TSTP Solution File: SWV429^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV429^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 21:51:26 EDT 2023
% Result : Theorem 0.22s 0.54s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV429^1 : TPTP v8.1.2. Released v3.6.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 06:18:11 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 % File : SWV429^1 : TPTP v8.1.2. Released v3.6.0.
% 0.22/0.51 % Domain : Software Verification (Security)
% 0.22/0.51 % Problem : ICL^=> logic mapping to modal logic implies 'refl'
% 0.22/0.51 % Version : [Ben08] axioms.
% 0.22/0.51 % English :
% 0.22/0.51
% 0.22/0.51 % Refs : [GA08] Garg & Abadi (2008), A Modal Deconstruction of Access
% 0.22/0.51 % : [Ben08] Benzmueller (2008), Automating Access Control Logics i
% 0.22/0.51 % : [BP09] Benzmueller & Paulson (2009), Exploring Properties of
% 0.22/0.51 % Source : [Ben08]
% 0.22/0.51 % Names :
% 0.22/0.51
% 0.22/0.51 % Status : Theorem
% 0.22/0.51 % Rating : 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.22/0.51 % Syntax : Number of formulae : 58 ( 25 unt; 32 typ; 25 def)
% 0.22/0.51 % Number of atoms : 79 ( 25 equ; 0 cnn)
% 0.22/0.51 % Maximal formula atoms : 6 ( 3 avg)
% 0.22/0.51 % Number of connectives : 59 ( 3 ~; 1 |; 2 &; 52 @)
% 0.22/0.51 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.22/0.51 % Maximal formula depth : 5 ( 1 avg)
% 0.22/0.51 % Number of types : 3 ( 1 usr)
% 0.22/0.51 % Number of type conns : 130 ( 130 >; 0 *; 0 +; 0 <<)
% 0.22/0.51 % Number of symbols : 37 ( 34 usr; 6 con; 0-3 aty)
% 0.22/0.51 % Number of variables : 49 ( 41 ^; 4 !; 4 ?; 49 :)
% 0.22/0.51 % SPC : TH0_THM_EQU_NAR
% 0.22/0.51
% 0.22/0.51 % Comments :
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 %----Include axioms of multi modal logic
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 %----Our possible worlds are are encoded as terms the type $i;
% 0.22/0.51 %----Here is a constant for the current world:
% 0.22/0.51 thf(current_world,type,
% 0.22/0.51 current_world: $i ).
% 0.22/0.51
% 0.22/0.51 %----Modal logic propositions are then becoming predicates of type ( $i> $o);
% 0.22/0.51 %----We introduce some atomic multi-modal logic propositions as constants of
% 0.22/0.51 %----type ( $i> $o):
% 0.22/0.51 thf(prop_a,type,
% 0.22/0.51 prop_a: $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(prop_b,type,
% 0.22/0.51 prop_b: $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(prop_c,type,
% 0.22/0.51 prop_c: $i > $o ).
% 0.22/0.51
% 0.22/0.51 %----The idea is that an atomic multi-modal logic proposition P (of type
% 0.22/0.51 %---- $i > $o) holds at a world W (of type $i) iff W is in P resp. (P @ W)
% 0.22/0.51 %----Now we define the multi-modal logic connectives by reducing them to set
% 0.22/0.51 %----operations
% 0.22/0.51 %----mfalse corresponds to emptyset (of type $i)
% 0.22/0.51 thf(mfalse_decl,type,
% 0.22/0.51 mfalse: $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mfalse,definition,
% 0.22/0.51 ( mfalse
% 0.22/0.51 = ( ^ [X: $i] : $false ) ) ).
% 0.22/0.51
% 0.22/0.51 %----mtrue corresponds to the universal set (of type $i)
% 0.22/0.51 thf(mtrue_decl,type,
% 0.22/0.51 mtrue: $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mtrue,definition,
% 0.22/0.51 ( mtrue
% 0.22/0.51 = ( ^ [X: $i] : $true ) ) ).
% 0.22/0.51
% 0.22/0.51 %----mnot corresponds to set complement
% 0.22/0.51 thf(mnot_decl,type,
% 0.22/0.51 mnot: ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mnot,definition,
% 0.22/0.51 ( mnot
% 0.22/0.51 = ( ^ [X: $i > $o,U: $i] :
% 0.22/0.51 ~ ( X @ U ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----mor corresponds to set union
% 0.22/0.51 thf(mor_decl,type,
% 0.22/0.51 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mor,definition,
% 0.22/0.51 ( mor
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.22/0.51 ( ( X @ U )
% 0.22/0.51 | ( Y @ U ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----mand corresponds to set intersection
% 0.22/0.51 thf(mand_decl,type,
% 0.22/0.51 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mand,definition,
% 0.22/0.51 ( mand
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.22/0.51 ( ( X @ U )
% 0.22/0.51 & ( Y @ U ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----mimpl defined via mnot and mor
% 0.22/0.51 thf(mimpl_decl,type,
% 0.22/0.51 mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mimpl,definition,
% 0.22/0.51 ( mimpl
% 0.22/0.51 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----miff defined via mand and mimpl
% 0.22/0.51 thf(miff_decl,type,
% 0.22/0.51 miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(miff,definition,
% 0.22/0.51 ( miff
% 0.22/0.51 = ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----mbox
% 0.22/0.51 thf(mbox_decl,type,
% 0.22/0.51 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mbox,definition,
% 0.22/0.51 ( mbox
% 0.22/0.51 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.22/0.51 ! [Y: $i] :
% 0.22/0.51 ( ( R @ X @ Y )
% 0.22/0.51 => ( P @ Y ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----mdia
% 0.22/0.51 thf(mdia_decl,type,
% 0.22/0.51 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mdia,definition,
% 0.22/0.51 ( mdia
% 0.22/0.51 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.22/0.51 ? [Y: $i] :
% 0.22/0.51 ( ( R @ X @ Y )
% 0.22/0.51 & ( P @ Y ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----For mall and mexists, i.e., first order modal logic, we declare a new
% 0.22/0.51 %----base type individuals
% 0.22/0.51 thf(individuals_decl,type,
% 0.22/0.51 individuals: $tType ).
% 0.22/0.51
% 0.22/0.51 %----mall
% 0.22/0.51 thf(mall_decl,type,
% 0.22/0.51 mall: ( individuals > $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mall,definition,
% 0.22/0.51 ( mall
% 0.22/0.51 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.22/0.51 ! [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----mexists
% 0.22/0.51 thf(mexists_decl,type,
% 0.22/0.51 mexists: ( individuals > $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mexists,definition,
% 0.22/0.51 ( mexists
% 0.22/0.51 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.22/0.51 ? [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----Validity of a multi modal logic formula can now be encoded as
% 0.22/0.51 thf(mvalid_decl,type,
% 0.22/0.51 mvalid: ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mvalid,definition,
% 0.22/0.51 ( mvalid
% 0.22/0.51 = ( ^ [P: $i > $o] :
% 0.22/0.51 ! [W: $i] : ( P @ W ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----Satisfiability of a multi modal logic formula can now be encoded as
% 0.22/0.51 thf(msatisfiable_decl,type,
% 0.22/0.51 msatisfiable: ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(msatisfiable,definition,
% 0.22/0.51 ( msatisfiable
% 0.22/0.51 = ( ^ [P: $i > $o] :
% 0.22/0.51 ? [W: $i] : ( P @ W ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----Countersatisfiability of a multi modal logic formula can now be encoded as
% 0.22/0.51 thf(mcountersatisfiable_decl,type,
% 0.22/0.51 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(mcountersatisfiable,definition,
% 0.22/0.51 ( mcountersatisfiable
% 0.22/0.51 = ( ^ [P: $i > $o] :
% 0.22/0.51 ? [W: $i] :
% 0.22/0.51 ~ ( P @ W ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----Invalidity of a multi modal logic formula can now be encoded as
% 0.22/0.51 thf(minvalid_decl,type,
% 0.22/0.51 minvalid: ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(minvalid,definition,
% 0.22/0.51 ( minvalid
% 0.22/0.51 = ( ^ [P: $i > $o] :
% 0.22/0.51 ! [W: $i] :
% 0.22/0.51 ~ ( P @ W ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 %----Include axioms of ICL logic
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 %----The encoding of ICL logic employs only one accessibility relation which
% 0.22/0.51 %----introduce here as a constant 'rel'; we don't need multimodal logic.
% 0.22/0.51 thf(rel_type,type,
% 0.22/0.51 rel: $i > $i > $o ).
% 0.22/0.51
% 0.22/0.51 %----ICL logic distiguishes between atoms and principals; for this we introduce
% 0.22/0.51 %----a predicate 'icl_atom' ...
% 0.22/0.51 thf(icl_atom_type,type,
% 0.22/0.51 icl_atom: ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(icl_atom,definition,
% 0.22/0.51 ( icl_atom
% 0.22/0.51 = ( ^ [P: $i > $o] : ( mbox @ rel @ P ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %---- ... and also a predicate 'icl_princ'
% 0.22/0.51 thf(icl_princ_type,type,
% 0.22/0.51 icl_princ: ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(icl_princ,definition,
% 0.22/0.51 ( icl_princ
% 0.22/0.51 = ( ^ [P: $i > $o] : P ) ) ).
% 0.22/0.51
% 0.22/0.51 %----ICL and connective
% 0.22/0.51 thf(icl_and_type,type,
% 0.22/0.51 icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(icl_and,definition,
% 0.22/0.51 ( icl_and
% 0.22/0.51 = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----ICL or connective
% 0.22/0.51 thf(icl_or_type,type,
% 0.22/0.51 icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(icl_or,definition,
% 0.22/0.51 ( icl_or
% 0.22/0.51 = ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----ICL implication connective
% 0.22/0.51 thf(icl_impl_type,type,
% 0.22/0.51 icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(icl_impl,definition,
% 0.22/0.51 ( icl_impl
% 0.22/0.51 = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mimpl @ A @ B ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----ICL true connective
% 0.22/0.51 thf(icl_true_type,type,
% 0.22/0.51 icl_true: $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(icl_true,definition,
% 0.22/0.51 icl_true = mtrue ).
% 0.22/0.51
% 0.22/0.51 %----ICL false connective
% 0.22/0.51 thf(icl_false_type,type,
% 0.22/0.51 icl_false: $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(icl_false,definition,
% 0.22/0.51 icl_false = mfalse ).
% 0.22/0.51
% 0.22/0.51 %----ICL says connective
% 0.22/0.51 thf(icl_says_type,type,
% 0.22/0.51 icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(icl_says,definition,
% 0.22/0.51 ( icl_says
% 0.22/0.51 = ( ^ [A: $i > $o,S: $i > $o] : ( mbox @ rel @ ( mor @ A @ S ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----An ICL formula is K-valid if its translation into modal logic is valid
% 0.22/0.51 thf(iclval_decl_type,type,
% 0.22/0.51 iclval: ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(icl_s4_valid,definition,
% 0.22/0.51 ( iclval
% 0.22/0.51 = ( ^ [X: $i > $o] : ( mvalid @ X ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 %----Include axioms of ICL^=> logic
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %----The new connective 'speaks for'
% 0.22/0.52 thf(icl_impl_princ_type,type,
% 0.22/0.52 icl_impl_princ: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(icl_impl_princ,definition,
% 0.22/0.52 ( icl_impl_princ
% 0.22/0.52 = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mimpl @ A @ B ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %----We introduce an arbitrary principal a
% 0.22/0.52 thf(a,type,
% 0.22/0.52 a: $i > $o ).
% 0.22/0.52
% 0.22/0.52 %----Can we prove 'refl'?
% 0.22/0.52 thf(conj,conjecture,
% 0.22/0.52 iclval @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ a ) ) ).
% 0.22/0.52
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.o0uC6glx95/cvc5---1.0.5_1348.p...
% 0.22/0.52 (declare-sort $$unsorted 0)
% 0.22/0.52 (declare-fun tptp.current_world () $$unsorted)
% 0.22/0.52 (declare-fun tptp.prop_a ($$unsorted) Bool)
% 0.22/0.52 (declare-fun tptp.prop_b ($$unsorted) Bool)
% 0.22/0.52 (declare-fun tptp.prop_c ($$unsorted) Bool)
% 0.22/0.52 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mfalse (lambda ((X $$unsorted)) false)))
% 0.22/0.52 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mtrue (lambda ((X $$unsorted)) true)))
% 0.22/0.52 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.22/0.52 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.22/0.52 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.22/0.52 (declare-fun tptp.mimpl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.22/0.52 (declare-fun tptp.miff ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))
% 0.22/0.52 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))
% 0.22/0.52 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))
% 0.22/0.52 (declare-sort tptp.individuals 0)
% 0.22/0.52 (declare-fun tptp.mall ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.22/0.52 (declare-fun tptp.mexists ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.22/0.52 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.52 (assert (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))
% 0.22/0.52 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.52 (assert (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))
% 0.22/0.52 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.52 (assert (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))
% 0.22/0.52 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.52 (assert (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))
% 0.22/0.52 (declare-fun tptp.rel ($$unsorted $$unsorted) Bool)
% 0.22/0.52 (declare-fun tptp.icl_atom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.icl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) P) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.icl_princ ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.icl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.icl_and ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.icl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.icl_or ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.icl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.icl_impl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.icl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.icl_true ($$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.icl_true tptp.mtrue))
% 0.22/0.54 (declare-fun tptp.icl_false ($$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.icl_false tptp.mfalse))
% 0.22/0.54 (declare-fun tptp.icl_says ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.icl_says (lambda ((A (-> $$unsorted Bool)) (S (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mor A) S)) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.iclval ((-> $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.iclval (lambda ((X (-> $$unsorted Bool))) (@ tptp.mvalid X))))
% 0.22/0.54 (declare-fun tptp.icl_impl_princ ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.icl_impl_princ (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.a ($$unsorted) Bool)
% 0.22/0.54 (assert (let ((_let_1 (@ tptp.icl_princ tptp.a))) (not (@ tptp.iclval (@ (@ tptp.icl_impl_princ _let_1) _let_1)))))
% 0.22/0.54 (set-info :filename cvc5---1.0.5_1348)
% 0.22/0.54 (check-sat-assuming ( true ))
% 0.22/0.54 ------- get file name : TPTP file name is SWV429^1
% 0.22/0.54 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1348.smt2...
% 0.22/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.54 % SZS status Theorem for SWV429^1
% 0.22/0.54 % SZS output start Proof for SWV429^1
% 0.22/0.54 (
% 0.22/0.54 (let ((_let_1 (@ tptp.icl_princ tptp.a))) (let ((_let_2 (not (@ tptp.iclval (@ (@ tptp.icl_impl_princ _let_1) _let_1))))) (let ((_let_3 (= tptp.icl_impl_princ (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))) (let ((_let_4 (= tptp.iclval (lambda ((X (-> $$unsorted Bool))) (@ tptp.mvalid X))))) (let ((_let_5 (= tptp.icl_says (lambda ((A (-> $$unsorted Bool)) (S (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mor A) S)) __flatten_var_0))))) (let ((_let_6 (= tptp.icl_false tptp.mfalse))) (let ((_let_7 (= tptp.icl_true tptp.mtrue))) (let ((_let_8 (= tptp.icl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))) (let ((_let_9 (= tptp.icl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))) (let ((_let_10 (= tptp.icl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))) (let ((_let_11 (= tptp.icl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))) (let ((_let_12 (= tptp.icl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) P) __flatten_var_0))))) (let ((_let_13 (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))) (let ((_let_14 (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))) (let ((_let_15 (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))) (let ((_let_16 (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))) (let ((_let_17 (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_18 (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_19 (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))) (let ((_let_20 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))) (let ((_let_21 (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))) (let ((_let_22 (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))) (let ((_let_23 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_24 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_25 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_26 (= tptp.mtrue (lambda ((X $$unsorted)) true)))) (let ((_let_27 (= tptp.mfalse (lambda ((X $$unsorted)) false)))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (ASSUME :args (_let_25)))) (let ((_let_31 (ASSUME :args (_let_24)))) (let ((_let_32 (ASSUME :args (_let_23)))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (ASSUME :args (_let_18)))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (ASSUME :args (_let_16)))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (ASSUME :args (_let_13)))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (ASSUME :args (_let_11)))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (EQ_RESOLVE (SYMM (ASSUME :args (_let_7))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args ((= tptp.mtrue tptp.icl_true) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (EQ_RESOLVE (SYMM (ASSUME :args (_let_6))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args ((= tptp.mfalse tptp.icl_false) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args (_let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.55 )
% 0.22/0.55 % SZS output end Proof for SWV429^1
% 0.22/0.55 % cvc5---1.0.5 exiting
% 0.22/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------