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))) (let ((_let_12 (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))) (let ((_let_13 (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))) (let ((_let_14 (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))) (let ((_let_15 (ho_4 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) tptp.mactual))) (let ((_let_16 (ho_4 (ho_6 k_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) tptp.mactual))) (let ((_let_17 (ho_4 (ho_6 (ho_8 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) tptp.mactual))) (let ((_let_18 (not _let_17))) (let ((_let_19 (not _let_15))) (let ((_let_20 (or _let_19 _let_18 _let_16))) (let ((_let_21 (or _let_19 _let_16))) (let ((_let_22 (forall ((X $$unsorted)) (or (not (ho_4 (ho_6 k_5 X) tptp.mactual)) (ho_4 (ho_6 k_13 X) tptp.mactual))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (not _let_22))) (let ((_let_25 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_9)) (ASSUME :args (_let_10)) (ASSUME :args (_let_11)) (ASSUME :args (_let_12)) (ASSUME :args (_let_13)) (ASSUME :args (_let_14))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_25 :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X $$unsorted)) (or (not (@ (@ tptp.eiw_di X) tptp.mactual)) (@ (@ tptp.empty X) tptp.mactual)))) _let_24))))))) (let ((_let_27 (or))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_24))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_22))) (REFL :args (_let_23)) :args _let_27)) _let_26 :args (_let_23 true _let_22)))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG (REFL :args (_let_21)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_15))) :args _let_27)) :args ((or _let_15 _let_21))) _let_28 :args (_let_15 true _let_21)))) (let ((_let_30 (forall ((BOUND_VARIABLE_2127 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_2127) tptp.mactual)) (not (ho_4 (ho_6 (ho_8 k_7 BOUND_VARIABLE_2127) BOUND_VARIABLE_2127) tptp.mactual)) (ho_4 (ho_6 k_13 BOUND_VARIABLE_2127) tptp.mactual))))) (let ((_let_31 (forall ((X $$unsorted)) (or (not (ho_4 (ho_6 k_5 X) tptp.mactual)) (not (ho_4 (ho_6 k_13 X) tptp.mactual)))))) (let ((_let_32 (forall ((X $$unsorted)) (or (not (ho_4 (ho_6 k_5 X) tptp.mactual)) (not (ho_4 (ho_6 k_13 X) tptp.mactual)))))) (let ((_let_33 (not _let_31))) (let ((_let_34 (_let_30))) (let ((_let_35 (or _let_19 _let_17))) (let ((_let_36 (forall ((X $$unsorted)) (or (not (ho_4 (ho_6 k_5 X) tptp.mactual)) (ho_4 (ho_6 (ho_8 k_7 X) X) tptp.mactual))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_25 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X $$unsorted)) (or (not (@ (@ tptp.eiw_di X) tptp.mactual)) (@ (@ (@ tptp.qmltpeq X) X) tptp.mactual))) _let_36))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_16 _let_18 (not _let_20)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_19 _let_17 (not _let_35)))) _let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_5 X)))) :args (_let_36))) _let_37 :args (_let_35 false _let_36)) :args (_let_17 false _let_15 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_34) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_5 BOUND_VARIABLE_2127)))) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_25 :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (forall ((BOUND_VARIABLE_2127 $$unsorted)) (or (not (@ (@ tptp.eiw_di BOUND_VARIABLE_2127) tptp.mactual)) (not (@ (@ (@ tptp.qmltpeq BOUND_VARIABLE_2127) BOUND_VARIABLE_2127) tptp.mactual)) (@ (@ tptp.empty BOUND_VARIABLE_2127) tptp.mactual))) (forall ((X $$unsorted)) (or (not (@ (@ tptp.eiw_di X) tptp.mactual)) (not (@ (@ tptp.empty X) tptp.mactual))))) (or _let_30 _let_31)))))) :args ((or _let_31 _let_30))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_31 (= X X)))) :args ((or _let_32 _let_33))) (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_25 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X $$unsorted)) (or (not (@ (@ tptp.eiw_di X) tptp.mactual)) (not (@ (@ tptp.empty X) tptp.mactual))))) (not _let_32)))))) :args (_let_33 true _let_32)) :args (_let_30 true _let_31)) :args (_let_20 false _let_30)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 1)) _let_28 :args ((not _let_16) true _let_21)) _let_29 :args (false false _let_17 false _let_20 true _let_16 false _let_15)) :args (_let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 (forall ((W tptp.mworld)) (@ (@ tptp.mrel W) W)) (forall ((W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ tptp.eiw_di X) W))) (forall ((W tptp.mworld) (V tptp.mworld) (X $$unsorted)) (let ((_let_1 (@ tptp.eiw_di X))) (=> (and (@ _let_1 W) (@ (@ tptp.mrel V) W)) (@ _let_1 V)))) _let_6 _let_5 _let_4 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq X) Y)) (@ (@ tptp.qmltpeq Y) X)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Z $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ _let_1 Y)) (@ (@ tptp.qmltpeq Y) Z))) (@ _let_1 Z)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference A) C)) (@ (@ tptp.set_difference B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.set_difference C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.singleton A)) (@ tptp.singleton B))) __flatten_var_0))) __flatten_var_0)))) _let_3 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.in A) C))) (@ (@ tptp.in B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.in C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.in A) B)) (@ tptp.mnot (@ (@ tptp.in B) A))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.empty tptp.empty_set)) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.singleton A))) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference _let_1) B)) _let_1)) (@ tptp.mnot (@ (@ tptp.in A) B))) __flatten_var_0)))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton A)) B)) tptp.empty_set)) (@ (@ tptp.in A) B)) __flatten_var_0))) __flatten_var_0)))) _let_2 _let_1 (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.singleton A))) (let ((_let_2 (@ tptp.qmltpeq (@ (@ tptp.set_difference _let_1) B)))) (@ (@ (@ tptp.mor (@ _let_2 tptp.empty_set)) (@ _let_2 _let_1)) __flatten_var_0))))) __flatten_var_0))))) true))))))))))))))))))))))))))))))))))))))))
% 0.23/0.61 )
% 0.23/0.61 % SZS output end Proof for SET926^20
% 0.23/0.61 % cvc5---1.0.5 exiting
% 0.23/0.61 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------