TSTP Solution File: SET004^4 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET004^4 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 14:36:37 EDT 2023
% Result : Theorem 0.16s 0.55s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET004^4 : TPTP v8.1.2. Released v8.1.0.
% 0.05/0.14 % Command : do_cvc5 %s %d
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 08:25:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.16/0.45 %----Proving TH0
% 0.16/0.45 %------------------------------------------------------------------------------
% 0.16/0.45 % File : SET004^4 : TPTP v8.1.2. Released v8.1.0.
% 0.16/0.45 % Domain : Set Theory
% 0.16/0.45 % Problem : TPTP problem SET013+4.p with axiomatized equality
% 0.16/0.45 % Version : [BP13] axioms.
% 0.16/0.45 % English :
% 0.16/0.45
% 0.16/0.45 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.16/0.45 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.16/0.45 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.16/0.45 % Source : [TPTP]
% 0.16/0.45 % Names : SET013+1 [QMLTP]
% 0.16/0.45 % Status : Theorem
% 0.16/0.45 % Rating : 0.46 v8.1.0
% 0.16/0.45 % Syntax : Number of formulae : 71 ( 11 unt; 26 typ; 10 def)
% 0.16/0.45 % Number of atoms : 270 ( 10 equ; 0 cnn)
% 0.16/0.45 % Maximal formula atoms : 10 ( 6 avg)
% 0.16/0.45 % Number of connectives : 460 ( 1 ~; 1 |; 3 &; 451 @)
% 0.16/0.45 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.45 % Maximal formula depth : 14 ( 9 avg)
% 0.16/0.45 % Number of types : 3 ( 1 usr)
% 0.16/0.45 % Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% 0.16/0.45 % Number of symbols : 26 ( 25 usr; 2 con; 0-3 aty)
% 0.16/0.45 % Number of variables : 117 ( 109 ^; 6 !; 2 ?; 117 :)
% 0.16/0.45 % SPC : TH0_THM_EQU_NAR
% 0.16/0.45
% 0.16/0.45 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.16/0.45 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.16/0.45 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.16/0.45 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.16/0.45 % $modalities == $modal_system_S4].
% 0.16/0.45 %------------------------------------------------------------------------------
% 0.16/0.45 thf(mworld,type,
% 0.16/0.45 mworld: $tType ).
% 0.16/0.45
% 0.16/0.45 thf(mrel_type,type,
% 0.16/0.45 mrel: mworld > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mactual_type,type,
% 0.16/0.45 mactual: mworld ).
% 0.16/0.45
% 0.16/0.45 thf(mlocal_type,type,
% 0.16/0.45 mlocal: ( mworld > $o ) > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mlocal_def,definition,
% 0.16/0.45 ( mlocal
% 0.16/0.45 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mnot_type,type,
% 0.16/0.45 mnot: ( mworld > $o ) > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mand_type,type,
% 0.16/0.45 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mor_type,type,
% 0.16/0.45 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mimplies_type,type,
% 0.16/0.45 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mequiv_type,type,
% 0.16/0.45 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mnot_def,definition,
% 0.16/0.45 ( mnot
% 0.16/0.45 = ( ^ [A: mworld > $o,W: mworld] :
% 0.16/0.45 ~ ( A @ W ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mand_def,definition,
% 0.16/0.45 ( mand
% 0.16/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.45 ( ( A @ W )
% 0.16/0.45 & ( B @ W ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mor_def,definition,
% 0.16/0.45 ( mor
% 0.16/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.45 ( ( A @ W )
% 0.16/0.45 | ( B @ W ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mimplies_def,definition,
% 0.16/0.45 ( mimplies
% 0.16/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.45 ( ( A @ W )
% 0.16/0.45 => ( B @ W ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mequiv_def,definition,
% 0.16/0.45 ( mequiv
% 0.16/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.45 ( ( A @ W )
% 0.16/0.45 <=> ( B @ W ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mbox_type,type,
% 0.16/0.45 mbox: ( mworld > $o ) > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mbox_def,definition,
% 0.16/0.45 ( mbox
% 0.16/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.16/0.45 ! [V: mworld] :
% 0.16/0.45 ( ( mrel @ W @ V )
% 0.16/0.45 => ( Phi @ V ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mdia_type,type,
% 0.16/0.45 mdia: ( mworld > $o ) > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mdia_def,definition,
% 0.16/0.45 ( mdia
% 0.16/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.16/0.45 ? [V: mworld] :
% 0.16/0.45 ( ( mrel @ W @ V )
% 0.16/0.45 & ( Phi @ V ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mrel_reflexive,axiom,
% 0.16/0.45 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.16/0.45
% 0.16/0.45 thf(mrel_transitive,axiom,
% 0.16/0.45 ! [W: mworld,V: mworld,U: mworld] :
% 0.16/0.45 ( ( ( mrel @ W @ V )
% 0.16/0.45 & ( mrel @ V @ U ) )
% 0.16/0.45 => ( mrel @ W @ U ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mforall_di_type,type,
% 0.16/0.45 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mforall_di_def,definition,
% 0.16/0.45 ( mforall_di
% 0.16/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.16/0.45 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(mexists_di_type,type,
% 0.16/0.45 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(mexists_di_def,definition,
% 0.16/0.45 ( mexists_di
% 0.16/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.16/0.45 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(empty_set_decl,type,
% 0.16/0.45 empty_set: $i ).
% 0.16/0.45
% 0.16/0.45 thf(qmltpeq_decl,type,
% 0.16/0.45 qmltpeq: $i > $i > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(equal_set_decl,type,
% 0.16/0.45 equal_set: $i > $i > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(member_decl,type,
% 0.16/0.45 member: $i > $i > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(subset_decl,type,
% 0.16/0.45 subset: $i > $i > mworld > $o ).
% 0.16/0.45
% 0.16/0.45 thf(singleton_decl,type,
% 0.16/0.45 singleton: $i > $i ).
% 0.16/0.45
% 0.16/0.45 thf(product_decl,type,
% 0.16/0.45 product: $i > $i ).
% 0.16/0.45
% 0.16/0.45 thf(unordered_pair_decl,type,
% 0.16/0.45 unordered_pair: $i > $i > $i ).
% 0.16/0.45
% 0.16/0.45 thf(intersection_decl,type,
% 0.16/0.45 intersection: $i > $i > $i ).
% 0.16/0.45
% 0.16/0.45 thf(difference_decl,type,
% 0.16/0.45 difference: $i > $i > $i ).
% 0.16/0.45
% 0.16/0.45 thf(sum_decl,type,
% 0.16/0.45 sum: $i > $i ).
% 0.16/0.45
% 0.16/0.45 thf(union_decl,type,
% 0.16/0.45 union: $i > $i > $i ).
% 0.16/0.45
% 0.16/0.45 thf(power_set_decl,type,
% 0.16/0.45 power_set: $i > $i ).
% 0.16/0.45
% 0.16/0.45 thf(reflexivity,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(symmetry,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [X: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(transitivity,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [X: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [Y: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(difference_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(difference_substitution_2,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(intersection_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(intersection_substitution_2,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(power_set_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(product_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(singleton_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(sum_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(union_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(union_substitution_2,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(unordered_pair_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(unordered_pair_substitution_2,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(equal_set_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(equal_set_substitution_2,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(member_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(member_substitution_2,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(subset_substitution_1,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(subset_substitution_2,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(subset_0,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mequiv @ ( subset @ A @ B )
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(equal_set_0,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(power_set_0,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [X: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(intersection_0,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [X: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(union_0,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [X: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(empty_set_0,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(difference_0,axiom,
% 0.16/0.45 ( mlocal
% 0.16/0.45 @ ( mforall_di
% 0.16/0.45 @ ^ [B: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [A: $i] :
% 0.16/0.45 ( mforall_di
% 0.16/0.45 @ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 0.16/0.47
% 0.16/0.47 thf(singleton_0,axiom,
% 0.16/0.47 ( mlocal
% 0.16/0.47 @ ( mforall_di
% 0.16/0.47 @ ^ [X: $i] :
% 0.16/0.47 ( mforall_di
% 0.16/0.47 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 0.16/0.47
% 0.16/0.47 thf(unordered_pair_0,axiom,
% 0.16/0.47 ( mlocal
% 0.16/0.47 @ ( mforall_di
% 0.16/0.47 @ ^ [X: $i] :
% 0.16/0.47 ( mforall_di
% 0.16/0.47 @ ^ [A: $i] :
% 0.16/0.47 ( mforall_di
% 0.16/0.47 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 0.16/0.47
% 0.16/0.47 thf(sum_0,axiom,
% 0.16/0.47 ( mlocal
% 0.16/0.47 @ ( mforall_di
% 0.16/0.47 @ ^ [X: $i] :
% 0.16/0.47 ( mforall_di
% 0.16/0.47 @ ^ [A: $i] :
% 0.16/0.47 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 0.16/0.47 @ ( mexists_di
% 0.16/0.47 @ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.16/0.47
% 0.16/0.47 thf(product_0,axiom,
% 0.16/0.47 ( mlocal
% 0.16/0.47 @ ( mforall_di
% 0.16/0.47 @ ^ [X: $i] :
% 0.16/0.47 ( mforall_di
% 0.16/0.47 @ ^ [A: $i] :
% 0.16/0.47 ( mequiv @ ( member @ X @ ( product @ A ) )
% 0.16/0.47 @ ( mforall_di
% 0.16/0.47 @ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.16/0.47
% 0.16/0.47 thf(thI06,conjecture,
% 0.16/0.47 ( mlocal
% 0.16/0.47 @ ( mforall_di
% 0.16/0.47 @ ^ [A: $i] :
% 0.16/0.47 ( mforall_di
% 0.16/0.47 @ ^ [B: $i] : ( equal_set @ ( intersection @ A @ B ) @ ( intersection @ B @ A ) ) ) ) ) ).
% 0.16/0.47
% 0.16/0.47 %------------------------------------------------------------------------------
% 0.16/0.47 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.medLmfhhdu/cvc5---1.0.5_24685.p...
% 0.16/0.47 (declare-sort $$unsorted 0)
% 0.16/0.47 (declare-sort tptp.mworld 0)
% 0.16/0.47 (declare-fun tptp.mrel (tptp.mworld tptp.mworld) Bool)
% 0.16/0.47 (declare-fun tptp.mactual () tptp.mworld)
% 0.16/0.47 (declare-fun tptp.mlocal ((-> tptp.mworld Bool)) Bool)
% 0.16/0.47 (assert (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))
% 0.16/0.47 (declare-fun tptp.mnot ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.16/0.47 (declare-fun tptp.mand ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.16/0.47 (declare-fun tptp.mor ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.16/0.47 (declare-fun tptp.mimplies ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.16/0.47 (declare-fun tptp.mequiv ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.16/0.47 (assert (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))
% 0.16/0.47 (assert (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))
% 0.16/0.47 (assert (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))
% 0.16/0.47 (assert (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))
% 0.16/0.47 (assert (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))
% 0.16/0.47 (declare-fun tptp.mbox ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.16/0.47 (assert (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.16/0.47 (declare-fun tptp.mdia ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.16/0.47 (assert (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.16/0.47 (assert (forall ((W tptp.mworld)) (@ (@ tptp.mrel W) W)))
% 0.16/0.47 (assert (forall ((W tptp.mworld) (V tptp.mworld) (U tptp.mworld)) (let ((_let_1 (@ tptp.mrel W))) (=> (and (@ _let_1 V) (@ (@ tptp.mrel V) U)) (@ _let_1 U)))))
% 0.16/0.47 (declare-fun tptp.mforall_di ((-> $$unsorted tptp.mworld Bool) tptp.mworld) Bool)
% 0.16/0.47 (assert (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W)))))
% 0.16/0.47 (declare-fun tptp.mexists_di ((-> $$unsorted tptp.mworld Bool) tptp.mworld) Bool)
% 0.16/0.47 (assert (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W)))))
% 0.16/0.47 (declare-fun tptp.empty_set () $$unsorted)
% 0.16/0.47 (declare-fun tptp.qmltpeq ($$unsorted $$unsorted tptp.mworld) Bool)
% 0.16/0.47 (declare-fun tptp.equal_set ($$unsorted $$unsorted tptp.mworld) Bool)
% 0.16/0.47 (declare-fun tptp.member ($$unsorted $$unsorted tptp.mworld) Bool)
% 0.16/0.47 (declare-fun tptp.subset ($$unsorted $$unsorted tptp.mworld) Bool)
% 0.16/0.47 (declare-fun tptp.singleton ($$unsorted) $$unsorted)
% 0.16/0.47 (declare-fun tptp.product ($$unsorted) $$unsorted)
% 0.16/0.47 (declare-fun tptp.unordered_pair ($$unsorted $$unsorted) $$unsorted)
% 0.16/0.47 (declare-fun tptp.intersection ($$unsorted $$unsorted) $$unsorted)
% 0.16/0.47 (declare-fun tptp.difference ($$unsorted $$unsorted) $$unsorted)
% 0.16/0.47 (declare-fun tptp.sum ($$unsorted) $$unsorted)
% 0.16/0.47 (declare-fun tptp.union ($$unsorted $$unsorted) $$unsorted)
% 0.16/0.47 (declare-fun tptp.power_set ($$unsorted) $$unsorted)
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.qmltpeq X) X) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq X) Y)) (@ (@ tptp.qmltpeq Y) X)) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$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)))))
% 0.16/0.47 (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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.difference A) C)) (@ (@ tptp.difference B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.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)))))
% 0.16/0.47 (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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.intersection A) C)) (@ (@ tptp.intersection B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.intersection C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (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.power_set A)) (@ tptp.power_set B))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (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.product A)) (@ tptp.product B))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (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)))))
% 0.16/0.47 (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.sum A)) (@ tptp.sum B))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.union A) C)) (@ (@ tptp.union B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.union C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.unordered_pair A) C)) (@ (@ tptp.unordered_pair B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.unordered_pair C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.equal_set A) C))) (@ (@ tptp.equal_set B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.equal_set C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.member A) C))) (@ (@ tptp.member B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.member C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.subset A) C))) (@ (@ tptp.subset B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.subset C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (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.subset A) B)) (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mimplies (@ _let_1 A)) (@ _let_1 B)) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.equal_set A) B)) (@ (@ tptp.mand (@ (@ tptp.subset A) B)) (@ (@ tptp.subset B) A))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.power_set A))) (@ (@ tptp.subset X) A)) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ 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.member X))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.intersection A) B))) (@ (@ tptp.mand (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.union A) B))) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mnot (@ (@ tptp.member X) tptp.empty_set)) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((E $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.member B))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.difference E) A))) (@ (@ tptp.mand (@ _let_1 E)) (@ tptp.mnot (@ _let_1 A)))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.singleton A))) (@ (@ tptp.qmltpeq X) A)) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ 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.qmltpeq X))) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ (@ tptp.unordered_pair A) B))) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.47 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.sum A))) (@ tptp.mexists_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mand (@ (@ tptp.member Y) A)) (@ (@ tptp.member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.55 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.product A))) (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.member Y) A)) (@ (@ tptp.member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.16/0.55 (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)) (@ (@ (@ tptp.equal_set (@ (@ tptp.intersection A) B)) (@ (@ tptp.intersection B) A)) __flatten_var_0))) __flatten_var_0))))))
% 0.16/0.55 (set-info :filename cvc5---1.0.5_24685)
% 0.16/0.55 (check-sat-assuming ( true ))
% 0.16/0.55 ------- get file name : TPTP file name is SET004^4
% 0.16/0.55 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24685.smt2...
% 0.16/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.16/0.55 % SZS status Theorem for SET004^4
% 0.16/0.55 % SZS output start Proof for SET004^4
% 0.16/0.55 (
% 0.16/0.55 (let ((_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)) (@ (@ (@ tptp.equal_set (@ (@ tptp.intersection A) B)) (@ (@ tptp.intersection B) A)) __flatten_var_0))) __flatten_var_0))))))) (let ((_let_2 (@ 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.equal_set A) B)) (@ (@ tptp.mand (@ (@ tptp.subset A) B)) (@ (@ tptp.subset B) A))) __flatten_var_0))) __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.mequiv (@ (@ tptp.subset A) B)) (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mimplies (@ _let_1 A)) (@ _let_1 B)) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_4 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.member C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_5 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.qmltpeq X) X) __flatten_var_0)))))) (let ((_let_6 (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W)))))) (let ((_let_7 (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W)))))) (let ((_let_8 (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))) (let ((_let_9 (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))) (let ((_let_10 (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))) (let ((_let_11 (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))) (let ((_let_12 (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))) (let ((_let_13 (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))) (let ((_let_14 (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))) (let ((_let_15 (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))) (let ((_let_16 (ho_6 k_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_17 (ho_10 (ho_9 k_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_18 (or (not (ho_4 (ho_7 _let_16 _let_17) tptp.mactual)) (ho_4 (ho_7 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24) tptp.mactual)))) (let ((_let_19 (forall ((X $$unsorted) (BOUND_VARIABLE_4190 $$unsorted)) (let ((_let_1 (ho_6 k_19 BOUND_VARIABLE_4190))) (or (not (ho_4 (ho_7 _let_1 X) tptp.mactual)) (ho_4 (ho_7 _let_1 BOUND_VARIABLE_4190) tptp.mactual)))))) (let ((_let_20 (forall ((BOUND_VARIABLE_4729 $$unsorted)) (let ((_let_1 (ho_6 k_19 BOUND_VARIABLE_4729))) (or (not (ho_4 (ho_7 _let_1 (ho_10 (ho_9 k_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21)) tptp.mactual)) (ho_4 (ho_7 _let_1 BOUND_VARIABLE_4729) tptp.mactual)))))) (let ((_let_21 (not _let_18))) (let ((_let_22 (ho_4 (ho_7 (ho_6 k_20 _let_17) _let_17) tptp.mactual))) (let ((_let_23 (= _let_22 _let_20))) (let ((_let_24 (not _let_20))) (let ((_let_25 (forall ((X $$unsorted)) (= (forall ((BOUND_VARIABLE_4729 $$unsorted)) (let ((_let_1 (ho_6 k_19 BOUND_VARIABLE_4729))) (or (not (ho_4 (ho_7 _let_1 X) tptp.mactual)) (ho_4 (ho_7 _let_1 BOUND_VARIABLE_4729) tptp.mactual)))) (ho_4 (ho_7 (ho_6 k_20 X) X) tptp.mactual))))) (let ((_let_26 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_7)) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_10)) (ASSUME :args (_let_11)) (ASSUME :args (_let_12)) (ASSUME :args (_let_13)) (ASSUME :args (_let_14)) (ASSUME :args (_let_15))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_26 :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X $$unsorted)) (= (@ (@ (@ tptp.subset X) X) tptp.mactual) (forall ((BOUND_VARIABLE_4729 $$unsorted)) (let ((_let_1 (@ tptp.member BOUND_VARIABLE_4729))) (or (not (@ (@ _let_1 X) tptp.mactual)) (@ (@ _let_1 BOUND_VARIABLE_4729) tptp.mactual)))))) _let_25))))))) (let ((_let_28 (ho_4 (ho_7 (ho_6 k_18 _let_17) _let_17) tptp.mactual))) (let ((_let_29 (= _let_28 _let_22))) (let ((_let_30 (not _let_22))) (let ((_let_31 (forall ((X $$unsorted)) (= (ho_4 (ho_7 (ho_6 k_20 X) X) tptp.mactual) (ho_4 (ho_7 (ho_6 k_18 X) X) tptp.mactual))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_26 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X $$unsorted)) (= (@ (@ (@ tptp.subset X) X) tptp.mactual) (@ (@ (@ tptp.equal_set X) X) tptp.mactual))) _let_31))))))) (let ((_let_33 (forall ((X $$unsorted)) (let ((_let_1 (ho_10 (ho_9 k_11 X) X))) (ho_4 (ho_7 (ho_6 k_18 _let_1) _let_1) tptp.mactual))))) (let ((_let_34 (not _let_28))) (let ((_let_35 (not _let_33))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_26 :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X $$unsorted)) (let ((_let_1 (@ (@ tptp.intersection X) X))) (@ (@ (@ tptp.equal_set _let_1) _let_1) tptp.mactual)))) _let_35))))))) (let ((_let_37 (or))) (let ((_let_38 (_let_24))) (let ((_let_39 (forall ((BOUND_VARIABLE_4240 $$unsorted)) (not (ho_4 (ho_7 (ho_6 k_5 BOUND_VARIABLE_4240) BOUND_VARIABLE_4240) tptp.mactual))))) (let ((_let_40 (forall ((BOUND_VARIABLE_2021 $$unsorted)) (not (ho_4 (ho_7 (ho_6 k_5 BOUND_VARIABLE_2021) BOUND_VARIABLE_2021) tptp.mactual))))) (let ((_let_41 (ho_4 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21) tptp.mactual))) (let ((_let_42 (forall ((X $$unsorted)) (ho_4 (ho_7 (ho_6 k_5 X) X) tptp.mactual)))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO _let_26 :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X $$unsorted)) (@ (@ (@ tptp.qmltpeq X) X) tptp.mactual)) _let_42))))))) (let ((_let_44 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_45 (_let_40))) (let ((_let_46 (_let_19))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_46) :args (_let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_26 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (forall ((BOUND_VARIABLE_4240 $$unsorted)) (not (@ (@ (@ tptp.qmltpeq BOUND_VARIABLE_4240) BOUND_VARIABLE_4240) tptp.mactual))) (forall ((X $$unsorted) (BOUND_VARIABLE_4190 $$unsorted)) (let ((_let_1 (@ tptp.member BOUND_VARIABLE_4190))) (or (not (@ (@ _let_1 X) tptp.mactual)) (@ (@ _let_1 BOUND_VARIABLE_4190) tptp.mactual))))) (or _let_39 _let_19)))))) :args ((or _let_19 _let_39))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_40 (= BOUND_VARIABLE_2021 BOUND_VARIABLE_4240)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args _let_44) :args _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args _let_44) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args ((not _let_40) false _let_41)) :args ((not _let_39) true _let_40)) :args (_let_19 true _let_39)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_38)) :args _let_38)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_20))) (REFL :args (_let_21)) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_23)) :args ((or _let_22 _let_24 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_29)) :args ((or _let_28 _let_30 (not _let_29)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_36) :args (_let_35))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_33))) (REFL :args (_let_34)) :args _let_37)) _let_36 :args (_let_34 true _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_18 X)))) :args (_let_31)))) _let_32 :args (_let_29 false _let_31)) :args (_let_30 true _let_28 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_20 X)))) :args (_let_25)))) _let_27 :args (_let_23 false _let_25)) :args (_let_24 true _let_22 false _let_23)) :args (_let_21 true _let_20)) :args (false false _let_19 true _let_18)) :args (_let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 (forall ((W tptp.mworld)) (@ (@ tptp.mrel W) W)) (forall ((W tptp.mworld) (V tptp.mworld) (U tptp.mworld)) (let ((_let_1 (@ tptp.mrel W))) (=> (and (@ _let_1 V) (@ (@ tptp.mrel V) U)) (@ _let_1 U)))) _let_7 _let_6 _let_5 (@ 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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.difference A) C)) (@ (@ tptp.difference B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.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.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.intersection A) C)) (@ (@ tptp.intersection B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.intersection 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.power_set A)) (@ tptp.power_set 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.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.product A)) (@ tptp.product 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.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.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.sum A)) (@ tptp.sum 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 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.union A) C)) (@ (@ tptp.union B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.union 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.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.unordered_pair A) C)) (@ (@ tptp.unordered_pair B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.unordered_pair 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.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.equal_set A) C))) (@ (@ tptp.equal_set B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.equal_set 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.mforall_di (lambda ((C $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.member A) C))) (@ (@ tptp.member B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) _let_4 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((A $$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.subset A) C))) (@ (@ tptp.subset 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 $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.subset C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) _let_3 _let_2 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.power_set A))) (@ (@ tptp.subset X) A)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ 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.member X))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.intersection A) B))) (@ (@ tptp.mand (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.union A) B))) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mnot (@ (@ tptp.member X) tptp.empty_set)) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((B $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((E $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.member B))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.difference E) A))) (@ (@ tptp.mand (@ _let_1 E)) (@ tptp.mnot (@ _let_1 A)))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.singleton A))) (@ (@ tptp.qmltpeq X) A)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ 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.qmltpeq X))) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ (@ tptp.unordered_pair A) B))) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.sum A))) (@ tptp.mexists_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mand (@ (@ tptp.member Y) A)) (@ (@ tptp.member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((A $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.product A))) (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mimplies (@ (@ tptp.member Y) A)) (@ (@ tptp.member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))
% 0.16/0.55 )
% 0.16/0.55 % SZS output end Proof for SET004^4
% 0.16/0.55 % cvc5---1.0.5 exiting
% 0.16/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------