TSTP Solution File: SWV425^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV425^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 21:51:23 EDT 2023
% Result : Theorem 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV425^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 09:32:26 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : SWV425^1 : TPTP v8.1.2. Released v3.6.0.
% 0.21/0.50 % Domain : Software Verification (Security)
% 0.21/0.50 % Problem : ICL logic mapping to modal logic implies 'unit'
% 0.21/0.50 % Version : [Ben08] axioms.
% 0.21/0.50 % English :
% 0.21/0.50
% 0.21/0.50 % Refs : [GA08] Garg & Abadi (2008), A Modal Deconstruction of Access
% 0.21/0.50 % : [Ben08] Benzmueller (2008), Automating Access Control Logics i
% 0.21/0.50 % : [BP09] Benzmueller & Paulson (2009), Exploring Properties of
% 0.21/0.50 % Source : [Ben08]
% 0.21/0.50 % Names :
% 0.21/0.50
% 0.21/0.50 % Status : CounterCounterSatisfiable
% 0.21/0.50 % Rating : 0.25 v8.1.0, 0.20 v7.5.0, 0.00 v4.0.0, 1.00 v3.7.0
% 0.21/0.50 % Syntax : Number of formulae : 57 ( 24 unt; 32 typ; 24 def)
% 0.21/0.50 % Number of atoms : 77 ( 24 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 9 ( 3 avg)
% 0.21/0.50 % Number of connectives : 58 ( 3 ~; 1 |; 2 &; 51 @)
% 0.21/0.50 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 6 ( 1 avg)
% 0.21/0.50 % Number of types : 3 ( 1 usr)
% 0.21/0.50 % Number of type conns : 124 ( 124 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 39 ( 36 usr; 8 con; 0-3 aty)
% 0.21/0.50 % Number of variables : 47 ( 39 ^; 4 !; 4 ?; 47 :)
% 0.21/0.50 % SPC : TH0_CSA_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments :
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----Include axioms of multi modal logic
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----Our possible worlds are are encoded as terms the type $i;
% 0.21/0.50 %----Here is a constant for the current world:
% 0.21/0.50 thf(current_world,type,
% 0.21/0.50 current_world: $i ).
% 0.21/0.50
% 0.21/0.50 %----Modal logic propositions are then becoming predicates of type ( $i> $o);
% 0.21/0.50 %----We introduce some atomic multi-modal logic propositions as constants of
% 0.21/0.50 %----type ( $i> $o):
% 0.21/0.50 thf(prop_a,type,
% 0.21/0.50 prop_a: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(prop_b,type,
% 0.21/0.50 prop_b: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(prop_c,type,
% 0.21/0.50 prop_c: $i > $o ).
% 0.21/0.50
% 0.21/0.50 %----The idea is that an atomic multi-modal logic proposition P (of type
% 0.21/0.50 %---- $i > $o) holds at a world W (of type $i) iff W is in P resp. (P @ W)
% 0.21/0.50 %----Now we define the multi-modal logic connectives by reducing them to set
% 0.21/0.50 %----operations
% 0.21/0.50 %----mfalse corresponds to emptyset (of type $i)
% 0.21/0.50 thf(mfalse_decl,type,
% 0.21/0.50 mfalse: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mfalse,definition,
% 0.21/0.50 ( mfalse
% 0.21/0.50 = ( ^ [X: $i] : $false ) ) ).
% 0.21/0.50
% 0.21/0.50 %----mtrue corresponds to the universal set (of type $i)
% 0.21/0.50 thf(mtrue_decl,type,
% 0.21/0.50 mtrue: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mtrue,definition,
% 0.21/0.50 ( mtrue
% 0.21/0.50 = ( ^ [X: $i] : $true ) ) ).
% 0.21/0.50
% 0.21/0.50 %----mnot corresponds to set complement
% 0.21/0.50 thf(mnot_decl,type,
% 0.21/0.50 mnot: ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mnot,definition,
% 0.21/0.50 ( mnot
% 0.21/0.50 = ( ^ [X: $i > $o,U: $i] :
% 0.21/0.50 ~ ( X @ U ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----mor corresponds to set union
% 0.21/0.50 thf(mor_decl,type,
% 0.21/0.50 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mor,definition,
% 0.21/0.50 ( mor
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.21/0.50 ( ( X @ U )
% 0.21/0.50 | ( Y @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----mand corresponds to set intersection
% 0.21/0.50 thf(mand_decl,type,
% 0.21/0.50 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mand,definition,
% 0.21/0.50 ( mand
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.21/0.50 ( ( X @ U )
% 0.21/0.50 & ( Y @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----mimpl defined via mnot and mor
% 0.21/0.50 thf(mimpl_decl,type,
% 0.21/0.50 mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mimpl,definition,
% 0.21/0.50 ( mimpl
% 0.21/0.50 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----miff defined via mand and mimpl
% 0.21/0.50 thf(miff_decl,type,
% 0.21/0.50 miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(miff,definition,
% 0.21/0.50 ( miff
% 0.21/0.50 = ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----mbox
% 0.21/0.50 thf(mbox_decl,type,
% 0.21/0.50 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mbox,definition,
% 0.21/0.50 ( mbox
% 0.21/0.50 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.21/0.50 ! [Y: $i] :
% 0.21/0.50 ( ( R @ X @ Y )
% 0.21/0.50 => ( P @ Y ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----mdia
% 0.21/0.50 thf(mdia_decl,type,
% 0.21/0.50 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mdia,definition,
% 0.21/0.50 ( mdia
% 0.21/0.50 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.21/0.50 ? [Y: $i] :
% 0.21/0.50 ( ( R @ X @ Y )
% 0.21/0.50 & ( P @ Y ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----For mall and mexists, i.e., first order modal logic, we declare a new
% 0.21/0.50 %----base type individuals
% 0.21/0.50 thf(individuals_decl,type,
% 0.21/0.50 individuals: $tType ).
% 0.21/0.50
% 0.21/0.50 %----mall
% 0.21/0.50 thf(mall_decl,type,
% 0.21/0.50 mall: ( individuals > $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mall,definition,
% 0.21/0.50 ( mall
% 0.21/0.50 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.21/0.50 ! [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----mexists
% 0.21/0.50 thf(mexists_decl,type,
% 0.21/0.50 mexists: ( individuals > $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mexists,definition,
% 0.21/0.50 ( mexists
% 0.21/0.50 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.21/0.50 ? [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Validity of a multi modal logic formula can now be encoded as
% 0.21/0.50 thf(mvalid_decl,type,
% 0.21/0.50 mvalid: ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mvalid,definition,
% 0.21/0.50 ( mvalid
% 0.21/0.50 = ( ^ [P: $i > $o] :
% 0.21/0.50 ! [W: $i] : ( P @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Satisfiability of a multi modal logic formula can now be encoded as
% 0.21/0.50 thf(msatisfiable_decl,type,
% 0.21/0.50 msatisfiable: ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(msatisfiable,definition,
% 0.21/0.50 ( msatisfiable
% 0.21/0.50 = ( ^ [P: $i > $o] :
% 0.21/0.50 ? [W: $i] : ( P @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Countersatisfiability of a multi modal logic formula can now be encoded as
% 0.21/0.50 thf(mcountersatisfiable_decl,type,
% 0.21/0.50 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mcountersatisfiable,definition,
% 0.21/0.50 ( mcountersatisfiable
% 0.21/0.50 = ( ^ [P: $i > $o] :
% 0.21/0.50 ? [W: $i] :
% 0.21/0.50 ~ ( P @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Invalidity of a multi modal logic formula can now be encoded as
% 0.21/0.50 thf(minvalid_decl,type,
% 0.21/0.50 minvalid: ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(minvalid,definition,
% 0.21/0.50 ( minvalid
% 0.21/0.50 = ( ^ [P: $i > $o] :
% 0.21/0.50 ! [W: $i] :
% 0.21/0.50 ~ ( P @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----Include axioms of ICL logic
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----The encoding of ICL logic employs only one accessibility relation which
% 0.21/0.50 %----introduce here as a constant 'rel'; we don't need multimodal logic.
% 0.21/0.50 thf(rel_type,type,
% 0.21/0.50 rel: $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 %----ICL logic distiguishes between atoms and principals; for this we introduce
% 0.21/0.50 %----a predicate 'icl_atom' ...
% 0.21/0.50 thf(icl_atom_type,type,
% 0.21/0.50 icl_atom: ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_atom,definition,
% 0.21/0.50 ( icl_atom
% 0.21/0.50 = ( ^ [P: $i > $o] : ( mbox @ rel @ P ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %---- ... and also a predicate 'icl_princ'
% 0.21/0.50 thf(icl_princ_type,type,
% 0.21/0.50 icl_princ: ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_princ,definition,
% 0.21/0.50 ( icl_princ
% 0.21/0.50 = ( ^ [P: $i > $o] : P ) ) ).
% 0.21/0.50
% 0.21/0.50 %----ICL and connective
% 0.21/0.50 thf(icl_and_type,type,
% 0.21/0.50 icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_and,definition,
% 0.21/0.50 ( icl_and
% 0.21/0.50 = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----ICL or connective
% 0.21/0.50 thf(icl_or_type,type,
% 0.21/0.50 icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_or,definition,
% 0.21/0.50 ( icl_or
% 0.21/0.50 = ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----ICL implication connective
% 0.21/0.50 thf(icl_impl_type,type,
% 0.21/0.50 icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_impl,definition,
% 0.21/0.50 ( icl_impl
% 0.21/0.50 = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mimpl @ A @ B ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----ICL true connective
% 0.21/0.50 thf(icl_true_type,type,
% 0.21/0.50 icl_true: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_true,definition,
% 0.21/0.50 icl_true = mtrue ).
% 0.21/0.50
% 0.21/0.50 %----ICL false connective
% 0.21/0.50 thf(icl_false_type,type,
% 0.21/0.50 icl_false: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_false,definition,
% 0.21/0.50 icl_false = mfalse ).
% 0.21/0.50
% 0.21/0.50 %----ICL says connective
% 0.21/0.50 thf(icl_says_type,type,
% 0.21/0.50 icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_says,definition,
% 0.21/0.50 ( icl_says
% 0.21/0.50 = ( ^ [A: $i > $o,S: $i > $o] : ( mbox @ rel @ ( mor @ A @ S ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----An ICL formula is K-valid if its translation into modal logic is valid
% 0.21/0.50 thf(iclval_decl_type,type,
% 0.21/0.50 iclval: ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_s4_valid,definition,
% 0.21/0.50 ( iclval
% 0.21/0.50 = ( ^ [X: $i > $o] : ( mvalid @ X ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----We introduce an arbitrary atom s
% 0.21/0.50 thf(s,type,
% 0.21/0.50 s: $i > $o ).
% 0.21/0.51
% 0.21/0.51 %----We introduce an arbitrary principal a
% 0.21/0.51 thf(a,type,
% 0.21/0.51 a: $i > $o ).
% 0.21/0.51
% 0.21/0.51 %----Can we prove 'unit'?
% 0.21/0.51 thf(unit,conjecture,
% 0.21/0.51 iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Da67FvFDMp/cvc5---1.0.5_8002.p...
% 0.21/0.51 (declare-sort $$unsorted 0)
% 0.21/0.51 (declare-fun tptp.current_world () $$unsorted)
% 0.21/0.51 (declare-fun tptp.prop_a ($$unsorted) Bool)
% 0.21/0.51 (declare-fun tptp.prop_b ($$unsorted) Bool)
% 0.21/0.51 (declare-fun tptp.prop_c ($$unsorted) Bool)
% 0.21/0.51 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mfalse (lambda ((X $$unsorted)) false)))
% 0.21/0.51 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mtrue (lambda ((X $$unsorted)) true)))
% 0.21/0.51 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.21/0.51 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.21/0.51 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.21/0.51 (declare-fun tptp.mimpl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.21/0.51 (declare-fun tptp.miff ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))
% 0.21/0.51 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))
% 0.21/0.51 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))
% 0.21/0.51 (declare-sort tptp.individuals 0)
% 0.21/0.51 (declare-fun tptp.mall ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.21/0.51 (declare-fun tptp.mexists ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.21/0.51 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.21/0.51 (assert (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))
% 0.21/0.51 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.21/0.51 (assert (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))
% 0.21/0.51 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.21/0.51 (assert (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))
% 0.21/0.51 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.21/0.51 (assert (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))
% 0.21/0.51 (declare-fun tptp.rel ($$unsorted $$unsorted) Bool)
% 0.21/0.51 (declare-fun tptp.icl_atom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.icl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) P) __flatten_var_0))))
% 0.21/0.51 (declare-fun tptp.icl_princ ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.icl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))
% 0.21/0.51 (declare-fun tptp.icl_and ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.51 (assert (= tptp.icl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))
% 0.21/0.55 (declare-fun tptp.icl_or ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.55 (assert (= tptp.icl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))
% 0.21/0.55 (declare-fun tptp.icl_impl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.55 (assert (= tptp.icl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))
% 0.21/0.55 (declare-fun tptp.icl_true ($$unsorted) Bool)
% 0.21/0.55 (assert (= tptp.icl_true tptp.mtrue))
% 0.21/0.55 (declare-fun tptp.icl_false ($$unsorted) Bool)
% 0.21/0.55 (assert (= tptp.icl_false tptp.mfalse))
% 0.21/0.55 (declare-fun tptp.icl_says ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.55 (assert (= tptp.icl_says (lambda ((A (-> $$unsorted Bool)) (S (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mor A) S)) __flatten_var_0))))
% 0.21/0.55 (declare-fun tptp.iclval ((-> $$unsorted Bool)) Bool)
% 0.21/0.55 (assert (= tptp.iclval (lambda ((X (-> $$unsorted Bool))) (@ tptp.mvalid X))))
% 0.21/0.55 (declare-fun tptp.s ($$unsorted) Bool)
% 0.21/0.55 (declare-fun tptp.a ($$unsorted) Bool)
% 0.21/0.55 (assert (let ((_let_1 (@ tptp.icl_atom tptp.s))) (not (@ tptp.iclval (@ (@ tptp.icl_impl _let_1) (@ (@ tptp.icl_says (@ tptp.icl_princ tptp.a)) _let_1))))))
% 0.21/0.55 (set-info :filename cvc5---1.0.5_8002)
% 0.21/0.55 (check-sat-assuming ( true ))
% 0.21/0.55 ------- get file name : TPTP file name is SWV425^1
% 0.21/0.55 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_8002.smt2...
% 0.21/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.55 % SZS status Theorem for SWV425^1
% 0.21/0.55 % SZS output start Proof for SWV425^1
% 0.21/0.55 (
% 0.21/0.55 (let ((_let_1 (@ tptp.icl_atom tptp.s))) (let ((_let_2 (not (@ tptp.iclval (@ (@ tptp.icl_impl _let_1) (@ (@ tptp.icl_says (@ tptp.icl_princ tptp.a)) _let_1)))))) (let ((_let_3 (= tptp.iclval (lambda ((X (-> $$unsorted Bool))) (@ tptp.mvalid X))))) (let ((_let_4 (= tptp.icl_says (lambda ((A (-> $$unsorted Bool)) (S (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mor A) S)) __flatten_var_0))))) (let ((_let_5 (= tptp.icl_false tptp.mfalse))) (let ((_let_6 (= tptp.icl_true tptp.mtrue))) (let ((_let_7 (= tptp.icl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))) (let ((_let_8 (= tptp.icl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))) (let ((_let_9 (= tptp.icl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))) (let ((_let_10 (= tptp.icl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))) (let ((_let_11 (= tptp.icl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) P) __flatten_var_0))))) (let ((_let_12 (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))) (let ((_let_13 (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))) (let ((_let_14 (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))) (let ((_let_15 (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))) (let ((_let_16 (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_17 (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_18 (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))) (let ((_let_19 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))) (let ((_let_20 (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))) (let ((_let_21 (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))) (let ((_let_22 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_23 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_24 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_25 (= tptp.mtrue (lambda ((X $$unsorted)) true)))) (let ((_let_26 (= tptp.mfalse (lambda ((X $$unsorted)) false)))) (let ((_let_27 (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (ho_4 k_6 BOUND_VARIABLE_1210))))) (let ((_let_28 (forall ((BOUND_VARIABLE_1176 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1176) BOUND_VARIABLE_1176)) (ho_4 k_6 BOUND_VARIABLE_1176))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (ASSUME :args (_let_24)))) (let ((_let_32 (ASSUME :args (_let_23)))) (let ((_let_33 (ASSUME :args (_let_22)))) (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) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_34 _let_33 _let_32 _let_31 _let_30 _let_29) :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 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (ASSUME :args (_let_17)))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (ASSUME :args (_let_15)))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (ASSUME :args (_let_12)))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _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) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (ASSUME :args (_let_10)))) (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) :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) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (EQ_RESOLVE (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) :args (_let_7 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) :args ((= tptp.mtrue tptp.icl_true) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (EQ_RESOLVE (SYMM (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) :args ((= tptp.mfalse tptp.icl_false) 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) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (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) :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) :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or (not (forall ((BOUND_VARIABLE_1176 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1176) BOUND_VARIABLE_1176)) (@ tptp.s BOUND_VARIABLE_1176)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ tptp.s BOUND_VARIABLE_1210))) (forall ((BOUND_VARIABLE_1241 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1241) BOUND_VARIABLE_1241)) (@ tptp.a BOUND_VARIABLE_1241))) (forall ((W $$unsorted) (Y $$unsorted)) (not (@ (@ tptp.rel W) Y))))) (not (or (not _let_28) _let_27 (forall ((BOUND_VARIABLE_1241 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1241) BOUND_VARIABLE_1241)) (ho_4 k_5 BOUND_VARIABLE_1241))) (forall ((W $$unsorted) (Y $$unsorted)) (not (ho_4 (ho_3 k_2 W) Y)))))))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_OR_ELIM _let_52 :args (1)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (SYMM (ALPHA_EQUIV :args (_let_28 (= BOUND_VARIABLE_1176 BOUND_VARIABLE_1210))))) (NOT_NOT_ELIM (NOT_OR_ELIM _let_52 :args (0))) :args (_let_27 false _let_28)) :args (false false _let_27)) :args (_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)))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.55 )
% 0.21/0.55 % SZS output end Proof for SWV425^1
% 0.21/0.55 % cvc5---1.0.5 exiting
% 0.21/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------