TSTP Solution File: SYN416^4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYN416^4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 : Fri Sep 1 02:03:04 EDT 2023
% Result : Theorem 0.15s 0.43s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYN416^4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : do_cvc5 %s %d
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Aug 26 19:03:59 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.40 %----Proving TH0
% 0.15/0.40 %------------------------------------------------------------------------------
% 0.15/0.40 % File : SYN416^4 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.40 % Domain : Logic Calculi (Intuitionistic logic)
% 0.15/0.40 % Problem : Pelletier Problem 16
% 0.15/0.40 % Version : [Goe33] axioms.
% 0.15/0.40 % English :
% 0.15/0.40
% 0.15/0.40 % Refs : [Goe33] Goedel (1933), An Interpretation of the Intuitionistic
% 0.15/0.40 % : [Gol06] Goldblatt (2006), Mathematical Modal Logic: A View of
% 0.15/0.40 % : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% 0.15/0.40 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.15/0.40 % : [BP10] Benzmueller & Paulson (2009), Exploring Properties of
% 0.15/0.40 % Source : [Ben09]
% 0.15/0.40 % Names :
% 0.15/0.40
% 0.15/0.40 % Status : CounterCounterSatisfiable
% 0.15/0.40 % Rating : 0.50 v8.1.0, 0.60 v7.5.0, 0.40 v7.4.0, 0.50 v7.2.0, 0.33 v5.4.0, 0.67 v5.0.0, 0.33 v4.1.0, 0.50 v4.0.0
% 0.15/0.40 % Syntax : Number of formulae : 44 ( 20 unt; 22 typ; 19 def)
% 0.15/0.40 % Number of atoms : 75 ( 19 equ; 0 cnn)
% 0.15/0.40 % Maximal formula atoms : 12 ( 3 avg)
% 0.15/0.40 % Number of connectives : 66 ( 3 ~; 1 |; 2 &; 58 @)
% 0.15/0.40 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.15/0.40 % Maximal formula depth : 8 ( 2 avg)
% 0.15/0.40 % Number of types : 2 ( 0 usr)
% 0.15/0.40 % Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% 0.15/0.40 % Number of symbols : 28 ( 26 usr; 5 con; 0-3 aty)
% 0.15/0.40 % Number of variables : 40 ( 31 ^; 7 !; 2 ?; 40 :)
% 0.15/0.40 % SPC : TH0_CSA_EQU_NAR
% 0.15/0.40
% 0.15/0.40 % Comments : This is an ILTP problem embedded in TH0
% 0.15/0.40 % : In classical logic this is a Theorem.
% 0.15/0.40 %------------------------------------------------------------------------------
% 0.15/0.40 %------------------------------------------------------------------------------
% 0.15/0.40 %----Modal Logic S4 in HOL
% 0.15/0.40 %----We define an accessibility relation irel
% 0.15/0.40 thf(irel_type,type,
% 0.15/0.40 irel: $i > $i > $o ).
% 0.15/0.40
% 0.15/0.40 %----We require reflexivity and transitivity for irel
% 0.15/0.40 thf(refl_axiom,axiom,
% 0.15/0.40 ! [X: $i] : ( irel @ X @ X ) ).
% 0.15/0.40
% 0.15/0.40 thf(trans_axiom,axiom,
% 0.15/0.40 ! [X: $i,Y: $i,Z: $i] :
% 0.15/0.40 ( ( ( irel @ X @ Y )
% 0.15/0.40 & ( irel @ Y @ Z ) )
% 0.15/0.40 => ( irel @ X @ Z ) ) ).
% 0.15/0.40
% 0.15/0.40 %----We define S4 connective mnot (as set complement)
% 0.15/0.40 thf(mnot_decl_type,type,
% 0.15/0.40 mnot: ( $i > $o ) > $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(mnot,definition,
% 0.15/0.40 ( mnot
% 0.15/0.40 = ( ^ [X: $i > $o,U: $i] :
% 0.15/0.40 ~ ( X @ U ) ) ) ).
% 0.15/0.40
% 0.15/0.40 %----We define S4 connective mor (as set union)
% 0.15/0.40 thf(mor_decl_type,type,
% 0.15/0.40 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(mor,definition,
% 0.15/0.40 ( mor
% 0.15/0.40 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.15/0.40 ( ( X @ U )
% 0.15/0.40 | ( Y @ U ) ) ) ) ).
% 0.15/0.40
% 0.15/0.40 %----We define S4 connective mand (as set intersection)
% 0.15/0.40 thf(mand_decl_type,type,
% 0.15/0.40 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(mand,definition,
% 0.15/0.40 ( mand
% 0.15/0.40 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.15/0.40 ( ( X @ U )
% 0.15/0.40 & ( Y @ U ) ) ) ) ).
% 0.15/0.40
% 0.15/0.40 %----We define S4 connective mimpl
% 0.15/0.40 thf(mimplies_decl_type,type,
% 0.15/0.40 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(mimplies,definition,
% 0.15/0.40 ( mimplies
% 0.15/0.40 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.15/0.40
% 0.15/0.40 %----Definition of mbox_s4; since irel is reflexive and transitive,
% 0.15/0.40 %----it is easy to show that the K and the T axiom hold for mbox_s4
% 0.15/0.40 thf(mbox_s4_decl_type,type,
% 0.15/0.40 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(mbox_s4,definition,
% 0.15/0.40 ( mbox_s4
% 0.15/0.40 = ( ^ [P: $i > $o,X: $i] :
% 0.15/0.40 ! [Y: $i] :
% 0.15/0.40 ( ( irel @ X @ Y )
% 0.15/0.40 => ( P @ Y ) ) ) ) ).
% 0.15/0.40
% 0.15/0.40 %----Intuitionistic Logic in Modal Logic S4
% 0.15/0.40 %----Definition of iatom: iatom P = P
% 0.15/0.40 %----Goedel maps atoms to atoms
% 0.15/0.40 thf(iatom_type,type,
% 0.15/0.40 iatom: ( $i > $o ) > $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(iatom,definition,
% 0.15/0.40 ( iatom
% 0.15/0.40 = ( ^ [P: $i > $o] : P ) ) ).
% 0.15/0.40
% 0.15/0.40 %----Definition of inot: inot P = mnot (mbox_s4 P)
% 0.15/0.40 thf(inot_type,type,
% 0.15/0.40 inot: ( $i > $o ) > $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(inot,definition,
% 0.15/0.40 ( inot
% 0.15/0.40 = ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ) ).
% 0.15/0.40
% 0.15/0.40 %----Definition of true and false
% 0.15/0.40 thf(itrue_type,type,
% 0.15/0.40 itrue: $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(itrue,definition,
% 0.15/0.40 ( itrue
% 0.15/0.40 = ( ^ [W: $i] : $true ) ) ).
% 0.15/0.40
% 0.15/0.40 thf(ifalse_type,type,
% 0.15/0.40 ifalse: $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(ifalse,definition,
% 0.15/0.41 ( ifalse
% 0.15/0.41 = ( inot @ itrue ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of iand: iand P Q = (mand P Q)
% 0.15/0.41 thf(iand_type,type,
% 0.15/0.41 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(iand,definition,
% 0.15/0.41 ( iand
% 0.15/0.41 = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of ior: ior P Q = (mor (mbox_s4 P) (mbox_s4 Q))
% 0.15/0.41 thf(ior_type,type,
% 0.15/0.41 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(ior,definition,
% 0.15/0.41 ( ior
% 0.15/0.41 = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of iimplies: iimplies P Q =
% 0.15/0.41 %---- (mimplies (mbox_s4 P) (mbox_s4 Q))
% 0.15/0.41 thf(iimplies_type,type,
% 0.15/0.41 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(iimplies,definition,
% 0.15/0.41 ( iimplies
% 0.15/0.41 = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of iimplied: iimplied P Q = (iimplies Q P)
% 0.15/0.41 thf(iimplied_type,type,
% 0.15/0.41 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(iimplied,definition,
% 0.15/0.41 ( iimplied
% 0.15/0.41 = ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of iequiv: iequiv P Q =
% 0.15/0.41 %---- (iand (iimplies P Q) (iimplies Q P))
% 0.15/0.41 thf(iequiv_type,type,
% 0.15/0.41 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(iequiv,definition,
% 0.15/0.41 ( iequiv
% 0.15/0.41 = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of ixor: ixor P Q = (inot (iequiv P Q)
% 0.15/0.41 thf(ixor_type,type,
% 0.15/0.41 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(ixor,definition,
% 0.15/0.41 ( ixor
% 0.15/0.41 = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of validity
% 0.15/0.41 thf(ivalid_type,type,
% 0.15/0.41 ivalid: ( $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(ivalid,definition,
% 0.15/0.41 ( ivalid
% 0.15/0.41 = ( ^ [Phi: $i > $o] :
% 0.15/0.41 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of satisfiability
% 0.15/0.41 thf(isatisfiable_type,type,
% 0.15/0.41 isatisfiable: ( $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(isatisfiable,definition,
% 0.15/0.41 ( isatisfiable
% 0.15/0.41 = ( ^ [Phi: $i > $o] :
% 0.15/0.41 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of countersatisfiability
% 0.15/0.41 thf(icountersatisfiable_type,type,
% 0.15/0.41 icountersatisfiable: ( $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(icountersatisfiable,definition,
% 0.15/0.41 ( icountersatisfiable
% 0.15/0.41 = ( ^ [Phi: $i > $o] :
% 0.15/0.41 ? [W: $i] :
% 0.15/0.41 ~ ( Phi @ W ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Definition of invalidity
% 0.15/0.41 thf(iinvalid_type,type,
% 0.15/0.41 iinvalid: ( $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(iinvalid,definition,
% 0.15/0.41 ( iinvalid
% 0.15/0.41 = ( ^ [Phi: $i > $o] :
% 0.15/0.41 ! [W: $i] :
% 0.15/0.41 ~ ( Phi @ W ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 thf(p_type,type,
% 0.15/0.41 p: $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(q_type,type,
% 0.15/0.41 q: $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(pel16,conjecture,
% 0.15/0.41 ivalid @ ( ior @ ( iimplies @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( iimplies @ ( iatom @ q ) @ ( iatom @ p ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.G7FCIVO1i4/cvc5---1.0.5_1735.p...
% 0.15/0.41 (declare-sort $$unsorted 0)
% 0.15/0.41 (declare-fun tptp.irel ($$unsorted $$unsorted) Bool)
% 0.15/0.41 (assert (forall ((X $$unsorted)) (@ (@ tptp.irel X) X)))
% 0.15/0.41 (assert (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ tptp.irel X))) (=> (and (@ _let_1 Y) (@ (@ tptp.irel Y) Z)) (@ _let_1 Z)))))
% 0.15/0.41 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.41 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.15/0.41 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.41 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.15/0.41 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.41 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.15/0.41 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.41 (assert (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.15/0.43 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))
% 0.15/0.43 (declare-fun tptp.iatom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))
% 0.15/0.43 (declare-fun tptp.inot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))
% 0.15/0.43 (declare-fun tptp.itrue ($$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.itrue (lambda ((W $$unsorted)) true)))
% 0.15/0.43 (declare-fun tptp.ifalse ($$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.ifalse (@ tptp.inot tptp.itrue)))
% 0.15/0.43 (declare-fun tptp.iand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))
% 0.15/0.43 (declare-fun tptp.ior ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.15/0.43 (declare-fun tptp.iimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.15/0.43 (declare-fun tptp.iimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))
% 0.15/0.43 (declare-fun tptp.iequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))
% 0.15/0.43 (declare-fun tptp.ixor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.43 (assert (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))
% 0.15/0.43 (declare-fun tptp.ivalid ((-> $$unsorted Bool)) Bool)
% 0.15/0.43 (assert (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.15/0.43 (declare-fun tptp.isatisfiable ((-> $$unsorted Bool)) Bool)
% 0.15/0.43 (assert (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.15/0.43 (declare-fun tptp.icountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.15/0.43 (assert (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.15/0.43 (declare-fun tptp.iinvalid ((-> $$unsorted Bool)) Bool)
% 0.15/0.43 (assert (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.15/0.43 (declare-fun tptp.p ($$unsorted) Bool)
% 0.15/0.43 (declare-fun tptp.q ($$unsorted) Bool)
% 0.15/0.43 (assert (let ((_let_1 (@ tptp.iatom tptp.p))) (let ((_let_2 (@ tptp.iatom tptp.q))) (not (@ tptp.ivalid (@ (@ tptp.ior (@ (@ tptp.iimplies _let_1) _let_2)) (@ (@ tptp.iimplies _let_2) _let_1)))))))
% 0.15/0.43 (set-info :filename cvc5---1.0.5_1735)
% 0.15/0.43 (check-sat-assuming ( true ))
% 0.15/0.43 ------- get file name : TPTP file name is SYN416^4
% 0.15/0.43 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1735.smt2...
% 0.15/0.43 --- Run --ho-elim --full-saturate-quant at 10...
% 0.15/0.43 % SZS status Theorem for SYN416^4
% 0.15/0.43 % SZS output start Proof for SYN416^4
% 0.15/0.43 (
% 0.15/0.43 (let ((_let_1 (@ tptp.iatom tptp.p))) (let ((_let_2 (@ tptp.iatom tptp.q))) (let ((_let_3 (not (@ tptp.ivalid (@ (@ tptp.ior (@ (@ tptp.iimplies _let_1) _let_2)) (@ (@ tptp.iimplies _let_2) _let_1)))))) (let ((_let_4 (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_5 (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_6 (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_7 (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_8 (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))) (let ((_let_9 (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))) (let ((_let_10 (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))) (let ((_let_11 (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))) (let ((_let_12 (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))) (let ((_let_13 (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))) (let ((_let_14 (= tptp.ifalse (@ tptp.inot tptp.itrue)))) (let ((_let_15 (= tptp.itrue (lambda ((W $$unsorted)) true)))) (let ((_let_16 (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))) (let ((_let_17 (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))) (let ((_let_18 (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))) (let ((_let_19 (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))) (let ((_let_20 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_21 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_22 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_23 (forall ((BOUND_VARIABLE_1351 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1351) BOUND_VARIABLE_1351)) (ho_4 k_6 BOUND_VARIABLE_1351))))) (let ((_let_24 (forall ((BOUND_VARIABLE_1310 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1310) BOUND_VARIABLE_1310)) (ho_4 k_6 BOUND_VARIABLE_1310))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (ASSUME :args (_let_22)))) (let ((_let_27 (ASSUME :args (_let_21)))) (let ((_let_28 (ASSUME :args (_let_20)))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_28 _let_27 _let_26) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (ASSUME :args (_let_17)))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_31 _let_30 _let_29 _let_28 _let_27 _let_26) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (ASSUME :args (_let_4)) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_7)) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26) :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or (not (forall ((BOUND_VARIABLE_1300 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1300) BOUND_VARIABLE_1300)) (@ tptp.p BOUND_VARIABLE_1300)))) (forall ((BOUND_VARIABLE_1310 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1310) BOUND_VARIABLE_1310)) (@ tptp.q BOUND_VARIABLE_1310))) (not (forall ((BOUND_VARIABLE_1351 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1351) BOUND_VARIABLE_1351)) (@ tptp.q BOUND_VARIABLE_1351)))) (forall ((BOUND_VARIABLE_1361 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1361) BOUND_VARIABLE_1361)) (@ tptp.p BOUND_VARIABLE_1361))) (forall ((W $$unsorted) (Y $$unsorted)) (not (@ (@ tptp.irel W) Y))))) (not (or (not (forall ((BOUND_VARIABLE_1300 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1300) BOUND_VARIABLE_1300)) (ho_4 k_5 BOUND_VARIABLE_1300)))) _let_24 _let_25 (forall ((BOUND_VARIABLE_1361 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1361) BOUND_VARIABLE_1361)) (ho_4 k_5 BOUND_VARIABLE_1361))) (forall ((W $$unsorted) (Y $$unsorted)) (not (ho_4 (ho_3 k_2 W) Y)))))))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_NOT_ELIM (NOT_OR_ELIM _let_40 :args (2))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (SYMM (ALPHA_EQUIV :args (_let_24 (= BOUND_VARIABLE_1310 BOUND_VARIABLE_1351))))) (NOT_OR_ELIM _let_40 :args (1)) :args (_let_25 true _let_24)) :args (false true _let_23)) :args ((forall ((X $$unsorted)) (@ (@ tptp.irel X) X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ tptp.irel X))) (=> (and (@ _let_1 Y) (@ (@ tptp.irel Y) Z)) (@ _let_1 Z)))) _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 true)))))))))))))))))))))))))))))))))))))))))))
% 0.15/0.44 )
% 0.15/0.44 % SZS output end Proof for SYN416^4
% 0.15/0.44 % cvc5---1.0.5 exiting
% 0.15/0.44 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------