TSTP Solution File: SYN001^4.002 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYN001^4.002 : TPTP v8.1.2. Released v4.0.0.
% 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 : Fri Sep 1 02:00:47 EDT 2023
% Result : Theorem 0.22s 0.56s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN001^4.002 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n027.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 : Sat Aug 26 19:34:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.48 %----Proving TH0
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 % File : SYN001^4.002 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.49 % Domain : Logic Calculi (Intuitionistic logic)
% 0.22/0.49 % Problem : ILTP Problem SYJ212+1.002
% 0.22/0.49 % Version : [Goe33] axioms.
% 0.22/0.49 % English :
% 0.22/0.49
% 0.22/0.49 % Refs : [Goe33] Goedel (1933), An Interpretation of the Intuitionistic
% 0.22/0.49 % : [Gol06] Goldblatt (2006), Mathematical Modal Logic: A View of
% 0.22/0.49 % : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% 0.22/0.49 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.22/0.49 % : [BP10] Benzmueller & Paulson (2009), Exploring Properties of
% 0.22/0.49 % Source : [Ben09]
% 0.22/0.49 % Names : SYJ212+1.002 [ROK06]
% 0.22/0.49
% 0.22/0.49 % Status : CounterCounterSatisfiable
% 0.22/0.49 % Rating : 1.00 v8.1.0, 0.80 v7.5.0, 0.60 v7.4.0, 0.75 v7.2.0, 0.67 v6.2.0, 0.33 v5.4.0, 1.00 v5.0.0, 0.33 v4.1.0, 0.50 v4.0.1, 0.00 v4.0.0
% 0.22/0.49 % Syntax : Number of formulae : 44 ( 20 unt; 22 typ; 19 def)
% 0.22/0.49 % Number of atoms : 77 ( 19 equ; 0 cnn)
% 0.22/0.49 % Maximal formula atoms : 14 ( 3 avg)
% 0.22/0.49 % Number of connectives : 68 ( 3 ~; 1 |; 2 &; 60 @)
% 0.22/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.22/0.49 % Maximal formula depth : 9 ( 2 avg)
% 0.22/0.49 % Number of types : 2 ( 0 usr)
% 0.22/0.49 % Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% 0.22/0.49 % Number of symbols : 28 ( 26 usr; 5 con; 0-3 aty)
% 0.22/0.49 % Number of variables : 40 ( 31 ^; 7 !; 2 ?; 40 :)
% 0.22/0.49 % SPC : TH0_CSA_EQU_NAR
% 0.22/0.49
% 0.22/0.49 % Comments : This is an ILTP problem embedded in TH0
% 0.22/0.49 % : In classical logic this is a Theorem.
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 %----Modal Logic S4 in HOL
% 0.22/0.49 %----We define an accessibility relation irel
% 0.22/0.49 thf(irel_type,type,
% 0.22/0.49 irel: $i > $i > $o ).
% 0.22/0.49
% 0.22/0.49 %----We require reflexivity and transitivity for irel
% 0.22/0.49 thf(refl_axiom,axiom,
% 0.22/0.49 ! [X: $i] : ( irel @ X @ X ) ).
% 0.22/0.49
% 0.22/0.49 thf(trans_axiom,axiom,
% 0.22/0.49 ! [X: $i,Y: $i,Z: $i] :
% 0.22/0.49 ( ( ( irel @ X @ Y )
% 0.22/0.49 & ( irel @ Y @ Z ) )
% 0.22/0.49 => ( irel @ X @ Z ) ) ).
% 0.22/0.49
% 0.22/0.49 %----We define S4 connective mnot (as set complement)
% 0.22/0.49 thf(mnot_decl_type,type,
% 0.22/0.49 mnot: ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mnot,definition,
% 0.22/0.49 ( mnot
% 0.22/0.49 = ( ^ [X: $i > $o,U: $i] :
% 0.22/0.49 ~ ( X @ U ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----We define S4 connective mor (as set union)
% 0.22/0.49 thf(mor_decl_type,type,
% 0.22/0.49 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mor,definition,
% 0.22/0.49 ( mor
% 0.22/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.22/0.49 ( ( X @ U )
% 0.22/0.49 | ( Y @ U ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----We define S4 connective mand (as set intersection)
% 0.22/0.49 thf(mand_decl_type,type,
% 0.22/0.49 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mand,definition,
% 0.22/0.49 ( mand
% 0.22/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.22/0.49 ( ( X @ U )
% 0.22/0.49 & ( Y @ U ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----We define S4 connective mimpl
% 0.22/0.49 thf(mimplies_decl_type,type,
% 0.22/0.49 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mimplies,definition,
% 0.22/0.49 ( mimplies
% 0.22/0.49 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Definition of mbox_s4; since irel is reflexive and transitive,
% 0.22/0.49 %----it is easy to show that the K and the T axiom hold for mbox_s4
% 0.22/0.49 thf(mbox_s4_decl_type,type,
% 0.22/0.49 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mbox_s4,definition,
% 0.22/0.49 ( mbox_s4
% 0.22/0.49 = ( ^ [P: $i > $o,X: $i] :
% 0.22/0.49 ! [Y: $i] :
% 0.22/0.49 ( ( irel @ X @ Y )
% 0.22/0.49 => ( P @ Y ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Intuitionistic Logic in Modal Logic S4
% 0.22/0.49 %----Definition of iatom: iatom P = P
% 0.22/0.49 %----Goedel maps atoms to atoms
% 0.22/0.49 thf(iatom_type,type,
% 0.22/0.49 iatom: ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(iatom,definition,
% 0.22/0.49 ( iatom
% 0.22/0.49 = ( ^ [P: $i > $o] : P ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Definition of inot: inot P = mnot (mbox_s4 P)
% 0.22/0.49 thf(inot_type,type,
% 0.22/0.49 inot: ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(inot,definition,
% 0.22/0.49 ( inot
% 0.22/0.49 = ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Definition of true and false
% 0.22/0.49 thf(itrue_type,type,
% 0.22/0.49 itrue: $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(itrue,definition,
% 0.22/0.49 ( itrue
% 0.22/0.49 = ( ^ [W: $i] : $true ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ifalse_type,type,
% 0.22/0.50 ifalse: $i > $o ).
% 0.22/0.50
% 0.22/0.50 thf(ifalse,definition,
% 0.22/0.50 ( ifalse
% 0.22/0.50 = ( inot @ itrue ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of iand: iand P Q = (mand P Q)
% 0.22/0.50 thf(iand_type,type,
% 0.22/0.50 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.50
% 0.22/0.50 thf(iand,definition,
% 0.22/0.50 ( iand
% 0.22/0.50 = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of ior: ior P Q = (mor (mbox_s4 P) (mbox_s4 Q))
% 0.22/0.50 thf(ior_type,type,
% 0.22/0.50 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.50
% 0.22/0.50 thf(ior,definition,
% 0.22/0.50 ( ior
% 0.22/0.50 = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of iimplies: iimplies P Q =
% 0.22/0.50 %---- (mimplies (mbox_s4 P) (mbox_s4 Q))
% 0.22/0.50 thf(iimplies_type,type,
% 0.22/0.50 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.50
% 0.22/0.50 thf(iimplies,definition,
% 0.22/0.50 ( iimplies
% 0.22/0.50 = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of iimplied: iimplied P Q = (iimplies Q P)
% 0.22/0.50 thf(iimplied_type,type,
% 0.22/0.50 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.50
% 0.22/0.50 thf(iimplied,definition,
% 0.22/0.50 ( iimplied
% 0.22/0.50 = ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of iequiv: iequiv P Q =
% 0.22/0.50 %---- (iand (iimplies P Q) (iimplies Q P))
% 0.22/0.50 thf(iequiv_type,type,
% 0.22/0.50 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.50
% 0.22/0.50 thf(iequiv,definition,
% 0.22/0.50 ( iequiv
% 0.22/0.50 = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of ixor: ixor P Q = (inot (iequiv P Q)
% 0.22/0.50 thf(ixor_type,type,
% 0.22/0.50 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.50
% 0.22/0.50 thf(ixor,definition,
% 0.22/0.50 ( ixor
% 0.22/0.50 = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of validity
% 0.22/0.50 thf(ivalid_type,type,
% 0.22/0.50 ivalid: ( $i > $o ) > $o ).
% 0.22/0.50
% 0.22/0.50 thf(ivalid,definition,
% 0.22/0.50 ( ivalid
% 0.22/0.50 = ( ^ [Phi: $i > $o] :
% 0.22/0.50 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of satisfiability
% 0.22/0.50 thf(isatisfiable_type,type,
% 0.22/0.50 isatisfiable: ( $i > $o ) > $o ).
% 0.22/0.50
% 0.22/0.50 thf(isatisfiable,definition,
% 0.22/0.50 ( isatisfiable
% 0.22/0.50 = ( ^ [Phi: $i > $o] :
% 0.22/0.50 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of countersatisfiability
% 0.22/0.50 thf(icountersatisfiable_type,type,
% 0.22/0.50 icountersatisfiable: ( $i > $o ) > $o ).
% 0.22/0.50
% 0.22/0.50 thf(icountersatisfiable,definition,
% 0.22/0.50 ( icountersatisfiable
% 0.22/0.50 = ( ^ [Phi: $i > $o] :
% 0.22/0.50 ? [W: $i] :
% 0.22/0.50 ~ ( Phi @ W ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %----Definition of invalidity
% 0.22/0.50 thf(iinvalid_type,type,
% 0.22/0.50 iinvalid: ( $i > $o ) > $o ).
% 0.22/0.50
% 0.22/0.50 thf(iinvalid,definition,
% 0.22/0.50 ( iinvalid
% 0.22/0.50 = ( ^ [Phi: $i > $o] :
% 0.22/0.50 ! [W: $i] :
% 0.22/0.50 ~ ( Phi @ W ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 thf(a1_type,type,
% 0.22/0.50 a1: $i > $o ).
% 0.22/0.50
% 0.22/0.50 thf(a2_type,type,
% 0.22/0.50 a2: $i > $o ).
% 0.22/0.50
% 0.22/0.50 thf(con,conjecture,
% 0.22/0.50 ivalid @ ( iequiv @ ( iequiv @ ( inot @ ( inot @ ( iatom @ a1 ) ) ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.mGeCfKYjL8/cvc5---1.0.5_4942.p...
% 0.22/0.50 (declare-sort $$unsorted 0)
% 0.22/0.50 (declare-fun tptp.irel ($$unsorted $$unsorted) Bool)
% 0.22/0.50 (assert (forall ((X $$unsorted)) (@ (@ tptp.irel X) X)))
% 0.22/0.50 (assert (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ tptp.irel X))) (=> (and (@ _let_1 Y) (@ (@ tptp.irel Y) Z)) (@ _let_1 Z)))))
% 0.22/0.50 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.50 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.22/0.50 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.50 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.22/0.50 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.50 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.22/0.50 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.50 (assert (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.22/0.56 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))
% 0.22/0.56 (declare-fun tptp.iatom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))
% 0.22/0.56 (declare-fun tptp.inot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))
% 0.22/0.56 (declare-fun tptp.itrue ($$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.itrue (lambda ((W $$unsorted)) true)))
% 0.22/0.56 (declare-fun tptp.ifalse ($$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.ifalse (@ tptp.inot tptp.itrue)))
% 0.22/0.56 (declare-fun tptp.iand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))
% 0.22/0.56 (declare-fun tptp.ior ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.22/0.56 (declare-fun tptp.iimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.22/0.56 (declare-fun tptp.iimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))
% 0.22/0.56 (declare-fun tptp.iequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))
% 0.22/0.56 (declare-fun tptp.ixor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.56 (assert (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))
% 0.22/0.56 (declare-fun tptp.ivalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.56 (assert (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.56 (declare-fun tptp.isatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.56 (assert (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.56 (declare-fun tptp.icountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.56 (assert (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.56 (declare-fun tptp.iinvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.56 (assert (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.56 (declare-fun tptp.a1 ($$unsorted) Bool)
% 0.22/0.56 (declare-fun tptp.a2 ($$unsorted) Bool)
% 0.22/0.56 (assert (let ((_let_1 (@ tptp.iatom tptp.a1))) (let ((_let_2 (@ tptp.iatom tptp.a2))) (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ (@ tptp.iequiv (@ tptp.inot (@ tptp.inot _let_1))) _let_2)) (@ (@ tptp.iequiv _let_2) _let_1)))))))
% 0.22/0.56 (set-info :filename cvc5---1.0.5_4942)
% 0.22/0.56 (check-sat-assuming ( true ))
% 0.22/0.56 ------- get file name : TPTP file name is SYN001^4.002
% 0.22/0.56 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4942.smt2...
% 0.22/0.56 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.56 % SZS status Theorem for SYN001^4.002
% 0.22/0.56 % SZS output start Proof for SYN001^4.002
% 0.22/0.56 (
% 0.22/0.56 (let ((_let_1 (@ tptp.iatom tptp.a1))) (let ((_let_2 (@ tptp.iatom tptp.a2))) (let ((_let_3 (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ (@ tptp.iequiv (@ tptp.inot (@ tptp.inot _let_1))) _let_2)) (@ (@ tptp.iequiv _let_2) _let_1)))))) (let ((_let_4 (= tptp.iinvalid (lambda ((Phi (-> $$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 ((X $$unsorted)) (@ (@ tptp.irel X) X)))) (let ((_let_24 (forall ((BOUND_VARIABLE_1381 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1381))))) (let ((_let_25 (forall ((BOUND_VARIABLE_1316 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1316) BOUND_VARIABLE_1316))))) (let ((_let_26 (not _let_25))) (let ((_let_27 (forall ((BOUND_VARIABLE_1283 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1283) BOUND_VARIABLE_1283)) (ho_4 k_6 BOUND_VARIABLE_1283))))) (let ((_let_28 (and _let_27 _let_26))) (let ((_let_29 (forall ((BOUND_VARIABLE_1390 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1390) BOUND_VARIABLE_1390)) (ho_4 k_5 BOUND_VARIABLE_1390))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28 _let_24))) (let ((_let_32 (not _let_24))) (let ((_let_33 (not _let_27))) (let ((_let_34 (or _let_33 _let_25))) (let ((_let_35 (and _let_34 _let_32))) (let ((_let_36 (or _let_35 _let_29))) (let ((_let_37 (and _let_36 _let_31))) (let ((_let_38 (forall ((BOUND_VARIABLE_1452 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1452) BOUND_VARIABLE_1452)) (ho_4 k_5 BOUND_VARIABLE_1452))))) (let ((_let_39 (forall ((BOUND_VARIABLE_1462 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1462) BOUND_VARIABLE_1462)) (ho_4 k_6 BOUND_VARIABLE_1462))))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38))) (let ((_let_42 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) (ho_4 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))) (let ((_let_43 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20)) (ho_4 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20)))) (let ((_let_44 (not _let_38))) (let ((_let_45 (or _let_44 _let_39))) (let ((_let_46 (and _let_45 _let_41))) (let ((_let_47 (forall ((BOUND_VARIABLE_1521 $$unsorted) (BOUND_VARIABLE_1578 $$unsorted) (BOUND_VARIABLE_1569 $$unsorted) (BOUND_VARIABLE_1562 $$unsorted) (BOUND_VARIABLE_1555 $$unsorted) (BOUND_VARIABLE_1547 $$unsorted)) (or (and (or (and (or (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1547) BOUND_VARIABLE_1547)) (ho_4 k_6 BOUND_VARIABLE_1547)) (not (forall ((BOUND_VARIABLE_1316 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1316) BOUND_VARIABLE_1316))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1555) BOUND_VARIABLE_1555))) (not (forall ((BOUND_VARIABLE_1390 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1390) BOUND_VARIABLE_1390)) (ho_4 k_5 BOUND_VARIABLE_1390))))) (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1562) BOUND_VARIABLE_1562)) (ho_4 k_5 BOUND_VARIABLE_1562)) (or (not (forall ((BOUND_VARIABLE_1283 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1283) BOUND_VARIABLE_1283)) (ho_4 k_6 BOUND_VARIABLE_1283)))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1569) BOUND_VARIABLE_1569))) (not (forall ((BOUND_VARIABLE_1381 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1381) BOUND_VARIABLE_1381)))))) (not (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1521) Y))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1521) BOUND_VARIABLE_1578)))))) (let ((_let_48 (or _let_46 _let_47))) (let ((_let_49 (forall ((BOUND_VARIABLE_1532 $$unsorted) (BOUND_VARIABLE_1607 $$unsorted) (BOUND_VARIABLE_1597 $$unsorted) (BOUND_VARIABLE_1589 $$unsorted)) (or (and (or (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1589) BOUND_VARIABLE_1589)) (ho_4 k_5 BOUND_VARIABLE_1589)) (not (forall ((BOUND_VARIABLE_1462 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1462) BOUND_VARIABLE_1462)) (ho_4 k_6 BOUND_VARIABLE_1462))))) (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1597) BOUND_VARIABLE_1597)) (ho_4 k_6 BOUND_VARIABLE_1597)) (not (forall ((BOUND_VARIABLE_1452 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1452) BOUND_VARIABLE_1452)) (ho_4 k_5 BOUND_VARIABLE_1452)))))) (not (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1532) Y))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1532) BOUND_VARIABLE_1607)))))) (let ((_let_50 (or _let_37 _let_49))) (let ((_let_51 (ALPHA_EQUIV :args (_let_38 (= BOUND_VARIABLE_1452 BOUND_VARIABLE_1390))))) (let ((_let_52 (_let_38))) (let ((_let_53 (ASSUME :args _let_52))) (let ((_let_54 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 (ho_4 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_57 (and _let_43 _let_40))) (let ((_let_58 (or _let_33 (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))))) (let ((_let_59 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)) (ho_4 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)))) (let ((_let_60 (and _let_59 _let_44))) (let ((_let_61 (or _let_57 _let_60))) (let ((_let_62 (and _let_42 _let_58 _let_32))) (let ((_let_63 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)) (ho_4 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))) (let ((_let_64 (and _let_63 _let_26))) (let ((_let_65 (or _let_64 (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_66 (and _let_65 _let_30))) (let ((_let_67 (or _let_66 _let_62))) (let ((_let_68 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_69 (not _let_68))) (let ((_let_70 (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) Y))))) (let ((_let_71 (not _let_70))) (let ((_let_72 (and _let_67 _let_71))) (let ((_let_73 (or _let_72 _let_69))) (let ((_let_74 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_75 (not _let_74))) (let ((_let_76 (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) Y))))) (let ((_let_77 (not _let_76))) (let ((_let_78 (and _let_61 _let_77))) (let ((_let_79 (or _let_78 _let_75))) (let ((_let_80 (not _let_43))) (let ((_let_81 (not _let_42))) (let ((_let_82 (ALPHA_EQUIV :args (_let_39 (= BOUND_VARIABLE_1462 BOUND_VARIABLE_1283))))) (let ((_let_83 (EQUIV_ELIM2 _let_82))) (let ((_let_84 (or))) (let ((_let_85 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))))) (let ((_let_86 (_let_40))) (let ((_let_87 (_let_57))) (let ((_let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_27))))) (let ((_let_89 (_let_25))) (let ((_let_90 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_91 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_89) :args _let_90) :args _let_89)))) (let ((_let_92 (SYMM (ALPHA_EQUIV :args (_let_25 (= BOUND_VARIABLE_1316 BOUND_VARIABLE_1381)))))) (let ((_let_93 (REORDERING (EQUIV_ELIM1 _let_92) :args ((or _let_25 _let_32))))) (let ((_let_94 (not _let_58))) (let ((_let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_24))))) (let ((_let_96 (_let_62))) (let ((_let_97 (not _let_67))) (let ((_let_98 (_let_72))) (let ((_let_99 (_let_70))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_99) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_99)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_98) (CONG (REFL :args _let_98) (REFL :args (_let_97)) (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_84)) :args ((or _let_70 _let_72 _let_97))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_73 1)) (CONG (REFL :args (_let_73)) (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_84)) :args ((or _let_68 _let_73))) (CNF_OR_NEG :args (_let_73 0)) :args ((or _let_73 _let_97) false _let_70 false _let_68 true _let_72)))) (let ((_let_101 (not _let_47))) (let ((_let_102 (_let_101))) (let ((_let_103 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_102)) :args _let_102)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_101) _let_47))) (REFL :args ((not _let_73))) :args _let_84)))) (let ((_let_104 (CNF_OR_NEG :args (_let_48 1)))) (let ((_let_105 (forall ((BOUND_VARIABLE_1381 $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1381) BOUND_VARIABLE_1381))))) (let ((_let_106 (forall ((BOUND_VARIABLE_1316 $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1316) BOUND_VARIABLE_1316))))) (let ((_let_107 (forall ((BOUND_VARIABLE_1283 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1283) BOUND_VARIABLE_1283)) (@ tptp.a1 BOUND_VARIABLE_1283))))) (let ((_let_108 (forall ((BOUND_VARIABLE_1390 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1390) BOUND_VARIABLE_1390)) (@ tptp.a2 BOUND_VARIABLE_1390))))) (let ((_let_109 (forall ((BOUND_VARIABLE_1452 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1452) BOUND_VARIABLE_1452)) (@ tptp.a2 BOUND_VARIABLE_1452))))) (let ((_let_110 (forall ((BOUND_VARIABLE_1462 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1462) BOUND_VARIABLE_1462)) (@ tptp.a1 BOUND_VARIABLE_1462))))) (let ((_let_111 (ASSUME :args (_let_22)))) (let ((_let_112 (ASSUME :args (_let_21)))) (let ((_let_113 (ASSUME :args (_let_20)))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_113 _let_112 _let_111) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (ASSUME :args (_let_17)))) (let ((_let_117 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_116 _let_115 _let_114 _let_113 _let_112 _let_111) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_125 (NOT_AND (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_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111) :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (and (or (and (or (not _let_109) _let_110) (or (not _let_110) _let_109)) (forall ((BOUND_VARIABLE_1521 $$unsorted) (BOUND_VARIABLE_1578 $$unsorted) (BOUND_VARIABLE_1569 $$unsorted) (BOUND_VARIABLE_1562 $$unsorted) (BOUND_VARIABLE_1555 $$unsorted) (BOUND_VARIABLE_1547 $$unsorted)) (or (and (or (and (or (and (or (not (@ (@ tptp.irel BOUND_VARIABLE_1547) BOUND_VARIABLE_1547)) (@ tptp.a1 BOUND_VARIABLE_1547)) (not (forall ((BOUND_VARIABLE_1316 $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1316) BOUND_VARIABLE_1316))))) (not (@ (@ tptp.irel BOUND_VARIABLE_1555) BOUND_VARIABLE_1555))) (not (forall ((BOUND_VARIABLE_1390 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1390) BOUND_VARIABLE_1390)) (@ tptp.a2 BOUND_VARIABLE_1390))))) (and (or (not (@ (@ tptp.irel BOUND_VARIABLE_1562) BOUND_VARIABLE_1562)) (@ tptp.a2 BOUND_VARIABLE_1562)) (or (not (forall ((BOUND_VARIABLE_1283 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1283) BOUND_VARIABLE_1283)) (@ tptp.a1 BOUND_VARIABLE_1283)))) (not (@ (@ tptp.irel BOUND_VARIABLE_1569) BOUND_VARIABLE_1569))) (not (forall ((BOUND_VARIABLE_1381 $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1381) BOUND_VARIABLE_1381)))))) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1521) Y))))) (not (@ (@ tptp.irel BOUND_VARIABLE_1521) BOUND_VARIABLE_1578))))) (or (and (or (and (or (not _let_107) _let_106) (not _let_105)) _let_108) (or (not _let_108) (and _let_107 (not _let_106)) _let_105)) (forall ((BOUND_VARIABLE_1532 $$unsorted) (BOUND_VARIABLE_1607 $$unsorted) (BOUND_VARIABLE_1597 $$unsorted) (BOUND_VARIABLE_1589 $$unsorted)) (or (and (or (and (or (not (@ (@ tptp.irel BOUND_VARIABLE_1589) BOUND_VARIABLE_1589)) (@ tptp.a2 BOUND_VARIABLE_1589)) (not (forall ((BOUND_VARIABLE_1462 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1462) BOUND_VARIABLE_1462)) (@ tptp.a1 BOUND_VARIABLE_1462))))) (and (or (not (@ (@ tptp.irel BOUND_VARIABLE_1597) BOUND_VARIABLE_1597)) (@ tptp.a1 BOUND_VARIABLE_1597)) (not (forall ((BOUND_VARIABLE_1452 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1452) BOUND_VARIABLE_1452)) (@ tptp.a2 BOUND_VARIABLE_1452)))))) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1532) Y))))) (not (@ (@ tptp.irel BOUND_VARIABLE_1532) BOUND_VARIABLE_1607))))))) (not (and _let_48 _let_50)))))))))) (let ((_let_126 (CNF_OR_NEG :args (_let_50 1)))) (let ((_let_127 (not _let_49))) (let ((_let_128 (_let_127))) (let ((_let_129 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_128)) :args _let_128)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_127) _let_49))) (REFL :args ((not _let_79))) :args _let_84)))) (let ((_let_130 (CNF_OR_NEG :args (_let_79 0)))) (let ((_let_131 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_79 1)) (CONG (REFL :args (_let_79)) (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_74))) :args _let_84)) :args ((or _let_74 _let_79))))) (let ((_let_132 (not _let_61))) (let ((_let_133 (_let_78))) (let ((_let_134 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_133) (CONG (REFL :args _let_133) (REFL :args (_let_132)) (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_76))) :args _let_84)) :args ((or _let_76 _let_78 _let_132))))) (let ((_let_135 (_let_76))) (let ((_let_136 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_135) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_135)))) (let ((_let_137 (CNF_AND_NEG :args (_let_46)))) (let ((_let_138 (CNF_OR_NEG :args (_let_48 0)))) (let ((_let_139 (CNF_OR_NEG :args (_let_50 0)))) (let ((_let_140 (CNF_AND_NEG :args (_let_37)))) (let ((_let_141 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))))) (let ((_let_142 (_let_28))) (let ((_let_143 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_92) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_142) (CONG (REFL :args _let_142) (REFL :args (_let_33)) _let_141 :args _let_84)) :args ((or _let_25 _let_28 _let_33))) (CNF_OR_NEG :args (_let_31 2)) (CNF_OR_NEG :args (_let_31 1)) _let_140 _let_139 _let_125 _let_138 _let_137 (EQUIV_ELIM1 _let_82) (REORDERING (CNF_OR_NEG :args (_let_45 1)) :args ((or _let_40 _let_45))) (MACRO_RESOLUTION_TRUST _let_136 _let_134 _let_131 _let_130 _let_129 _let_126 _let_125 _let_104 _let_103 _let_100 (CNF_OR_NEG :args (_let_67 1)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_96) (CONG (REFL :args _let_96) (REFL :args (_let_81)) (REFL :args (_let_94)) _let_95 :args _let_84)) :args ((or _let_24 _let_62 _let_81 _let_94))) _let_93 _let_91 (CNF_OR_NEG :args (_let_61 0)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG (REFL :args (_let_56)) (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_84)) :args ((or _let_54 _let_56))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 0)) (CONG (REFL :args (_let_58)) _let_88 :args _let_84)) :args ((or _let_27 _let_58))) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_87) (CONG (REFL :args _let_87) (REFL :args (_let_80)) _let_85 :args _let_84)) :args ((or _let_39 _let_57 _let_80))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_86)) :args _let_86)) (CONG _let_85 (REFL :args ((not _let_56))) :args _let_84)) _let_83 :args ((or _let_39 _let_81 _let_80) false _let_76 false _let_74 true _let_78 true _let_79 true _let_49 true _let_50 false _let_48 false _let_47 false _let_73 false _let_67 false _let_62 true _let_24 true _let_25 false _let_61 false _let_54 false _let_58 false _let_57 true _let_56 true _let_27)) (REORDERING (CNF_OR_NEG :args (_let_36 1)) :args ((or _let_30 _let_36))) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_52)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_52)) (EQUIV_ELIM1 _let_51) (REORDERING (CNF_OR_NEG :args (_let_41 1)) :args ((or _let_44 _let_41))) :args (_let_44 false _let_25 true _let_24 true _let_28 true _let_31 true _let_37 true _let_50 false _let_48 false _let_46 false _let_27 false _let_45 false _let_39 false _let_36 false _let_43 false _let_42 false _let_29 false _let_41)))) (let ((_let_144 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_51) _let_143 :args (_let_30 true _let_38)))) (let ((_let_145 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))))) (let ((_let_146 (_let_39))) (let ((_let_147 (ASSUME :args _let_146))) (let ((_let_148 (forall ((X $$unsorted)) (ho_4 (ho_3 k_2 X) X)))) (let ((_let_149 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_150 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_151 (forall ((u |u_(-> $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_152 (forall ((x |u_(-> $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_153 (EQ_RESOLVE (ASSUME :args (_let_23)) (PREPROCESS :args ((= _let_23 _let_148)))))) (let ((_let_154 (MACRO_RESOLUTION_TRUST _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_153 :args _let_90) :args (_let_148))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_153 (PREPROCESS :args ((and _let_152 _let_151 _let_150 _let_149)))) :args ((and _let_148 _let_152 _let_151 _let_150 _let_149))) :args (0)) :args (_let_54 false _let_148)) :args (_let_26 false _let_54)))) (let ((_let_155 (not _let_63))) (let ((_let_156 (_let_64))) (let ((_let_157 (not _let_65))) (let ((_let_158 (_let_66))) (let ((_let_159 (not _let_59))) (let ((_let_160 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_38))))) (let ((_let_161 (_let_60))) (let ((_let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_147 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_146)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_161) (CONG (REFL :args _let_161) (REFL :args (_let_159)) _let_160 :args _let_84)) :args ((or _let_38 _let_60 _let_159))) _let_143 (CNF_OR_NEG :args (_let_61 1)) _let_134 _let_136 _let_131 _let_130 _let_129 _let_126 _let_125 _let_104 _let_103 _let_100 (CNF_OR_NEG :args (_let_67 0)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_158) (CONG (REFL :args _let_158) (REFL :args (_let_157)) _let_145 :args _let_84)) :args ((or _let_29 _let_66 _let_157))) _let_144 (CNF_OR_NEG :args (_let_65 0)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_156) (CONG (REFL :args _let_156) (REFL :args (_let_155)) _let_141 :args _let_84)) :args ((or _let_25 _let_64 _let_155))) _let_154 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_147 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_146)) :args (_let_40 true _let_59 true _let_38 true _let_60 true _let_61 true _let_76 false _let_74 true _let_78 true _let_79 true _let_49 true _let_50 false _let_48 false _let_47 false _let_73 false _let_67 false _let_66 true _let_29 false _let_65 false _let_64 true _let_25 false _let_63)))) (let ((_let_163 (not _let_34))) (let ((_let_164 (_let_35))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST _let_140 (MACRO_RESOLUTION_TRUST _let_139 (MACRO_RESOLUTION_TRUST _let_125 (MACRO_RESOLUTION_TRUST _let_138 (MACRO_RESOLUTION_TRUST _let_137 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG (REFL :args (_let_45)) _let_160 :args _let_84)) :args ((or _let_38 _let_45))) _let_143 :args (_let_45 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 0)) (CONG (REFL :args (_let_41)) _let_85 :args _let_84)) :args ((or _let_39 _let_41))) _let_162 :args (_let_41 true _let_39)) :args (_let_46 false _let_45 false _let_41)) :args (_let_48 false _let_46)) :args ((not _let_50) false _let_48)) :args ((not _let_37) true _let_50)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_36 0)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_164) (CONG (REFL :args _let_164) (REFL :args (_let_163)) _let_95 :args _let_84)) :args ((or _let_24 _let_35 _let_163))) (MACRO_RESOLUTION_TRUST _let_93 _let_154 :args (_let_32 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG (REFL :args (_let_34)) _let_88 :args _let_84)) :args ((or _let_27 _let_34))) (MACRO_RESOLUTION_TRUST _let_83 _let_162 :args (_let_33 true _let_39)) :args (_let_34 true _let_27)) :args (_let_35 true _let_24 false _let_34)) :args (_let_36 false _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG (REFL :args (_let_31)) _let_145 :args _let_84)) :args ((or _let_29 _let_31))) _let_144 :args (_let_31 true _let_29)) :args (false true _let_37 false _let_36 false _let_31)) :args (_let_23 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.57 )
% 0.22/0.57 % SZS output end Proof for SYN001^4.002
% 0.22/0.57 % cvc5---1.0.5 exiting
% 0.22/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------