TSTP Solution File: SET924^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET924^1 : TPTP v8.1.2. Released v8.1.0.
% 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 14:41:01 EDT 2023
% Result : Theorem 0.23s 0.56s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET924^1 : TPTP v8.1.2. Released v8.1.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 12:04:32 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.23/0.50 %----Proving TH0
% 0.23/0.51 %------------------------------------------------------------------------------
% 0.23/0.51 % File : SET924^1 : TPTP v8.1.2. Released v8.1.0.
% 0.23/0.51 % Domain : Set Theory
% 0.23/0.51 % Problem : TPTP problem SET924+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 : SET924+1 [QMLTP]
% 0.23/0.51
% 0.23/0.51 % Status : Theorem
% 0.23/0.51 % Rating : 0.08 v8.1.0
% 0.23/0.51 % Syntax : Number of formulae : 42 ( 10 unt; 18 typ; 10 def)
% 0.23/0.51 % Number of atoms : 114 ( 10 equ; 0 cnn)
% 0.23/0.51 % Maximal formula atoms : 9 ( 4 avg)
% 0.23/0.51 % Number of connectives : 177 ( 1 ~; 1 |; 2 &; 170 @)
% 0.23/0.51 % ( 1 <=>; 2 =>; 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 : 68 ( 68 >; 0 *; 0 +; 0 <<)
% 0.23/0.51 % Number of symbols : 18 ( 17 usr; 1 con; 0-3 aty)
% 0.23/0.51 % Number of variables : 57 ( 53 ^; 2 !; 2 ?; 57 :)
% 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 == $constant,
% 0.23/0.51 % $modalities == $modal_system_K].
% 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(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] : ( 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] : ( A @ X @ W ) ) ) ).
% 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 ).
% 0.23/0.52
% 0.23/0.52 thf(empty_decl,type,
% 0.23/0.52 empty: $i > mworld > $o ).
% 0.23/0.52
% 0.23/0.52 thf(singleton_decl,type,
% 0.23/0.52 singleton: $i > $i ).
% 0.23/0.52
% 0.23/0.52 thf(set_difference_decl,type,
% 0.23/0.52 set_difference: $i > $i > $i ).
% 0.23/0.52
% 0.23/0.52 thf(reflexivity,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(symmetry,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [X: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(transitivity,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [X: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [Y: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(set_difference_substitution_1,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [A: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [B: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(set_difference_substitution_2,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [A: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [B: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(singleton_substitution_1,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [A: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(empty_substitution_1,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [A: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(in_substitution_1,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [A: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [B: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(in_substitution_2,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [A: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [B: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(antisymmetry_r2_hidden,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [A: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(rc1_xboole_0,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mexists_di
% 0.23/0.52 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(rc2_xboole_0,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mexists_di
% 0.23/0.52 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(t67_zfmisc_1,conjecture,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [A: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(l34_zfmisc_1,axiom,
% 0.23/0.52 ( mlocal
% 0.23/0.52 @ ( mforall_di
% 0.23/0.52 @ ^ [A: $i] :
% 0.23/0.52 ( mforall_di
% 0.23/0.52 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.UqinUTlo1C/cvc5---1.0.5_16348.p...
% 0.23/0.52 (declare-sort $$unsorted 0)
% 0.23/0.52 (declare-sort tptp.mworld 0)
% 0.23/0.52 (declare-fun tptp.mrel (tptp.mworld tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mactual () tptp.mworld)
% 0.23/0.52 (declare-fun tptp.mlocal ((-> tptp.mworld Bool)) Bool)
% 0.23/0.52 (assert (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))
% 0.23/0.52 (declare-fun tptp.mnot ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mand ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mor ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mimplies ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (declare-fun tptp.mequiv ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (assert (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))
% 0.23/0.52 (assert (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))
% 0.23/0.52 (assert (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))
% 0.23/0.52 (assert (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))
% 0.23/0.52 (assert (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))
% 0.23/0.52 (declare-fun tptp.mbox ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (assert (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.23/0.52 (declare-fun tptp.mdia ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.23/0.52 (assert (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.23/0.52 (declare-fun tptp.mforall_di ((-> $$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)) (@ (@ 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 $$unsorted)) (@ (@ A X) W)))))
% 0.23/0.52 (declare-fun tptp.qmltpeq ($$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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ tptp.empty A))) (@ tptp.empty B)) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.56 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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)))))
% 0.23/0.56 (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 $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.in C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.56 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.in A) B)) (@ tptp.mnot (@ (@ tptp.in B) A))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.56 (assert (@ tptp.mlocal (@ tptp.mexists_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.empty A) __flatten_var_0)))))
% 0.23/0.56 (assert (@ tptp.mlocal (@ tptp.mexists_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mnot (@ tptp.empty A)) __flatten_var_0)))))
% 0.23/0.56 (assert (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.singleton A))) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference _let_1) B)) _let_1)) (@ tptp.mnot (@ (@ tptp.in A) B))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.56 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.singleton A))) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference _let_1) B)) _let_1)) (@ tptp.mnot (@ (@ tptp.in A) B))) __flatten_var_0)))) __flatten_var_0)))))
% 0.23/0.56 (set-info :filename cvc5---1.0.5_16348)
% 0.23/0.56 (check-sat-assuming ( true ))
% 0.23/0.56 ------- get file name : TPTP file name is SET924^1
% 0.23/0.56 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16348.smt2...
% 0.23/0.56 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.56 % SZS status Theorem for SET924^1
% 0.23/0.56 % SZS output start Proof for SET924^1
% 0.23/0.56 (
% 0.23/0.56 (let ((_let_1 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.singleton A))) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference _let_1) B)) _let_1)) (@ tptp.mnot (@ (@ tptp.in A) B))) __flatten_var_0)))) __flatten_var_0)))))) (let ((_let_2 (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.singleton A))) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference _let_1) B)) _let_1)) (@ tptp.mnot (@ (@ tptp.in A) B))) __flatten_var_0)))) __flatten_var_0))))))) (let ((_let_3 (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W)))))) (let ((_let_4 (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W)))))) (let ((_let_5 (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))) (let ((_let_6 (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))) (let ((_let_7 (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))) (let ((_let_8 (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))) (let ((_let_9 (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))) (let ((_let_10 (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))) (let ((_let_11 (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))) (let ((_let_12 (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))) (let ((_let_13 (forall ((X $$unsorted)) (let ((_let_1 (ho_8 k_9 X))) (= (not (ho_5 (ho_4 (ho_3 k_11 X) X) tptp.mactual)) (ho_5 (ho_4 (ho_3 k_2 (ho_8 (ho_7 k_6 _let_1) X)) _let_1) tptp.mactual)))))) (let ((_let_14 (forall ((X $$unsorted)) (let ((_let_1 (@ tptp.singleton X))) (= (not (@ (@ (@ tptp.in X) X) tptp.mactual)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference _let_1) X)) _let_1) tptp.mactual)))))) (let ((_let_15 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_4)) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_7)) (ASSUME :args (_let_8)) (ASSUME :args (_let_9)) (ASSUME :args (_let_10)) (ASSUME :args (_let_11)) (ASSUME :args (_let_12))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_15 :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_14 _let_13))))) (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_15 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not _let_14) (not _let_13)))))) :args (false true _let_13)) :args (_let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.qmltpeq X) X) __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.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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.singleton A)) (@ tptp.singleton B))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ tptp.empty A))) (@ tptp.empty B)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.in A) B)) (@ tptp.mnot (@ (@ tptp.in B) A))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mexists_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.empty A) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mexists_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mnot (@ tptp.empty A)) __flatten_var_0)))) _let_2 _let_1 true))))))))))))))))))
% 0.23/0.56 )
% 0.23/0.56 % SZS output end Proof for SET924^1
% 0.23/0.56 % cvc5---1.0.5 exiting
% 0.23/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------