TSTP Solution File: SWV433^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV433^2 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 21:51:28 EDT 2023
% Result : Theorem 0.21s 0.59s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV433^2 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 06:19:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.48 %----Proving TH0
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 % File : SWV433^2 : TPTP v8.1.2. Released v3.6.0.
% 0.21/0.49 % Domain : Software Verification (Security)
% 0.21/0.49 % Problem : ICL^=> logic mapping to modal logic implies that Example 2 holds
% 0.21/0.49 % Version : [Ben08] axioms : Augmented.
% 0.21/0.49 % English :
% 0.21/0.49
% 0.21/0.49 % Refs : [GA08] Garg & Abadi (2008), A Modal Deconstruction of Access
% 0.21/0.49 % : [Ben08] Benzmueller (2008), Automating Access Control Logics i
% 0.21/0.49 % : [BP09] Benzmueller & Paulson (2009), Exploring Properties of
% 0.21/0.49 % Source : [Ben08]
% 0.21/0.49 % Names :
% 0.21/0.49
% 0.21/0.49 % Status : Theorem
% 0.21/0.49 % Rating : 0.77 v8.1.0, 0.73 v7.5.0, 0.57 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.86 v6.1.0, 0.71 v5.5.0, 1.00 v5.4.0, 0.60 v5.3.0, 0.80 v5.1.0, 1.00 v5.0.0, 0.80 v4.1.0, 0.67 v3.7.0
% 0.21/0.49 % Syntax : Number of formulae : 67 ( 25 unt; 35 typ; 25 def)
% 0.21/0.49 % Number of atoms : 124 ( 25 equ; 0 cnn)
% 0.21/0.49 % Maximal formula atoms : 12 ( 3 avg)
% 0.21/0.49 % Number of connectives : 102 ( 3 ~; 1 |; 2 &; 95 @)
% 0.21/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.21/0.49 % Maximal formula depth : 8 ( 2 avg)
% 0.21/0.49 % Number of types : 3 ( 1 usr)
% 0.21/0.49 % Number of type conns : 135 ( 135 >; 0 *; 0 +; 0 <<)
% 0.21/0.49 % Number of symbols : 43 ( 40 usr; 9 con; 0-3 aty)
% 0.21/0.49 % Number of variables : 51 ( 41 ^; 6 !; 4 ?; 51 :)
% 0.21/0.49 % SPC : TH0_THM_EQU_NAR
% 0.21/0.49
% 0.21/0.49 % Comments :
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 %----Include axioms of multi modal logic
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 %----Our possible worlds are are encoded as terms the type $i;
% 0.21/0.49 %----Here is a constant for the current world:
% 0.21/0.49 thf(current_world,type,
% 0.21/0.49 current_world: $i ).
% 0.21/0.49
% 0.21/0.49 %----Modal logic propositions are then becoming predicates of type ( $i> $o);
% 0.21/0.49 %----We introduce some atomic multi-modal logic propositions as constants of
% 0.21/0.49 %----type ( $i> $o):
% 0.21/0.49 thf(prop_a,type,
% 0.21/0.49 prop_a: $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(prop_b,type,
% 0.21/0.49 prop_b: $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(prop_c,type,
% 0.21/0.49 prop_c: $i > $o ).
% 0.21/0.49
% 0.21/0.49 %----The idea is that an atomic multi-modal logic proposition P (of type
% 0.21/0.49 %---- $i > $o) holds at a world W (of type $i) iff W is in P resp. (P @ W)
% 0.21/0.49 %----Now we define the multi-modal logic connectives by reducing them to set
% 0.21/0.49 %----operations
% 0.21/0.49 %----mfalse corresponds to emptyset (of type $i)
% 0.21/0.49 thf(mfalse_decl,type,
% 0.21/0.49 mfalse: $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mfalse,definition,
% 0.21/0.49 ( mfalse
% 0.21/0.49 = ( ^ [X: $i] : $false ) ) ).
% 0.21/0.49
% 0.21/0.49 %----mtrue corresponds to the universal set (of type $i)
% 0.21/0.49 thf(mtrue_decl,type,
% 0.21/0.49 mtrue: $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mtrue,definition,
% 0.21/0.49 ( mtrue
% 0.21/0.49 = ( ^ [X: $i] : $true ) ) ).
% 0.21/0.49
% 0.21/0.49 %----mnot corresponds to set complement
% 0.21/0.49 thf(mnot_decl,type,
% 0.21/0.49 mnot: ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mnot,definition,
% 0.21/0.49 ( mnot
% 0.21/0.49 = ( ^ [X: $i > $o,U: $i] :
% 0.21/0.49 ~ ( X @ U ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----mor corresponds to set union
% 0.21/0.49 thf(mor_decl,type,
% 0.21/0.49 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mor,definition,
% 0.21/0.49 ( mor
% 0.21/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.21/0.49 ( ( X @ U )
% 0.21/0.49 | ( Y @ U ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----mand corresponds to set intersection
% 0.21/0.49 thf(mand_decl,type,
% 0.21/0.49 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mand,definition,
% 0.21/0.49 ( mand
% 0.21/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.21/0.49 ( ( X @ U )
% 0.21/0.49 & ( Y @ U ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----mimpl defined via mnot and mor
% 0.21/0.49 thf(mimpl_decl,type,
% 0.21/0.49 mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mimpl,definition,
% 0.21/0.49 ( mimpl
% 0.21/0.49 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----miff defined via mand and mimpl
% 0.21/0.49 thf(miff_decl,type,
% 0.21/0.49 miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(miff,definition,
% 0.21/0.49 ( miff
% 0.21/0.49 = ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----mbox
% 0.21/0.49 thf(mbox_decl,type,
% 0.21/0.49 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mbox,definition,
% 0.21/0.49 ( mbox
% 0.21/0.49 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.21/0.49 ! [Y: $i] :
% 0.21/0.49 ( ( R @ X @ Y )
% 0.21/0.49 => ( P @ Y ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----mdia
% 0.21/0.49 thf(mdia_decl,type,
% 0.21/0.49 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mdia,definition,
% 0.21/0.49 ( mdia
% 0.21/0.49 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.21/0.49 ? [Y: $i] :
% 0.21/0.49 ( ( R @ X @ Y )
% 0.21/0.49 & ( P @ Y ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----For mall and mexists, i.e., first order modal logic, we declare a new
% 0.21/0.49 %----base type individuals
% 0.21/0.49 thf(individuals_decl,type,
% 0.21/0.49 individuals: $tType ).
% 0.21/0.49
% 0.21/0.49 %----mall
% 0.21/0.49 thf(mall_decl,type,
% 0.21/0.49 mall: ( individuals > $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mall,definition,
% 0.21/0.49 ( mall
% 0.21/0.49 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.21/0.49 ! [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----mexists
% 0.21/0.49 thf(mexists_decl,type,
% 0.21/0.49 mexists: ( individuals > $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mexists,definition,
% 0.21/0.49 ( mexists
% 0.21/0.49 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.21/0.49 ? [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----Validity of a multi modal logic formula can now be encoded as
% 0.21/0.49 thf(mvalid_decl,type,
% 0.21/0.49 mvalid: ( $i > $o ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mvalid,definition,
% 0.21/0.49 ( mvalid
% 0.21/0.49 = ( ^ [P: $i > $o] :
% 0.21/0.49 ! [W: $i] : ( P @ W ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----Satisfiability of a multi modal logic formula can now be encoded as
% 0.21/0.49 thf(msatisfiable_decl,type,
% 0.21/0.49 msatisfiable: ( $i > $o ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(msatisfiable,definition,
% 0.21/0.49 ( msatisfiable
% 0.21/0.49 = ( ^ [P: $i > $o] :
% 0.21/0.49 ? [W: $i] : ( P @ W ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----Countersatisfiability of a multi modal logic formula can now be encoded as
% 0.21/0.49 thf(mcountersatisfiable_decl,type,
% 0.21/0.49 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(mcountersatisfiable,definition,
% 0.21/0.49 ( mcountersatisfiable
% 0.21/0.49 = ( ^ [P: $i > $o] :
% 0.21/0.49 ? [W: $i] :
% 0.21/0.49 ~ ( P @ W ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----Invalidity of a multi modal logic formula can now be encoded as
% 0.21/0.49 thf(minvalid_decl,type,
% 0.21/0.49 minvalid: ( $i > $o ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(minvalid,definition,
% 0.21/0.49 ( minvalid
% 0.21/0.49 = ( ^ [P: $i > $o] :
% 0.21/0.49 ! [W: $i] :
% 0.21/0.49 ~ ( P @ W ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 %----Include axioms of ICL logic
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 %----The encoding of ICL logic employs only one accessibility relation which
% 0.21/0.49 %----introduce here as a constant 'rel'; we don't need multimodal logic.
% 0.21/0.49 thf(rel_type,type,
% 0.21/0.49 rel: $i > $i > $o ).
% 0.21/0.49
% 0.21/0.49 %----ICL logic distiguishes between atoms and principals; for this we introduce
% 0.21/0.49 %----a predicate 'icl_atom' ...
% 0.21/0.49 thf(icl_atom_type,type,
% 0.21/0.49 icl_atom: ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(icl_atom,definition,
% 0.21/0.49 ( icl_atom
% 0.21/0.49 = ( ^ [P: $i > $o] : ( mbox @ rel @ P ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %---- ... and also a predicate 'icl_princ'
% 0.21/0.49 thf(icl_princ_type,type,
% 0.21/0.49 icl_princ: ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(icl_princ,definition,
% 0.21/0.49 ( icl_princ
% 0.21/0.49 = ( ^ [P: $i > $o] : P ) ) ).
% 0.21/0.49
% 0.21/0.49 %----ICL and connective
% 0.21/0.49 thf(icl_and_type,type,
% 0.21/0.49 icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(icl_and,definition,
% 0.21/0.49 ( icl_and
% 0.21/0.49 = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----ICL or connective
% 0.21/0.49 thf(icl_or_type,type,
% 0.21/0.49 icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(icl_or,definition,
% 0.21/0.49 ( icl_or
% 0.21/0.49 = ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----ICL implication connective
% 0.21/0.49 thf(icl_impl_type,type,
% 0.21/0.49 icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(icl_impl,definition,
% 0.21/0.49 ( icl_impl
% 0.21/0.49 = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mimpl @ A @ B ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----ICL true connective
% 0.21/0.49 thf(icl_true_type,type,
% 0.21/0.49 icl_true: $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(icl_true,definition,
% 0.21/0.49 icl_true = mtrue ).
% 0.21/0.49
% 0.21/0.49 %----ICL false connective
% 0.21/0.49 thf(icl_false_type,type,
% 0.21/0.49 icl_false: $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(icl_false,definition,
% 0.21/0.49 icl_false = mfalse ).
% 0.21/0.49
% 0.21/0.49 %----ICL says connective
% 0.21/0.49 thf(icl_says_type,type,
% 0.21/0.49 icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(icl_says,definition,
% 0.21/0.49 ( icl_says
% 0.21/0.49 = ( ^ [A: $i > $o,S: $i > $o] : ( mbox @ rel @ ( mor @ A @ S ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %----An ICL formula is K-valid if its translation into modal logic is valid
% 0.21/0.49 thf(iclval_decl_type,type,
% 0.21/0.49 iclval: ( $i > $o ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(icl_s4_valid,definition,
% 0.21/0.49 ( iclval
% 0.21/0.49 = ( ^ [X: $i > $o] : ( mvalid @ X ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.50 %----Include axioms for ICL notions of validity wrt S4
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----We add the reflexivity and the transitivity axiom to obtain S4.
% 0.21/0.50 thf(refl_axiom,axiom,
% 0.21/0.50 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ A ) @ A ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(trans_axiom,axiom,
% 0.21/0.50 ! [B: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ B ) @ ( mbox @ rel @ ( mbox @ rel @ B ) ) ) ) ).
% 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 new connective 'speaks for'
% 0.21/0.50 thf(icl_impl_princ_type,type,
% 0.21/0.50 icl_impl_princ: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(icl_impl_princ,definition,
% 0.21/0.50 ( icl_impl_princ
% 0.21/0.50 = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mimpl @ A @ B ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----The prinicpals
% 0.21/0.50 thf(admin,type,
% 0.21/0.50 admin: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(bob,type,
% 0.21/0.50 bob: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(alice,type,
% 0.21/0.50 alice: $i > $o ).
% 0.21/0.50
% 0.21/0.50 %----The atoms
% 0.21/0.50 thf(deletfile1,type,
% 0.21/0.50 deletefile1: $i > $o ).
% 0.21/0.50
% 0.21/0.50 %----The axioms of the example problem
% 0.21/0.50 %----(admin says deletefile1) => deletfile1
% 0.21/0.50 thf(ax1,axiom,
% 0.21/0.50 iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ admin ) @ ( icl_atom @ deletefile1 ) ) @ ( icl_atom @ deletefile1 ) ) ).
% 0.21/0.50
% 0.21/0.50 %----(admin says ((bob says deletefile1) => deletfile1))
% 0.21/0.50 thf(ax2,axiom,
% 0.21/0.50 iclval @ ( icl_says @ ( icl_princ @ admin ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ bob ) @ ( icl_atom @ deletefile1 ) ) @ ( icl_atom @ deletefile1 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----(bob says (alice ==> bob))
% 0.21/0.50 thf(ax3,axiom,
% 0.21/0.50 iclval @ ( icl_says @ ( icl_princ @ bob ) @ ( icl_impl_princ @ ( icl_princ @ alice ) @ ( icl_princ @ bob ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----(alice says deletefile1)
% 0.21/0.50 thf(ax4,axiom,
% 0.21/0.50 iclval @ ( icl_says @ ( icl_princ @ alice ) @ ( icl_atom @ deletefile1 ) ) ).
% 0.21/0.50
% 0.21/0.50 %----We prove deletefile1
% 0.21/0.50 thf(conj,conjecture,
% 0.21/0.50 iclval @ ( icl_atom @ deletefile1 ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.tyS5uokn3B/cvc5---1.0.5_20637.p...
% 0.21/0.50 (declare-sort $$unsorted 0)
% 0.21/0.50 (declare-fun tptp.current_world () $$unsorted)
% 0.21/0.50 (declare-fun tptp.prop_a ($$unsorted) Bool)
% 0.21/0.50 (declare-fun tptp.prop_b ($$unsorted) Bool)
% 0.21/0.50 (declare-fun tptp.prop_c ($$unsorted) Bool)
% 0.21/0.50 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mfalse (lambda ((X $$unsorted)) false)))
% 0.21/0.50 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mtrue (lambda ((X $$unsorted)) true)))
% 0.21/0.50 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.21/0.50 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.21/0.50 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.21/0.50 (declare-fun tptp.mimpl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.21/0.50 (declare-fun tptp.miff ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))
% 0.21/0.50 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))
% 0.21/0.50 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))
% 0.21/0.50 (declare-sort tptp.individuals 0)
% 0.21/0.50 (declare-fun tptp.mall ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.21/0.50 (declare-fun tptp.mexists ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.21/0.50 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.21/0.50 (assert (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))
% 0.21/0.50 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.21/0.50 (assert (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))
% 0.21/0.50 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.21/0.50 (assert (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))
% 0.21/0.50 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.21/0.50 (assert (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))
% 0.21/0.50 (declare-fun tptp.rel ($$unsorted $$unsorted) Bool)
% 0.21/0.50 (declare-fun tptp.icl_atom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.icl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) P) __flatten_var_0))))
% 0.21/0.50 (declare-fun tptp.icl_princ ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.icl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))
% 0.21/0.50 (declare-fun tptp.icl_and ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.icl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))
% 0.21/0.50 (declare-fun tptp.icl_or ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.icl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))
% 0.21/0.50 (declare-fun tptp.icl_impl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.icl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))
% 0.21/0.50 (declare-fun tptp.icl_true ($$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.icl_true tptp.mtrue))
% 0.21/0.50 (declare-fun tptp.icl_false ($$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.icl_false tptp.mfalse))
% 0.21/0.50 (declare-fun tptp.icl_says ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.icl_says (lambda ((A (-> $$unsorted Bool)) (S (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mor A) S)) __flatten_var_0))))
% 0.21/0.50 (declare-fun tptp.iclval ((-> $$unsorted Bool)) Bool)
% 0.21/0.50 (assert (= tptp.iclval (lambda ((X (-> $$unsorted Bool))) (@ tptp.mvalid X))))
% 0.21/0.50 (assert (forall ((A (-> $$unsorted Bool))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.rel) A)) A))))
% 0.21/0.50 (assert (forall ((B (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.mbox tptp.rel))) (let ((_let_2 (@ _let_1 B))) (@ tptp.mvalid (@ (@ tptp.mimpl _let_2) (@ _let_1 _let_2)))))))
% 0.21/0.50 (declare-fun tptp.icl_impl_princ ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.icl_impl_princ (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))
% 0.21/0.50 (declare-fun tptp.admin ($$unsorted) Bool)
% 0.21/0.50 (declare-fun tptp.bob ($$unsorted) Bool)
% 0.21/0.50 (declare-fun tptp.alice ($$unsorted) Bool)
% 0.21/0.50 (declare-fun tptp.deletefile1 ($$unsorted) Bool)
% 0.21/0.50 (assert (let ((_let_1 (@ tptp.icl_atom tptp.deletefile1))) (@ tptp.iclval (@ (@ tptp.icl_impl (@ (@ tptp.icl_says (@ tptp.icl_princ tptp.admin)) _let_1)) _let_1))))
% 0.21/0.50 (assert (let ((_let_1 (@ tptp.icl_atom tptp.deletefile1))) (@ tptp.iclval (@ (@ tptp.icl_says (@ tptp.icl_princ tptp.admin)) (@ (@ tptp.icl_impl (@ (@ tptp.icl_says (@ tptp.icl_princ tptp.bob)) _let_1)) _let_1)))))
% 0.21/0.59 (assert (let ((_let_1 (@ tptp.icl_princ tptp.bob))) (@ tptp.iclval (@ (@ tptp.icl_says _let_1) (@ (@ tptp.icl_impl_princ (@ tptp.icl_princ tptp.alice)) _let_1)))))
% 0.21/0.59 (assert (@ tptp.iclval (@ (@ tptp.icl_says (@ tptp.icl_princ tptp.alice)) (@ tptp.icl_atom tptp.deletefile1))))
% 0.21/0.59 (assert (not (@ tptp.iclval (@ tptp.icl_atom tptp.deletefile1))))
% 0.21/0.59 (set-info :filename cvc5---1.0.5_20637)
% 0.21/0.59 (check-sat-assuming ( true ))
% 0.21/0.59 ------- get file name : TPTP file name is SWV433^2
% 0.21/0.59 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20637.smt2...
% 0.21/0.59 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.59 % SZS status Theorem for SWV433^2
% 0.21/0.59 % SZS output start Proof for SWV433^2
% 0.21/0.59 (
% 0.21/0.59 (let ((_let_1 (@ tptp.icl_atom tptp.deletefile1))) (let ((_let_2 (not (@ tptp.iclval _let_1)))) (let ((_let_3 (@ tptp.icl_princ tptp.alice))) (let ((_let_4 (@ tptp.iclval (@ (@ tptp.icl_says _let_3) _let_1)))) (let ((_let_5 (@ tptp.icl_princ tptp.bob))) (let ((_let_6 (@ tptp.icl_says _let_5))) (let ((_let_7 (@ tptp.iclval (@ _let_6 (@ (@ tptp.icl_impl_princ _let_3) _let_5))))) (let ((_let_8 (@ tptp.icl_says (@ tptp.icl_princ tptp.admin)))) (let ((_let_9 (@ tptp.iclval (@ _let_8 (@ (@ tptp.icl_impl (@ _let_6 _let_1)) _let_1))))) (let ((_let_10 (@ tptp.iclval (@ (@ tptp.icl_impl (@ _let_8 _let_1)) _let_1)))) (let ((_let_11 (= tptp.icl_impl_princ (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))) (let ((_let_12 (forall ((A (-> $$unsorted Bool))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.rel) A)) A))))) (let ((_let_13 (= tptp.iclval (lambda ((X (-> $$unsorted Bool))) (@ tptp.mvalid X))))) (let ((_let_14 (= tptp.icl_says (lambda ((A (-> $$unsorted Bool)) (S (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mor A) S)) __flatten_var_0))))) (let ((_let_15 (= tptp.icl_false tptp.mfalse))) (let ((_let_16 (= tptp.icl_true tptp.mtrue))) (let ((_let_17 (= tptp.icl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))) (let ((_let_18 (= tptp.icl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))) (let ((_let_19 (= tptp.icl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))) (let ((_let_20 (= tptp.icl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))) (let ((_let_21 (= tptp.icl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.rel) P) __flatten_var_0))))) (let ((_let_22 (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))) (let ((_let_23 (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))) (let ((_let_24 (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))) (let ((_let_25 (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))) (let ((_let_26 (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_27 (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_28 (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))) (let ((_let_29 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))) (let ((_let_30 (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))) (let ((_let_31 (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))) (let ((_let_32 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_33 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_34 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_35 (= tptp.mtrue (lambda ((X $$unsorted)) true)))) (let ((_let_36 (= tptp.mfalse (lambda ((X $$unsorted)) false)))) (let ((_let_37 (forall ((BOUND_VARIABLE_1417 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1417) BOUND_VARIABLE_1417)) (ho_2 k_5 BOUND_VARIABLE_1417))))) (let ((_let_38 (ho_2 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_39 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_40 (ho_2 _let_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_38))) (let ((_let_43 (forall ((BOUND_VARIABLE_1474 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1474) BOUND_VARIABLE_1474)) (ho_2 k_5 BOUND_VARIABLE_1474))))) (let ((_let_44 (forall ((BOUND_VARIABLE_1698 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1698) BOUND_VARIABLE_1698)) (ho_2 k_5 BOUND_VARIABLE_1698))))) (let ((_let_45 (ho_2 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 (ho_2 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))) (let ((_let_48 (forall ((W $$unsorted) (Y $$unsorted)) (not (ho_2 (ho_4 k_3 W) Y))))) (let ((_let_49 (forall ((BOUND_VARIABLE_1449 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1449) BOUND_VARIABLE_1449)) (ho_2 k_6 BOUND_VARIABLE_1449))))) (let ((_let_50 (not _let_49))) (let ((_let_51 (not _let_37))) (let ((_let_52 (and _let_51 _let_50))) (let ((_let_53 (forall ((W $$unsorted) (Y $$unsorted)) (or (not (ho_2 (ho_4 k_3 W) Y)) (ho_2 k_8 Y))))) (let ((_let_54 (ho_2 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_55 (ho_2 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_54))) (let ((_let_58 (forall ((BOUND_VARIABLE_1593 $$unsorted)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1593) BOUND_VARIABLE_1593))))) (let ((_let_59 (or (not (ho_2 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (ho_2 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_60 (ho_2 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_61 (or _let_56 _let_60))) (let ((_let_62 (forall ((W $$unsorted) (Y $$unsorted)) (or (not (ho_2 (ho_4 k_3 W) Y)) (ho_2 k_6 Y))))) (let ((_let_63 (forall ((BOUND_VARIABLE_1558 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1558) BOUND_VARIABLE_1558)) (ho_2 k_7 BOUND_VARIABLE_1558))))) (let ((_let_64 (not _let_63))) (let ((_let_65 (and (not (forall ((BOUND_VARIABLE_1526 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1526) BOUND_VARIABLE_1526)) (ho_2 k_5 BOUND_VARIABLE_1526)))) _let_64))) (let ((_let_66 (or))) (let ((_let_67 (_let_51))) (let ((_let_68 (ho_2 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_38))) (let ((_let_71 (forall ((W $$unsorted) (Y $$unsorted)) (or (not (ho_2 (ho_4 k_3 W) Y)) (ho_2 k_5 Y))))) (let ((_let_72 (not _let_70))) (let ((_let_73 (not _let_71))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (ASSUME :args (_let_34)))) (let ((_let_77 (ASSUME :args (_let_33)))) (let ((_let_78 (ASSUME :args (_let_32)))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (ASSUME :args (_let_27)))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (ASSUME :args (_let_25)))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (ASSUME :args (_let_22)))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (ASSUME :args (_let_20)))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (EQ_RESOLVE (SYMM (ASSUME :args (_let_16))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args ((= tptp.mtrue tptp.icl_true) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (EQ_RESOLVE (SYMM (ASSUME :args (_let_15))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args ((= tptp.mfalse tptp.icl_false) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (AND_INTRO _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74))) (let ((_let_99 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO _let_98 :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_99 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((W $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.rel W) Y)) (@ tptp.deletefile1 Y)))) _let_73))))))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_100) :args (_let_73))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_71))) (REFL :args (_let_72)) :args _let_66)) _let_100 :args (_let_72 true _let_71)))) (let ((_let_102 (_let_48))) (let ((_let_103 (forall ((BOUND_VARIABLE_1474 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1474) BOUND_VARIABLE_1474)) (@ tptp.deletefile1 BOUND_VARIABLE_1474))))) (let ((_let_104 (_let_53))) (let ((_let_105 (_let_58))) (let ((_let_106 (_let_50))) (let ((_let_107 (not _let_54))) (let ((_let_108 (or _let_56 _let_107 _let_60))) (let ((_let_109 (forall ((BOUND_VARIABLE_1654 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1654) BOUND_VARIABLE_1654)) (not (ho_2 k_8 BOUND_VARIABLE_1654)) (ho_2 k_7 BOUND_VARIABLE_1654))))) (let ((_let_110 (forall ((W $$unsorted) (Y $$unsorted)) (or (not (ho_2 (ho_4 k_3 W) Y)) (ho_2 k_7 Y))))) (let ((_let_111 (not _let_57))) (let ((_let_112 (_let_109))) (let ((_let_113 (_let_110))) (let ((_let_114 (_let_62))) (let ((_let_115 (_let_64))) (let ((_let_116 (not _let_42))) (let ((_let_117 (forall ((BOUND_VARIABLE_1793 |u_(-> $$unsorted Bool)|) (W $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (ho_2 (ho_4 k_3 W) Y)) (ho_2 BOUND_VARIABLE_1793 Y)))) (ho_2 BOUND_VARIABLE_1793 W))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO _let_98 :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A (-> $$unsorted Bool)) (W $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.rel W) Y)) (@ A Y)))) (@ A W))) _let_117))))))) (let ((_let_119 (_let_37))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_119) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_119)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_38 _let_41 _let_116))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_70 1)) _let_101 :args ((not _let_38) true _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_118 :args (_let_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 BOUND_VARIABLE_1793 W) true))))) :args (_let_117)))) _let_118 :args (_let_40 false _let_117)) :args (_let_116 true _let_38 false _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_65 1)) :args ((or _let_64 (not _let_65)))) (REORDERING (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO _let_99 :args (_let_9 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (and (not (forall ((BOUND_VARIABLE_1526 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1526) BOUND_VARIABLE_1526)) (@ tptp.deletefile1 BOUND_VARIABLE_1526)))) (not (forall ((BOUND_VARIABLE_1558 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1558) BOUND_VARIABLE_1558)) (@ tptp.bob BOUND_VARIABLE_1558))))) _let_103 (forall ((BOUND_VARIABLE_1593 $$unsorted)) (not (@ (@ tptp.rel BOUND_VARIABLE_1593) BOUND_VARIABLE_1593))) (forall ((W $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.rel W) Y)) (@ tptp.admin Y)))) (or _let_65 _let_43 _let_58 _let_62)))))) :args ((or _let_43 _let_62 _let_58 _let_65))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_115)) :args _let_115)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) (REFL :args ((not _let_61))) :args _let_66)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_114) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_114)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_113) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_113)) (REORDERING (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO _let_99 :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (forall ((BOUND_VARIABLE_1654 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1654) BOUND_VARIABLE_1654)) (not (@ tptp.alice BOUND_VARIABLE_1654)) (@ tptp.bob BOUND_VARIABLE_1654))) (forall ((W $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.rel W) Y)) (@ tptp.bob Y)))) (or _let_109 _let_110)))))) :args ((or _let_110 _let_109))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_112) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_4 k_3 BOUND_VARIABLE_1654)))) :args _let_112)) (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_56 _let_60 _let_107 (not _let_108)))) (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_56 _let_54 _let_111))) (CNF_OR_NEG :args (_let_61 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG (REFL :args (_let_61)) (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_55))) :args _let_66)) :args ((or _let_55 _let_61))) :args ((or _let_61 _let_111) false _let_110 true _let_109 true _let_108 false _let_54 true _let_60 false _let_55)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_106)) :args _let_106)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) (REFL :args ((not _let_59))) :args _let_66)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_105) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_105)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_104) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_2 (ho_4 k_3 W) Y) false))))) :args _let_104)) (REORDERING (CNF_AND_POS :args (_let_52 1)) :args ((or _let_50 (not _let_52)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 0)) (CONG (REFL :args (_let_47)) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_66)) :args ((or _let_45 _let_47))) (REORDERING (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_99 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (forall ((BOUND_VARIABLE_1698 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1698) BOUND_VARIABLE_1698)) (@ tptp.deletefile1 BOUND_VARIABLE_1698))) (forall ((W $$unsorted) (Y $$unsorted)) (or (not (@ (@ tptp.rel W) Y)) (@ tptp.alice Y)))) (or _let_44 _let_53)))))) :args ((or _let_53 _let_44))) (REORDERING (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO _let_99 :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (and (not (forall ((BOUND_VARIABLE_1417 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1417) BOUND_VARIABLE_1417)) (@ tptp.deletefile1 BOUND_VARIABLE_1417)))) (not (forall ((BOUND_VARIABLE_1449 $$unsorted)) (or (not (@ (@ tptp.rel BOUND_VARIABLE_1449) BOUND_VARIABLE_1449)) (@ tptp.admin BOUND_VARIABLE_1449))))) _let_103 (forall ((W $$unsorted) (Y $$unsorted)) (not (@ (@ tptp.rel W) Y)))) (or _let_52 _let_43 _let_48)))))) :args ((or _let_48 _let_43 _let_52))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_102) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 0)) (CONG (REFL :args (_let_70)) (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_66)) :args ((or _let_68 _let_70))) _let_101 :args (_let_68 true _let_70)) :args ((not _let_48) false _let_68)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_67)) :args _let_67)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_37))) (REFL :args ((not _let_47))) :args _let_66)) (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_37 (= BOUND_VARIABLE_1417 BOUND_VARIABLE_1698)))) (REORDERING (EQUIV_ELIM1 (SYMM (ALPHA_EQUIV :args (_let_37 (= BOUND_VARIABLE_1417 BOUND_VARIABLE_1474))))) :args ((or _let_37 (not _let_43)))) :args (_let_37 false _let_65 false _let_63 true _let_62 false _let_61 true _let_59 true _let_58 false _let_57 true _let_49 false _let_45 false _let_53 false _let_52 true _let_48 true _let_47 true _let_44 true _let_43)) :args (false true _let_42 false _let_37)) :args (_let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _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 (forall ((B (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.mbox tptp.rel))) (let ((_let_2 (@ _let_1 B))) (@ tptp.mvalid (@ (@ tptp.mimpl _let_2) (@ _let_1 _let_2)))))) _let_11 _let_10 _let_9 _let_7 _let_4 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.59 )
% 0.21/0.59 % SZS output end Proof for SWV433^2
% 0.21/0.59 % cvc5---1.0.5 exiting
% 0.21/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------